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© QUALITY COUNCIL OF INDIANACQE 2006

INTRO-1 (1)

THEQUALITY ENGINEER

PRIMER

Eighth Edition - September 1, 2006

© by Quality Council of Indiana - All Rights Reserved

Bill WortmanQuality Council of Indiana602 West Paris AvenueWest Terre Haute, IN 47885TEL: (812) 533-4215FAX: (812) [email protected]://www.qualitycouncil.com

003


INTRO-5 (2)

CQE PRIMER CONTENTSI. CERTIFICATION OVERVIEW . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I-1

CQE BOK . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I-6

II. MANAGEMENT &LEADERSHIP . . . . . . . . . . . . . . . . . . . . . . . . . . . II-1QUALITY FOUNDATIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . II-2QUALITY MANAGEMENT SYSTEMS . . . . . . . . . . . . . . . . . . . . II-22

STRATEGIC PLANNING . . . . . . . . . . . . . . . . . . . . . . . . . . . . II-22STAKEHOLDERS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . II-33BENCHMARKING . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . II-37PROJECT MANAGEMENT . . . . . . . . . . . . . . . . . . . . . . . . . . II-40QUALITY INFORMATION SYSTEMS . . . . . . . . . . . . . . . . . . II-51

ASQ CODE OF ETHICS. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . II-55LEADERSHIP PRINCIPLES . . . . . . . . . . . . . . . . . . . . . . . . . . . . II-57FACILITATION TECHNIQUES . . . . . . . . . . . . . . . . . . . . . . . . . . II-78COMMUNICATION SKILLS . . . . . . . . . . . . . . . . . . . . . . . . . . . II-88CUSTOMER RELATIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . II-95SUPPLIER MANAGEMENT . . . . . . . . . . . . . . . . . . . . . . . . . . . II-103BARRIERS TO QUALITY IMPROVEMENT . . . . . . . . . . . . . . . II-111REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . II-113

III. QUALITY SYSTEMS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . III-1QUALITY SYSTEM ELEMENTS . . . . . . . . . . . . . . . . . . . . . . . . III-2QUALITY SYSTEM DOCUMENTATION . . . . . . . . . . . . . . . . . . III-8QUALITY STANDARDS & GUIDELINES . . . . . . . . . . . . . . . . . III-19

ISO 9001:2000 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . III-22MBNQA/BNQP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . III-31

QUALITY AUDITS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . III-35AUDIT TYPES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . III-37AUDIT COMPONENTS . . . . . . . . . . . . . . . . . . . . . . . . . . . . III-44

COST OF QUALITY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . III-52QUALITY COST CATEGORIES . . . . . . . . . . . . . . . . . . . . . III-54QUALITY COST BASES . . . . . . . . . . . . . . . . . . . . . . . . . . . III-60

QUALITY TRAINING . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . III-66TRAINING NEEDS ASSESSMENT III-68TRAINING EFFECTIVENESS . . . . . . . . . . . . . . . . . . . . . . . III-71

REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . III-73


INTRO-5 (3)

IV. PRODUCT & PROCESS DESIGN . . . . . . . . . . . . . . . . . . . . . . . IV-1QUALITY CHARACTERISTICS . . . . . . . . . . . . . . . . . . . . . . . . . IV-2DESIGN REVIEW . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . IV-6

DFSS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . IV-11QFD . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . IV-17ROBUST DESIGN . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . IV-20DFX . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . IV-28

TECHNICAL DRAWINGS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . IV-32GD&T DEFINITIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . IV-55

DESIGN VERIFICATION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . IV-61RELIABILITY AND MAINTAINABILITY . . . . . . . . . . . . . . . . . . IV-64

PREVENTIVE MAINTENANCE . . . . . . . . . . . . . . . . . . . . . . IV-65R&M INDICES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . IV-69BATHTUB CURVE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . IV-79HAZARD ASSESSMENT TOOLS . . . . . . . . . . . . . . . . . . . . IV-81

REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . IV-96

V. PRODUCT & PROCESS CONTROL . . . . . . . . . . . . . . . . . . . . . . . . V-1TOOLS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . V-4

CONTROL PLANS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . V-7MATERIAL CONTROL . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . V-12

MATERIAL IDENTIFICATION . . . . . . . . . . . . . . . . . . . . . . . . V-12MATERIAL SEGREGATION . . . . . . . . . . . . . . . . . . . . . . . . . V-14CLASSIFICATION OF DEFECTS . . . . . . . . . . . . . . . . . . . . . V-20MRB . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . V-21

ACCEPTANCE SAMPLING . . . . . . . . . . . . . . . . . . . . . . . . . . . . V-24SAMPLING CONCEPTS . . . . . . . . . . . . . . . . . . . . . . . . . . . . V-24SAMPLING STANDARDS . . . . . . . . . . . . . . . . . . . . . . . . . . . V-43SAMPLING INTEGRITY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . V-61

REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . V-63

VI. TESTING & MEASUREMENT . . . . . . . . . . . . . . . . . . . . . . . . . . VI-1MEASUREMENT TOOLS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . VI-2DEFINITIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . VI-38DESTRUCTIVE TESTS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . VI-42NONDESTRUCTIVE TESTS . . . . . . . . . . . . . . . . . . . . . . . . . . . VI-46METROLOGY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . VI-64MEASUREMENT SYSTEM ANALYSIS . . . . . . . . . . . . . . . . . . VI-78REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . VI-89


INTRO-5 (4)

VII. CONTROL & MANAGEMENT TOOLS . . . . . . . . . . . . . . . . . . . . VII-1QUALITY CONTROL TOOLS . . . . . . . . . . . . . . . . . . . . . . . . . . . VII-2

FLOW CHARTS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . VII-6HISTOGRAMS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . VII-11PARETO DIAGRAMS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . VII-17

MANAGEMENT & PLANNING TOOLS . . . . . . . . . . . . . . . . . . VII-23AFFINITY DIAGRAMS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . VII-24MATRIX DIAGRAMS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . VII-30PRIORITIZATION MATRICES . . . . . . . . . . . . . . . . . . . . . . . VII-34ACTIVITY NETWORK DIAGRAMS . . . . . . . . . . . . . . . . . . . VII-36

REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . VII-38

VIII. IMPROVEMENT TECHNIQUES . . . . . . . . . . . . . . . . . . . . . . . . VIII-1IMPROVEMENT MODELS . . . . . . . . . . . . . . . . . . . . . . . . . . . . VIII-2

PDCA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . VIII-3SIX SIGMA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . VIII-6KAIZEN . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . VIII-11LEAN TECHNIQUES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . VIII-12TQM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . VIII-29

CORRECTIVE & PREVENTIVE ACTIONS . . . . . . . . . . . . . . VIII-33ROOT CAUSE ANALYSIS . . . . . . . . . . . . . . . . . . . . . . . . . VIII-42MISTAKE PROOFING . . . . . . . . . . . . . . . . . . . . . . . . . . . . VIII-44

REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . VIII-46

IX. BASIC STATISTICS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . IX-1COLLECTING DATA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . IX-2

TYPES OF DATA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . IX-2MEASUREMENT SCALES . . . . . . . . . . . . . . . . . . . . . . . . . . IX-7DATA COLLECTION METHODS . . . . . . . . . . . . . . . . . . . . . . IX-9DATA ACCURACY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . IX-12DESCRIPTIVE STATISTICS . . . . . . . . . . . . . . . . . . . . . . . . IX-13GRAPHICAL RELATIONSHIPS . . . . . . . . . . . . . . . . . . . . . IX-24

QUANTITATIVE CONCEPTS . . . . . . . . . . . . . . . . . . . . . . . . . . IX-33STATISTICAL CONCLUSIONS . . . . . . . . . . . . . . . . . . . . . . IX-35PROBABILITY TERMS . . . . . . . . . . . . . . . . . . . . . . . . . . . . IX-37

PROBABILITY DISTRIBUTIONS . . . . . . . . . . . . . . . . . . . . . . . IX-46CONTINUOUS DISTRIBUTIONS . . . . . . . . . . . . . . . . . . . . . IX-46DISCRETE DISTRIBUTIONS . . . . . . . . . . . . . . . . . . . . . . . . IX-61

REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . IX-68


INTRO-5 (5)

X. STATISTICAL APPLICATIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . X-1STATISTICAL PROCESS CONTROL . . . . . . . . . . . . . . . . . . . . . X-2

OBJECTIVES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . X-2COMMON VS. SPECIAL CAUSES . . . . . . . . . . . . . . . . . . . . . X-4RATIONAL SUBGROUPING . . . . . . . . . . . . . . . . . . . . . . . . . . X-8CONTROL CHARTS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . X-11CONTROL CHART ANALYSIS . . . . . . . . . . . . . . . . . . . . . . . X-37PRE-CONTROL CHARTS . . . . . . . . . . . . . . . . . . . . . . . . . . . X-46SHORT-RUN SPC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . X-48

CAPABILITY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . X-53CAPABILITY STUDIES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . X-53PERFORMANCE VS. SPECIFICATIONS . . . . . . . . . . . . . . . X-56CAPABILITY INDICIES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . X-64PERFORMANCE INDICIES . . . . . . . . . . . . . . . . . . . . . . . . . . X-67

REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . X-68

XI. ADVANCED STATISTICS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . XI-1STATISTICAL DECISION MAKING . . . . . . . . . . . . . . . . . . . . . . XI-2

POINT ESTIMATES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . XI-3CONFIDENCE INTERVALS . . . . . . . . . . . . . . . . . . . . . . . . . . XI-4HYPOTHESIS TESTING . . . . . . . . . . . . . . . . . . . . . . . . . . . . XI-7PAIRED-COMPARISON TESTS . . . . . . . . . . . . . . . . . . . . . XI-32GOODNESS-OF-FIT TESTS . . . . . . . . . . . . . . . . . . . . . . . . XI-39CONTINGENCY TABLES . . . . . . . . . . . . . . . . . . . . . . . . . . XI-46

ANALYSIS OF VARIANCE . . . . . . . . . . . . . . . . . . . . . . . . . . . . XI-50RELATIONSHIPS BETWEEN VARIABLES . . . . . . . . . . . . . . . XI-60

LINEAR REGRESSION . . . . . . . . . . . . . . . . . . . . . . . . . . . . XI-60SIMPLE LINEAR CORRELATION . . . . . . . . . . . . . . . . . . . . XI-70TIME-SERIES ANALYSIS . . . . . . . . . . . . . . . . . . . . . . . . . . XI-73

DESIGN OF EXPERIMENTS . . . . . . . . . . . . . . . . . . . . . . . . . . XI-74TERMINOLOGY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . XI-76PLANNING EXPERIMENTS . . . . . . . . . . . . . . . . . . . . . . . . XI-86BLOCK EXPERIMENTS . . . . . . . . . . . . . . . . . . . . . . . . . . . XI-94FULL-FACTORIAL EXPERIMENTS . . . . . . . . . . . . . . . . . . XI-97FRACTIONAL FACTORIALS . . . . . . . . . . . . . . . . . . . . . . XI-101OTHER EXPERIMENTS . . . . . . . . . . . . . . . . . . . . . . . . . . XI-108

REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . XI-116

XII. APPENDIX/INDEX. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . XII-1ANSWERS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . XII-31


INTRO-6 (6)

CQE Primer Question Contents

Primer SectionQuestions

% Exam Primer CD II. Management &

Leadership9.5% 15 38 95

III. Quality Systems 9.5% 15 38 95IV. Product Design 15.5% 25 62 155V. Product Control 10% 16 40 100

VI. Testing &Measurement

10% 16 40 100

VII. Control & Mgmt Tools 9% 14 36 90VIII. Improvement

Techniques9.5% 15 38 95

IX. Basic Statistics 9% 14 36 90X. Stat Applications 8% 13 32 80

XI. Advanced Statistics 10% 16 40 100Total 100% 160 400 1000

Comparison B/T CQE Primer & ASQ BOK

Primer II III IV V VI VII VIII IX X XI

ASQBOK

IA º I

IIA º F

IIIA º E

IVA º C

IVD º F

VA & B

VC º E

VIA º C

VIF & G

VI D, E, H


I. CERTIFICATION OVERVIEW

I-1 (7)

I KNOW OF NO MORE ENCOURAGINGFACT THAN THE UNQUESTIONABLEABILITY OF MAN TO ELEVATE HIS LIFEBY A CONSCIOUS ENDEAVOR.

HENRY DAVID THOREAU

Professionalizing Quality Education



I-2 (8)

Preface

This text is designed to be a Primer for those interestedin taking the certification examination offered twice ayear by the American Society for Quality. Testquestions are provided at the end of each Section. These test questions and answers must be removed ifthis text is to be used as a reference during acertification examination. They are printed on blue paperfor easy distinction.

2006 CQE Primer Notable Changes

Overall: Primer expanded from 830 pages to 878 pages.There was a 12% replacement of questions. Added thenew BOK and Bloom’s taxonomy. Section by sectionchanges are noted in the Primer.



I-3 (9)

Certified Quality Engineer Exam

Objective

To provide recognized quality engineer fundamentaltraining and to prepare persons interested in takingthe CQE examination.

Certification

Certification is the independently verified prescribedlevel of knowledge as defined through a combinationof experience, education and examination.

The Certified Quality Engineer

Is a professional who can carry out in a responsiblemanner proven techniques which make up the body ofknowledge recognized by those who are experts inquality technology.



I-3 (10)

CQE Exam (Continued)

Eligibility

CQE participants must register with ASQheadquarters. Eligibility entails a combination ofeight years work experience and/or higher education.Three years of this requirement must be in a decisionmaking position.

Cost

The national test fee is determined by ASQ and isdetailed in the CQE brochure.

Location

Proctors are provided by ASQ sections in your area.

Duration

The test lasts 5 hours and will begin at an advisedtime (typically 8 A.M.).



I-4 (11)


Other Details

Can be obtained by calling ASQ headquarters at (800)248-1946 or (414) 272-8575. They will send a CQEbrochure free of charge.

Bibliography Sources

The reference sources recommended in the ASQbrochure are excellent. Four favorites are:

(1) Juran's Quality Handbook

(2) Western Electric's Statistical Quality ControlHandbook

(3) Gryna's Quality Planning and Analysis

(4) Grant & Leavenworth's Statistical Quality Control

ANSI/ASQ Z1.4 should be reviewed and taken into theexam. Other options are listed in the Primer.



I-5 (12)


Study

The author recommends that this Primer be taught bya qualified CQE using classroom lecture, studyassignments and a review of test questions. Trainingmay vary from 27 hours to 48 hours. Additionally, thestudent should spend about 90 hours of individualstudy on the Primer, test questions, and otherbibliography sources. If the student studies unaided,a minimum of 130 hours of preparation is suggested.

Exam Hints

The CQE applicant should take into the exam:

C Several #2 pencilsC A calculator (capable of determining standard

deviation and natural log)C The CQE Primer (without test questions)C A recommended quality referenceC ANSI/ASQ Z1.4-2003C A good statistical reference (one the student knows)C Scratch paper



I-5 (13)

Exam Hints (Continued)

Arrive early, get a good seat, organize your materials.

Answer all questions. There's no penalty for wronganswers.

Save difficult questions until the end.

Use good time management. If there are 160questions on the 5 hour exam, one must average 1.88minutes/question.

Some tests begin with difficult questions, avoid panic.

Keep test question numbers and the answer sheetaligned.

Bring any exam errata to your proctor's attention.

Mentally note weakness categories in case you haveto take the exam again. ASQ will report only flagrantareas.



I-6 (14)

ASQ CQE Body of Knowledge

I. Management and Leadership (15 Questions)

A. Quality Philosophies and Foundations

Explain how modern quality has evolved fromquality control through statistical process control(SPC) to total quality management and leadershipprinciples (including Deming’s 14 points), andhow quality has helped form various continuousimprovement tools including lean, six sigma,theory of constraints, etc. (Remember)

B. The Quality Management System (QMS)

1. Strategic planning (Apply)Identify and define top management’sresponsibility for the QMS, includingestablishing policies and objectives, settingorganization-wide goals, supporting qualityinitiatives, etc.



I-6 (15)

ASQ CQE BOK (Continued)

2. Deployment techniques (Apply)Define, describe, and use various deploymenttools in support of the QMS: benchmarking,stakeholder identification and analysis,performance measurement tools, and projectmanagement tools such as PERT charts, Ganttcharts, critical path method (CPM), resourceallocation, etc.

3. Quality information system (QIS) (Remember)Identify and define the basic elements of a QIS,including who will contribute data, the kind ofdata to be managed, who will have access tothe data, the level of flexibility for futureinformation needs, data analysis, etc.

C. ASQ Code of Ethics for Professional Conduct

Determine appropriate behavior in situationsrequiring ethical decisions. (Evaluate)



I-7 (16)


D. Leadership Principles and Techniques (Analyze)

Describe and apply various principles andtechniques for developing and organizing teamsand leading quality initiatives.

E. Facilitation Principles and Techniques (Analyze)

Define and describe the facilitator’s role andresponsibilities on a team. Define and applyvarious tools used with teams, includingbrainstorming, nominal group technique, conflictresolution, force-field analysis, etc.

F. Communication Skills (Analyze)

Describe and distinguish between variouscommunication methods for deliveringinformation and messages in a variety ofsituations across all levels of the organization.



I-7 (17)


G. Customer Relations (Analyze)

Define, apply, and analyze the results of customerrelation measures such as quality functiondeployment (QFD), customer satisfaction surveys,etc.

H. Supplier Management (Analyze)

Define, select, and apply various techniquesincluding supplier qualification, certification,evaluation, ratings, performance improvement,etc.

I. Barriers to Quality Improvement (Analyze)

Identify barriers to quality improvement, theircauses and impact, and describe methods forovercoming them.



I-8 (18)


II. The Quality System( 15 Questions)

A. Elements of the Quality System (Evaluate)

Define, describe, and interpret the basic elementsof a quality system, including planning, control,and improvement, from product and processdesign through quality cost systems, auditprograms, etc.

B. Documentation of the Quality System (Apply)

Identify and apply quality system documentationcomponents, including quality policies,procedures to support the system, configurationmanagement and document control to managework instructions, quality records, etc.

C. Quality Standards and Other Guidelines (Apply)

Define and distinguish between national andinternational standards and other requirementsand guidelines, including the Malcolm BaldrigeNational Quality Award (MBNQA), and describekey points of the ISO 9000 series of standardsand how they are used. [Note: Industry-specificstandards will not be tested.]



I-8 (19)


D. Quality Audits

1. Types of audits (Apply)Describe and distinguish between varioustypes of quality audits such as product,process, management (system), registration(certification), compliance (regulatory), first,second, and third party, etc.

2. Roles and responsibilities in audits

Identify and define roles and responsibilities foraudit participants such as audit team (leaderand members), client, auditee, etc.

(Understand)

3. Audit planning and implementation (Apply)Describe and apply the steps of a quality audit,from the audit planning stage throughconducting the audit, from the perspective ofan audit team member.

4. Audit reporting and follow up (Apply)Identify, describe, and apply the steps of auditreporting and follow up, including the need toverify corrective action.



I-9 (20)


E. Cost of Quality (COQ) (Analyze)

Identify and apply COQ concepts, including costcategories, data collection methods andclassification, and reporting and interpretingresults.

F. Quality Training (Apply)

Identify and define key elements of a trainingprogram, including conducting a needs analysis,developing curricula and materials, anddetermining the program’s effectiveness.

III. Product and Process Design (25 Questions)

A. Classification of Quality Characteristics(Evaluate)

Define, interpret, and classify qualitycharacteristics for new products and processes.[Note: The classification of product defects iscovered in IV.B.3.]



I-9 (21)


B. Design Inputs and Review (Analyze)

Identify sources of design inputs such ascustomer needs, regulatory requirements, etc.and how they translate into design concepts suchas robust design, QFD, and Design for X (DFX,where X can mean six sigma (DFSS),manufacturability (DFM), cost (DFC), etc.).Identify and apply common elements of thedesign review process, including roles andresponsibilities of participants.

C. Technical Drawings and Specifications(Evaluate)

Interpret technical drawings includingcharacteristics such as views, title blocks,dimensioning, tolerancing, GD&T symbols, etc.Interpret specification requirements in relation toproduct and process characteristics.

D. Design Verification (Evaluate)

Identify and apply various evaluations and teststo qualify and validate the design of new productsand processes to ensure their fitness for use.



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E. Reliability and Maintainability (Analyze)

1. Predictive and preventive maintenance toolsDescribe and apply these tools and techniquesto maintain and improve process and productreliability.

2. Reliability and maintainability indicesReview and analyze indices such as, MTTF,MTBF, MTTR, availability, failure rate, etc.

(Analyze)

3. Bathtub curve (Analyze)Identify, define, and distinguish between thebasic elements of the bathtub curve.

4. Reliability / Safety / Hazard Assessment Tools

Define, construct, and interpret the results offailure mode and effects analysis (FMEA),failure mode, effects, and criticality analysis(FMECA), and fault tree analysis (FTA).

(Analyze)



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IV. Product and Process Control (32 Questions)

A. Tools (Analyze)

Define, identify, and apply product and processcontrol methods such as developing control plans,identifying critical control points, developing andvalidating work instructions, etc.

B. Material Control

1. Material identification, status, and traceabilityDefine and distinguish these concepts, anddescribe methods for applying them in varioussituations. [Note: Product recall procedureswill not be tested.] (Analyze)

2. Material segregation (Evaluate)Describe material segregation and itsimportance, and evaluate appropriate methodsfor applying it in various situations.

3. Classification of defects (Evaluate)Define, describe, and classify the seriousnessof product and process defects.



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4. Material review board (MRB) (Analyze)Identify the purpose and function of an MRB,and make appropriate disposition decisions invarious situations.

C. Acceptance Sampling

1. Sampling concepts (Analyze)Define, describe, and apply the concepts ofproducer and consumer risk and related terms,including operating characteristic (OC) curves,acceptable quality limit (AQL), lot tolerancepercent defective (LTPD), average outgoingquality (AOQ), average outgoing quality limit(AOQL), etc.

2. Sampling standards and plans (Analyze)Interpret and apply ANSI/ASQ Z1.4 and Z1.9standards for attributes and variables sampling.Identify and distinguish between single, double,multiple, sequential, and continuous samplingmethods. Identify the characteristics ofDodge-Romig sampling tables and when theyshould be used.



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3. Sample integrity (Analyze)Identify the techniques for establishing andmaintaining sample integrity.

D. Measurement and Test

1. Measurement tools (Analyze)Select and describe appropriate uses ofinspection tools such as gage blocks, calipers,micrometers, optical comparators, etc.

2. Destructive and nondestructive testsDistinguish between destructive andnondestructive measurement test methods andapply them appropriately. (Analyze)

E. Metrology (Analyze)

Identify, describe, and apply metrologytechniques such as calibration systems,traceability to calibration standards,measurement error and its sources, and controland maintenance of measurement standards anddevices.



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F. Measurement System Analysis (MSA) (Evaluate)

Calculate, analyze, and interpret repeatability andreproducibility (Gage R&R) studies, measurementcorrelation, capability, bias, linearity, etc.,including both conventional and control chartmethods.

V. Continuous Improvement (30 Questions)

A. Quality Control Tools (Analyze)

Select, construct, apply, and interpret tools suchas 1) flowcharts, 2) Pareto charts, 3) cause andeffect diagrams, 4) control charts, 5) checksheets, 6) scatter diagrams, and 7) histograms.

B. Quality Management and Planning Tools

Select, construct, apply, and interpret tools suchas 1) affinity diagrams, 2) tree diagrams, 3)process decision program charts (PDPC), 4)matrix diagrams, 5) interrelationship digraphs, 6)prioritization matrices, and 7) activity networkdiagrams. (Analyze)



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C. Continuous Improvement Techniques (Analyze)

Define, describe, and distinguish between variouscontinuous improvement models: total qualitymanagement (TQM), kaizen, plan-do-check-act(PDCA), six sigma, theory of constraints (TOC),lean, etc.

D. Corrective Action (Evaluate)

Identify, describe, and apply elements of thecorrective action process including problemidentification, failure analysis, root causeanalysis, problem correction, recurrence control,verification of effectiveness, etc.

E. Preventive Action (Evaluate)

Identify, describe, and apply various preventiveaction tools such as errorproofing/poka-yoke,robust design, etc., and analyze theireffectiveness.



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VI. Quantitative Methods and Tools (43 Questions)

A. Collecting and Summarizing Data

1. Types of data (Apply)Define, classify, and compare discrete(attributes) and continuous (variables) data.

2. Measurement scales (Apply)Define, describe, and use nominal, ordinal,interval, and ratio scales.

3. Data collection methods (Apply)Describe various methods for collecting data,including tally or check sheets, data coding,automatic gaging, etc., and identify theirstrengths and weaknesses.

4. Data accuracy (Apply)Describe the characteristics or properties ofdata (e.g., source/resource issues, flexibility,versatility, etc.) and various types of data errorsor poor quality such as low accuracy,inconsistency, interpretation of data values,and redundancy. Identify factors that caninfluence data accuracy, and apply techniquesfor error detection and correction.



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5. Descriptive statistics (Evaluate)Describe, calculate, and interpret measures ofcentral tendency and dispersion (central limittheorem), and construct and interpretfrequency distributions including simple,categorical, grouped, ungrouped, andcumulative.

6. Graphical methods for depicting relationshipsConstruct, apply, and interpret diagrams andcharts such as stem-and-leaf plots,box-and-whisker plots, etc. [Note: Run chartsand scatter diagrams are covered in V.A.]

(Analyze)

7. Graphical methods for depicting distributionsConstruct, apply, and interpret diagrams suchas normal probability plots, Weibull plots, etc.[Note: Histograms are covered in V.A.]

(Analyze)



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B. Quantitative Concepts

1. Terminology (Analyze)Define and apply quantitative terms, includingpopulation, parameter, sample, statistic,random sampling, expected value, etc.

2. Drawing statistical conclusions (Evaluate)Distinguish between numeric and analyticalstudies. Assess the validity of statisticalconclusions by analyzing the assumptionsused and the robustness of the technique used.

3. Probability terms and concepts (Apply)Describe and apply concepts such asindependence, mutual ly exc lus ive ,multiplication rules, complementary probability,joint occurrence of events, etc.

C. Probability Distributions

1. Continuous distributions (Analyze)Define and distinguish between thesedistributions: normal, uniform, bivariate normal,exponential, lognormal, Weibull, chi square,Student’s t, F, etc.



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2. Discrete distributions (Analyze)Define and distinguish between thesed i s t r i b u t i o n s : b i n o m i a l , P o i s s o n ,hypergeometric, multinomial, etc.

D. Statistical Decision-Making

1. Point estimates and confidence intervalsDefine, describe, and assess the efficiency andbias of estimators. Calculate and interpretstandard error, tolerance intervals, andconfidence intervals. (Evaluate)

2. Hypothesis testing (Evaluate)Define, interpret, and apply hypothesis tests formeans, variances, and proportions. Apply andinterpret the concepts of significance level,power, type I and type II errors. Define anddistinguish between statistical and practicalsignificance.



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3. Paired-comparison tests (Apply)Define and use paired-comparison (parametric)hypothesis tests, and interpret the results.

4. Goodness-of-fit tests (Apply)Define and use chi square and othergoodness-of-fit tests, and interpret the results.

5. Analysis of variance (ANOVA) (Analyze)Define and use ANOVAs and interpret theresults.

6. Contingency tables (Analyze)Define, construct, and use contingency tablesto evaluate statistical significance.

E. Relationships Between Variables

1. Linear regression (Analyze)Calculate the regression equation for simpleregressions and least squares estimates.Construct and interpret hypothesis tests forregression statistics. Use regression modelsfor estimation and prediction, and analyze theuncertainty in the estimate. [Note: Non-linearmodels and parameters will not be tested.]



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2. Simple linear correlation (Analyze)Calculate the correlation coefficient and itsconfidence interval, and construct and interpreta hypothesis test for correlation statistics.[Note: Serial correlation will not be tested.]

3. Time-series analysis (Analyze)Define, describe, and use time-series analysisincluding moving average, and interprettime-series graphs to identify trends andseasonal or cyclical variation.

F. Statistical Process Control (SPC)

1. Objectives and benefits (Understand)Identify and explain objectives and benefits ofSPC such as assessing process performance.

2. Common and special causes (Analyze)Describe, identify, and distinguish betweenthese types of causes.



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3. Selection of variable (Analyze)Identify and select characteristics formonitoring by control chart.

4. Rational subgrouping (Apply)Define and apply the principles of rationalsubgrouping.

5. Control charts (Analyze)Identify, select, construct, and use variouscontrol charts, including X6 - R, X6 - s, individualsand moving range (ImR or XmR), movingaverage and moving range (MamR), p, np, c, u,and CUSUM charts.

6. Control chart analysis (Evaluate)Read and interpret control charts, use rules fordetermining statistical control.

7. PRE-control charts (Apply)Define and describe how these charts differfrom other control charts and how they shouldbe used.

8. Short-run SPC (Apply)Identify, define, and use short-run SPC rules.



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G. Process and Performance Capability

1. Process capability studies (Analyze)Define, describe, calculate, and use processcapability studies, including identifyingcharacteristics, specifications, and tolerances,developing sampling plans for such studies,establishing statistical control, etc.

2. Process performance vs. specificationsDistinguish between natural process limits andspecification limits, and calculate percentdefective. (Analyze)

3. Process capability indices (Evaluate)Define, select, and calculate Cp, Cpk, Cpm, and Cr,and evaluate process capability.

4. Process performance indices (Evaluate)Define, select, and calculate Pp and Ppk andevaluate process performance.



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H. Design and Analysis of Experiments

1. Terminology (Understand)Define terms such as dependent andindependent variables, factors, levels,response, treatment, error, and replication.

2. Planning and organizing experimentsDefine, describe, and apply the basic elementsof designed experiments, including determiningthe experiment objective, selecting factors,responses, and measurement methods,choosing the appropriate design, etc.

(Analyze)

3. Design principles (Apply)Define and apply the principles of power andsample size, balance, replication, order,efficiency, randomization, blocking, interaction,and confounding.



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4. One-factor experiments (Analyze)Construct one-factor experiments such ascompletely randomized, randomized block, andLatin square designs, and use computationaland graphical methods to analyze thesignificance of results.

5. Full-factorial experiments (Analyze)Construct full-factorial designs and usecomputational and graphical methods toanalyze the significance of results.

6. Two-level fractional factorial experimentsConstruct two-level fractional factorial designs(including Taguchi designs) and applycomputational and graphical methods toanalyze the significance of results. (Analyze)



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Levels of Cognition ( 2001)Based on Bloom’s Taxonomy

In addition to content specifics, the subtext for eachtopic in this BOK also indicates the intended complexitylevel of the test questions for that topic. These levelsare based on “Levels of Cognition” (from Bloom’sTaxonomy – Revised, 2001) and are presented below inrank order, from least complex to most complex.

RememberRecall or recognize terms, definitions, facts, ideas,materials, patterns, sequences, methods, principles, etc.

UnderstandRead and understand descriptions, communications,reports, tables, diagrams, directions, regulations, etc.

ApplyKnow when and how to use ideas, procedures, methods,formulas, principles, theories, etc.



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Levels of Cognition (Continued)

AnalyzeBreak down information into its constituent parts andrecognize their relationship to one another and how theyare organized; identify sublevel factors or salient datafrom a complex scenario.

EvaluateMake judgments about the value of proposed ideas,solutions, etc., by comparing the proposal to specificcriteria or standards.

CreatePut parts or elements together in such a way as toreveal a pattern or structure not clearly there before;identify which data or information from a complex set isappropriate to examine further or from which supportedconclusions can be drawn.


II. MANAGEMENT & LEADERSHIP

II-1 (40)

IF YOU DON'T KNOW WHEREYOU ARE GOING, YOU WILLP R O B A B L Y E N D U PSOMEWHERE ELSE.

LAURENCE J. PETER


II. MANAGEMENT & LEADERSHIPQUALITY FOUNDATIONS

II-2 (41)

Management and Leadership

Management and Leadership is presented in thefollowing topic areas:

C Quality foundationsC Quality management systemsC ASQ code of ethicsC Leadership principles C Facilitation techniquesC Communication skillsC Customer relationsC Supplier managementC Barriers to quality improvement



II-2 (42)

Quality Evolution

There have been a number of hot quality topic areas thatarrive, build, maintain, wane, and fade. In some cases,the topic disappears because of new technology orimproved techniques. In many cases, the latest “craze”merely builds and expands on the best ideas that camebefore it. Some examples follow:

Craftsmanship: A historic approach lasting from themiddle ages until today (in certain applications).

Standardization of parts: Beginning with Eli Whitney(1798 in the USA) and still continuing because of theneed for the interchangeability of parts.

Definition of a system: The scientific managementtechnique is attributed to Fredrick Taylor (1911).There are some on-going applications today.

Quality control: (1950s - 1960s). Originally associatedwith the proliferation of sampling plans, butcontinuing with modern applications such as controlplans.



II-3 (43)

Quality Evolution (Continued)

Quality assurance: (1970s - 1980s). Included manypreventative techniques, like SPC and quality costmeasurement. Still in wide usage and still necessary.

Total quality management: (1980s - 1990s). Built on thevery best of prior concepts and added the keyingredient of management direction.

Continuous quality improvement: (1980s - 2000s).Expanded the total quality management base, butrecognized the advantages of project improvementteams and an on-going, organized, improvementstructure.

Six sigma: (lean six sigma). Emphasizes the reductionof variation, consideration of internal processes,concentration on the bottom line, utilization ofadvanced technical tools, use of a formalized problemsolving approach (DMAIC), the elimination of internalwastes, and the need for key management leadershipand support.



II-3 (44)

Quality Evolution (Continued)

There has been a vast array of other concepts:

C Automated inspectionC Endorsement of international standardsC Competitive benchmarkingC Taguchi and other DOE approachesC The use of statistical softwareC Quality auditsC The recognition of the value of human resourcesC Design techniques (DFSS, DFM, FEMA, DFP, etc.)C The establishment of solid supplier relationshipsC Attention to internal and external customersC Quality function deployment (QFD)C Rapid prototype developmentC Award achievement (Deming prize, MBNQA)C Theory of constraints (TOC)C Kaizen techniquesC The use of color coded inventory control (kanban)C Mistake proofing devicesC Awareness of measurement uncertaintyC Formalized documentation systemsC Quality circles/quality teamsC Manufacturing cells and flexible manufacturing

The above list is far from inclusive.



II-4 (45)

Quality Philosophies and Approaches

Guru Contribution

Philip B. Crosby Senior manager involvement4 absolutes of quality managementQuality cost measurements

W. Edwards Deming Plan-do-study-act (wide American usage)Top management involvementConcentration on system improvementConstancy of purpose

Armand V.Feigenbaum

Total quality control/managementTop management involvement

Kaoru Ishikawa 4M (5M) or cause-and-effect diagramCompanywide quality controlNext operation as customer

Joseph M. Juran Top management involvementQuality Trilogy (project improvement)Quality cost measurementPareto Analysis

Walter A. Shewhart Assignable cause vs. chance causeControl chartsPlan-do-check-act (in product design)Use of statistics for improvement

Genichi Taguchi Loss function conceptsSignal to noise ratioExperimental design methodsConcept of design robustness



II-5 (46)

Philip B. Crosby(1928 - 2001)

Philip B. Crosby was the corporate vice president of ITTfor 14 years. Mr. Crosby consulted, spoke, and wroteabout strategic quality issues throughout hisprofessional life.

Awards:

Fellow, ASQPast president of ASQ

Books:

Quality Is Free (1979)12

The Art of Getting Your Own Sweet Way (1981)Quality Without Tears (1984)13

The Eternally Successful Organization (1988)Leading, the Art of Becoming an Executive (1990)Completeness Quality for the 21st Century (1992)Running Things (1992)Quality and Me: Lessons from an Evolving Life (1999)

Statement on quality:

Quality is conformance to requirements.



II-5 (47)

Philip B. Crosby (Continued)

Other quality deep thinkers could be viewed asacademicians, but Crosby was considered abusinessman. This explained the numbers of topmanagement that flocked to his quality college.

Crosby believed that quality was a significant part of thecompany and senior managers must take charge of it.He believed the quality professionals must becomemore knowledgeable and communicative about thebusiness. Crosby stated that corporate managementmust make the cost of quality a part of the financialsystem of their company.



II-6 (48)


Philip Crosby preached four absolutes of qualitymanagement:

1. Quality means conformance to requirements

The requirements are what the customer saysthey are and “do it right the first time.”

2. Quality comes from prevention

Correct problems in the system.

3. The quality performance standard is zero defects

You must insist on zero defects. Otherwise, it isacceptable to send out nonconforming goods.

4. Quality measurement is the price ofnonconformance

A measurement of quality is needed to getmanagement’s attention.



II-6 (49)


The four absolutes of quality management are basicrequirements for understanding the purpose of a qualitysystem. Philip Crosby also developed a 14 stepapproach to quality improvement:

1. Management commitment 2. Quality improvement teams 3. Measurement 4. Cost of quality 5. Quality awareness 6. Corrective action 7. Zero defects planning 8. Employee education 9. Zero defects day 10. Goal setting 11. Error cause removal 12. Recognition 13. Quality councils 14. Do it all over again



II-7 (50)

Dr. W. Edwards Deming(1900 - 1993)

Education:

B.S., University of Wyoming; M.S., University ofColorado; Ph.D., Physics, Yale.

Awards:

Shewhart Medal, ASQ, 1955Second Order Medal of the Sacred Treasure, 1960Honorary Member, ASQ, 1970, and numerous others.

Books:

Over 200 published papers, articles, and books.

Quality, Productivity, and Competitive Position (1982)Out of the Crisis (1986)


He was the founder of the third wave of the industrialrevolution.



II-7 (51)

Dr. W. Edwards Deming (Continued)

W. Edwards Deming was the one individual who stoodfor quality and for what it means. He is a national folkhero in Japan and was perhaps the leading speaker forthe quality revolution in the world.

He visited Japan between 1946 and 1948, for thepurpose of census taking. He developed a fondness forthe Japanese people during that time. JUSE (JapaneseUnion of Scientists and Engineers) invited Deming backin 1950 for executive courses in statistical methods. Herefused royalties on his seminar materials and insistedthat the proceeds be used to help the Japanese people.JUSE named their ultimate quality prize after him.

Deming would return to Japan on many other occasionsto teach and consult. He was well known in Japan, butnot so in America. Only when NBC published its whitepaper, “If Japan can, why can’t we?” did Americadiscover him. His message to America is listed in hisfamous 14 points and 7 deadly diseases.



II-8 (52)


The Fourteen Obligations of Top Management:

1. Create constancy of purpose for improvement ofproducts and service

2. Adopt a new philosophy; we are in a new economicage

3. Cease dependence upon inspection as a way toachieve quality

4. End the practice of awarding business based onprice tag

5. Constantly improve the process of planning,production, and service - this system includespeople

6. Institute training on-the-job

7. Institute improved supervision (leadership)



II-8 (53)


The Fourteen Obligations of Top Management:

8. Drive out fear

9. Break down barriers between departments

10. Eliminate slogans/targets asking for increasedproductivity without providing methods

11. Eliminate numerical quotas

12. Remove barriers that stand between workers andtheir pride of workmanship; the same for all salariedpeople

13. Institute programs for education and retraining

14. Put a total emphasis in the company to accomplishthe transformation



II-9 (54)

Dr. Deming’s Profound Knowledge

Dr. Deming’s profound knowledge includes thefollowing elements:

C Appreciation for a systemC Theory of variationC Theory of knowledgeC Understanding psychology

The system of profound knowledge is a framework forapplying management’s best efforts to the right tasks.It applies statistical principles to processes andsystems. The theory of knowledge is needed forprediction. A knowledge of psychology is needed todeal with people.



II-9 (55)

Seven Deadly Diseases That Management Must Cure:

1. Lack of constancy of purpose to plan a marketableproduct and service

2. Emphasis on short-term profits

3. Personal evaluation appraisal, by whatever name,the effects of which are devastating

4. Mobility of management; job hopping

5. Use of visible figures, with little or no considerationof figures that are unknown or unknowable

6. Excessive medical costs

7. Excessive costs of warranty, fueled by lawyers



II-10 (56)

Other Deming Concepts

Among other educational techniques, Deming promotedthe parable of the red beads, the PDSA cycle, and theconcept of 94% system variation (managementcontrollable) versus 6% special variation (some of whichmay be operator controllable).

Deming’s Chain Reaction

Deming shared the following chain reaction with Japanin the summer of 1950:

Improve quality º decrease costs (less rework, fewerdelays) º productivity Improves º capture the marketwith better quality and price º stay in business ºprovide jobs.



II-11 (57)

Dr. Armand V. Feigenbaum(1920 - )

Currently president of General Systems Company,Pittsfield, MA., Dr. Feigenbaum was associated withGeneral Electric for 26 years.

Education:

B.S., Union College; M.S./Ph.D., MIT

Awards: (A few shown)

Honorary Member, ASQ, 1986E. Jack Lancaster Award, ASQ, 1981Edwards Medal, ASQ, 1965Fellow, AAASLife Member, IEEE and ASME2-time president of ASQ 1961/63Founding chairman, International Academy for Quality

Books:

Quality Control: Principles, Practice (1951)Total Quality Control (1961)Total Quality Control, 3rd ed. (1983)Total Quality Control, 40th Anniversary Edition (1991)18



II-11 (58)

Dr. Armand V. Feigenbaum (Continued)

Statement on total quality control:

An effective system for integrating the qualitydevelopment, quality maintenance, and qualityimprovements of the various groups in an organizationso as to enable production and service at the mosteconomical levels allowing for full customersatisfaction.

Feigenbaum is generally given credit for establishingthe concept of “total quality control” in the late 1940s atGeneral Electric. His TQC statement was first publishedin 1961, but, at that time, the concept was so new, thatno one listened.

Feigenbaum states that the American industry muststrive to become as strong as it can be in its ownmarketplace. This has become valuable as globalcompetitiveness has spread into the U.S. Properdesign, production, selling, and servicing will providethe potential for supremacy in the marketplace.



II-12 (59)


The TQC philosophy maintains that all areas of thecompany must be involved in the quality effort. Thesuccess of TQC includes these principles:

C TQC is a companywide processC Quality is what the customer says it isC Quality and production costs are in partnershipC Higher quality will equate with lower costsC Both individual and team zeal are requiredC Quality is a way of managing, using leadershipC Quality and innovation can work togetherC All of management must be involved in qualityC Continuous improvement is requiredC Quality is an inexpensive route to productivity C Both customers and suppliers must be considered



II-12 (60)


Listed below are selected quality phrases of A.V.Feigenbaum:

“Quality does not travel under an exclusive foreignpassport.”

“Quality and costs are partners, not adversaries.”

Failure driven companies... “If it breaks we’ll fix it.”versus the quality excellence approach... “No defects,no problems, we are essentially moving toward perfectwork processes.”

“Quality is everybody’s job, but because it iseverybody’s job, it can become nobody’s job without theproper leadership and organization.”



II-13 (61)

Dr. Kaoru Ishikawa(1915 - 1989)

Education:

B.S. in chemistry and Doctorate of Engineering -University of Tokyo

Awards: (A few are noted)

Deming Prize (1952)Nihon Keizai Press PrizeIndustrial Standardization PrizeGrant Award (ASQ)Shewhart Medal (ASQ), first Japanese to be awardedHonorary Member, ASQ (1986)Ishikawa Award (ASQ) (established in his honor)

Books:

Authored the first Japanese book to define TQCGuide to Quality Control (1982)What is Total Quality Control? The Japanese Way (1985)



II-13 (62)

Dr. Kaoru Ishikawa (Continued)

Statement on total quality control:

To practice quality control is to develop, design,produce, and service a quality product that is mosteconomical, most useful, and always satisfactory to theconsumer.

Abstract:

Kaoru Ishikawa was involved with the quality movementin its earliest beginnings and remained so until his deathin 1989. Ishikawa’s training tapes, produced in 1981,contain many of the statements of quality that are invogue today. Subjects such as total quality control,next operation as customer, training of workers,empowerment, customer satisfaction, elimination ofsectionalism and humanistic management of workers,are examples.

To reduce confusion between Japanese style totalquality control and western style total quality control, hecalled the Japanese method the companywide qualitycontrol (CWQC).



II-14 (63)

Dr. Kaoru Ishikawa (Continued)

There are 6 main characteristics that make CWQCdifferent:

1. More education and training in quality control2. Quality circles are really only 20% of the activities

for CWQC3. Participation by all members of the company4. Having QC audits5. Using the seven tools and advanced statistical

methods6. Nationwide quality control promotion activities

CWQC involves the participation of workers from top tobottom of the organization and from the start to thefinish of the product life cycle. CWQC requires amanagement philosophy that has respect for humanity.

Kaoru Ishikawa was known for his lifelong efforts as thefather of Japanese quality control efforts. The fishbonediagram is also called the Ishikawa diagram in hishonor.



II-15 (64)

Dr. Joseph M. Juran(1904 - )

Founder and Chairman Emeritus of The Juran Institute.

Education:

B.S., University of Minnesota; J.D., Loyola University;and numerous honorary doctorates.

Awards:

Edwards Medal, ASQBrumbaugh Awards, ASQGrant Awards, ASQHonorary Member, ASQPlus 30 other medals and fellowships

Books: 15 books, 40 videotapes

Juran on Planning for Quality (1988)Juran on Leadership for Quality (1989)Juran on Quality by Design (1992)Quality Planning & Analysis (1993)Juran’s Control Handbook, 5th ed. (1999)



II-15 (65)

Dr. Joseph M. Juran (Continued)


Adopt a revolutionary rate of improvement in quality,making quality improvements by the thousands, yearafter year. Dr. Juran also defined quality as fitness foruse.

Abstract:

J.M. Juran started in quality after his graduation fromengineering school with an inspection position atWestern Electric’s Hawthorne plant in Chicago in 1924.He left Western Electric to begin a career in research,lecturing, consulting, and writing that has lasted over 50years.

The publication of his book...Quality Control Handbook,and his work in quality management, led to an invitationfrom JUSE in 1954. Juran’s first lectures in Japan wereto the 140 largest company CEOs, and later to 150senior managers. The right audience was there at thestart.



II-16 (66)

Dr. Joseph M. Juran (Continued)J.M. Juran has a basic belief that quality in America isimproving, but it must be improved at a revolutionaryrate. Quality improvements need to be made by thethousands, year after year. Only then does a companybecome a quality leader. Juran’s basics for success canbe described as follows:

C Top management must commit the time andresources for success

C CEOs must serve on the quality council (steeringcommittee)

C Specific quality improvement goals must be in thebusiness plan and include:

C The means to measure results against goalsC A review of results against goalsC A reward for superior quality performance

C The responsibility for improvements must beassigned to individuals

C People must be trained for improvement

C The workforce must be empowered to participate



II-16 (67)

Juran Trilogy

Juran has felt that managing for quality requires thesame attention that other functions obtain. Thus, hedeveloped the Juran trilogy or quality trilogy whichinvolves:

C Quality planningC Quality controlC Quality improvement

Juran sees these items as the keys to success. Topmanagement can follow this sequence just as theywould use one for financial budgeting, cost control, andprofit improvement.



II-17 (68)

Contrast of Big Q and Little Q

Dr. Juran developed a mechanism for contrastingquality in the smaller tactical sense (little Q) with qualityin the larger strategic sense (big Q). It provides anindividual with an instant recognition of what is beingdefined. For instance:

C Having a team solve a specific process problem isa little Q item

C Having teams throughout the company solveproblems is a big Q item

This methodology is often associated with quality costanalysis.



II-18 (69)

Dr. Walter A. Shewhart(1891 - 1967)

Education:

B.S. and M.S., University of Illinois; Ph.D. in Physics,University of California

Awards:

Holley Medal, ASMEHonorary Fellowship of the Royal Statistical SocietyFirst Honorary Member of ASQHonorary Professor Rutgers UniversityThe Shewhart Medal is named in his honor

Books:

Articles in Bell System Technical Journal

Economic Control of Quality of Manufactured Product(1931)

Statistical Method from the Viewpoint of Quality Control(1939)



II-18 (70)

Dr. Walter A. Shewhart (Continued)

Quote:

“Both pure and applied science have gradually pushedfurther and further the requirements for accuracy andprecision. However, applied science, particularly in themass production of interchangeable parts, is even moreexacting than pure science in certain matters ofaccuracy and precision.”

Abstract:

Shewhart worked for the Western Electric Company. In1924, Shewhart framed the problem in terms of“assignable cause” and “chance cause” variation andintroduced the control chart as a tool for distinguishingbetween the two. Bringing a production process into astate of statistical control, where the only variation ischance cause, is necessary to manage a processeconomically.



II-19 (71)

Dr. Walter A. Shewhart (Continued)

Walter Shewhart’s statistical process control chartshave become a quality legacy that continues today.Control charts are widely used to monitor processesand to determine when a process changes. Processchanges are only made when points on the control chartare outside acceptable ranges. Dr. Deming stated thatShewhart’s genius was in recognizing when to act, andwhen to leave a process alone.



II-19 (72)

The Shewhart Cycle

The Shewhart cycle (PDCA) and the Deming cycle(PDSA) are very helpful procedures for improvement.This problem solving methodology can be used with orwithout a special cause being indicated by use of anystatistical tool.

What Shewhart actually contributed to this techniquewas a four stage product design cycle (with iterations)which Deming presented to the Japanese in 1951.

This design cycle was adapted as a general problemsolving technique by the Japanese. Deming in turn,modified the Japanese approach to a continualimprovement spiral called PDSA. Deming gave creditfor the technique to Shewhart, although there were oneor more intermediate Japanese contributors.



II-20 (73)

Dr. Genichi Taguchi( 1924 - )

Dr. Taguchi was the past director of the AmericanSupplier Institute, Inc. He is called the “father of qualityengineering.”

Awards:

Deming Prize, 1960Rockwell Award, 1986MITI Purple Ribbon Award, 1989Indigo Award, Japan, 1989ASME Medal, 1992

Books:

System of Experimental Design, 2 volumesIntroduction to Quality Engineering (1986)Off-line Quality Control (1979)


Quality is related to the financial loss to society causedby a product during its life cycle.



II-20 (74)

Dr. Genichi Taguchi (Continued)

Abstract:

Quality engineering techniques were developed byGenichi Taguchi in the 1950s. The techniques enabledengineers to develop products and processes in afraction of the time as required by conventionalengineering practices.

He made his first visit to the U.S. in the summer of 1980to assist American industry in the pursuit of quality. In1983, Ford and Xerox began to promote Taguchi’ssystem, both internally and among suppliers. Taguchi’ssystem was appealing because it was a completesystem that started with the product concept andcontinued into design and then into manufacturingoperations. It optimizes the design of products andprocesses in a cost-effective manner.



II-21 (75)


Taguchi’s plan takes a different view of product quality:

1. The evaluation of quality

Use the loss function and signal-to-noise ratio asways to evaluate the cost of not meeting thetarget value. Taguchi feels the quality lossincreases parabolically as the product strays froma single target value.

2. Improvement of quality and cost factors

Use statistical methods for system design,parameter design, and tolerance design of theproduct. The methods could include QFD, signalto noise characteristics, and DOE (usingorthogonal arrays).

3. Monitoring and maintaining quality

Reduce the variability of the production line.Insist on consistency from the floor. Takemeasurements of quality characteristics from thefloor and use the feedback.



II-21 (76)


Taguchi methods and other design of experimenttechniques have been described as tools that tell ushow to make something happen, whereas moststatistical methods tell us what has happened.

The concept of robust products is now being exploredin the design phase to reduce quality losses.Robustness derives from consistency. Robust productsand processes demonstrate more insensitivity to thosevariables that are either difficult to control or non-controllable. Building parts to target (nominal) is thekey to success. One should work relentlessly to achievedesigns that can be produced consistently and demandconsistency from the factory.


II. MANAGEMENT & LEADERSHIPQUALITY MANAGEMENT SYSTEMS

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Strategic Planning

A strategic plan should evolve from good soundstrategic thinking. Strategic thinking is the process ofconsidering the same key issues and concerns that theCEO and upper management use to help shape anddirect the organization's future.

The CEO and top management must decide what theywant their company to look like at some point in thefuture. Some of the variables, that comprise strategicthinking include:

C Current productsC Employee abilitiesC MarketsC CompetitorsC Suppliers

C Market segmentsC R & DC FacilitiesC The environment



II-22 (78)

Strategic Planning (Continued)

Some of the critical issues that would arise from thestrategic thinking process are:

C Time framesC Market share growthC Product catalogsC Investment needsC Customer concernsC Counters to external threatsC Quality

Planning includes an analysis and organization of keyitems, plus a logical implementation plan.



II-22 (79)

Strategic Planning (Continued)

A short outline of the strategic planning process shouldinclude the following:

C Develop a vision for the companyC Gather data on the environment in which it operatesC Assess corporate strengths and weaknessC Make assumptions about outside factorsC Establish appropriate goalsC Develop implementation stepsC Evaluate performance to goalsC Reevaluate the above steps for perpetual use

Strategic planning and decision making should enhancethe health of the business.



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Organizational Performance Goals

The organization performs many useful functions for itsstakeholders. Stakeholders are parties or groups thathave an interest in the welfare and operation of thecompany. These stakeholders include: stockholders,customers, suppliers, company management,employees and their families, the community andsociety.

Organizational performance and the related strategicgoals may be determined for:

C Short-term or long-term emphasisC ProfitC Cycle timesC Marketplace responseC Resources



II-23 (81)

Performance Goals (Continued)

The profit margin required to operate a business shouldbe optimized for all stakeholder requirements. Anoptimal level of stockholder dividends, investments,personnel costs, and such, must be maintained.

For maintaining competitiveness, a reduced productcycle time must be emphasized. This applies to bothnew product development and existing product lines.Reduced cycle times will affect such things as thecompany's inventory, WIP, waste, and efficiency.

The marketplace response is an organizationalperformance measure. The ability to respond quickly tocompetitor quality, technology, product designs, safetyfeatures, or field service are collectively very important.



II-24 (82)

Mission Statements

A company mission statement will address how thecompany will realize its vision and strategic goals. Avision statement describes a future state, perhaps 5 to10 years into the future. The company missionstatement will also have concise statements ofobjectives to be achieved.

A departmental mission statement concisely states howthe strategic quality goals (and needs) of theorganization will be implemented. Specific quantitativegoals must be included in the mission statement.

The quality professional must be able to supply orgather information to answer such questions as:

C What does the organization need?

C What tasks can the department do?

C How can the department help the organization?

The end result is a departmental mission statement foruse as an operating guide.



II-25 (83)

Quality Principles

The term “principles” means a basic foundation ofbeliefs, truths... upon which others are based. Onemethod for the leaders (the quality manager and others)of the organization to gain “the truth.” A collectivephilosophy will be developed and shared with theorganization.

A common vision for the company will be developed andshared. In general, the total quality effort will stresssome of the following points:

C Customer satisfaction is a keyC Defects must be preventedC Manufacturing assumes responsibility for qualityC The process must be controlledC Every one participates in qualityC Quality is designed into the productC TQ is a group activityC Respect for humanityC Adopt a revolutionary rate of quality improvement



II-25 (84)

Quality Policies

Quality policies are often developed by top managementin order to link together policies among all departments.A document explaining the quality policy,responsibilities, rationale, and expected benefits shouldbe explained to the company personnel.

Some sample quality policies follow:

C The only acceptable level of defects is zeroC We will meet or exceed customer expectationsC Defective products will not be shippedC We will not ship anything before its timeC We will build relationships with our customersC We will ensure that quality is never compromised



II-26 (85)

Strategic and Tactical Quality Goals

Strategic quality goals should be of such an importantnature that they will fit into the strategic business plan.All departments will have quality goals or sub-goals thatcome from the strategic business plan (which they thenneed resources to attack).

For instance, the basic information could be divided intotwo groups:

C Those of a strategic nature: items that cut acrossmany departments and/or are issues that areapplicable companywide.

C Secondly, tactical ones: the many detailedsubgoals that are derived from strategic qualitygoals.



II-26 (86)

Strategic Goals

C Company vision, mission statement, quality policyC Shared total quality philosophyC Effects of quality systems...ISO 9001, MBNQA, etc.C Emergence of new competitorsC Highlights of new quality techniques and toolsC Uncontrollable environmental factorsC Field intelligence on the competition

Tactical Goals

C Status of customer complaints, returnsC Results of customer surveys, mailingsC In-house scrap, rework, defective ratesC Supplier ratings, deliveriesC Others that are important to an organization



II-27 (87)

The Quality Department Role

The quality department has a basic function in theorganization: to coordinate the quality efforts.Historically, the organization needed the quality functionto fill a narrow inspection-oriented role.

While the needs of the company for a quality effort aremet, the ultimate needs of the customer, are still oftenoverlooked. The customer has become moresophisticated and demanding.

The quality assurance department needs to develop itsabilities to study process capabilities and make surethat key quality characteristics are under control.Purchasing, production, engineering, manufacturing,marketing, vendors, suppliers, and related staffs mustwork together to meet the quality requirements.



II-28 (88)

Quality Department Role (Cont’d)

Often a quality council or management steering teamprovides guidance and direction for the organization,the quality department will have responsibilities thatsupport the improvement activities of the otherdepartments in the organization. These activities mayinvolve data collection, data analysis, product research,team building, feedback analysis from customers,market research, training, cross-functional planning,manufacturing engineering, purchasing, packaging, etc.



II-28 (89)

Quality Department Role (Cont’d)

Companywide problems could include:

C Process operations quality requirementsC Customer specifications from marketingC Purchasing and supplier quality requirementsC R & D product designsC Team building issuesC Quality cost dataC Quality information systemsC Quality planning

The other 20% of the quality problems may be internal tothe quality department itself. These problems include:

C Variation in lab testsC Calibration of instruments and gagesC Sampling proceduresC Auditing proceduresC Inspection results



II-29 (90)

The Quality Plan

The overall strategic business planning follows astructured process. The process will define the purposeand goals for the company, and then add the followthrough necessary to reach those goals. Qualityplanning, at the highest level of the organization, willprovide more recognition and commitment to the qualityeffort. Quality planning, at the strategic level, can bedescribed as strategic quality planning.

For total quality to succeed, a structured process shouldbe used. According to Juran, the process shouldinclude:

C A quality council (steering committee)C Quality policiesC Strategic quality goalsC Deployment of quality goalsC Resources for controlC Measurement of performanceC Quality audits



II-29 (91)

Establish a Quality Council

The quality council is a steering committee for thequality movement. The quality council has theresponsibility for the growth, control, and effectivenessof total quality (TQ), as well as the incorporation of TQinto the strategic business plan. Some of the specifictasks of the quality council may include:

C Develop an educational moduleC Define quality objectivesC Refine the improvement strategyC Determine and report cost of quality dataC Develop and maintain an awareness program



II-30 (92)

Quality Policies

Quality policies are guidelines that the organization'semployees and management can follow. This is definedin ISO 9001:2000 (Element 5.3), which requires that topmanagement not only develop an appropriate qualitypolicy, but that it be communicated and understoodthroughout the organization. In general, quality policiesshould be concise and meaningful. A quality policyusually has statements that indicate a company willmeet or exceed customer expectations, delight thecustomer, etc.



II-30 (93)

Strategic Quality Goals

Strategic quality goals may gain priority and emphasisfrom the quality council, as well as feedback fromcustomers, top management or other organizationallevels. The goals, determined to be of a strategic nature,become a part of the strategic business plan. Thequality goals are specific, quantified, and scheduled.“We will achieve 95% ratings from all of our designatedcustomers by August, 2007” would fit a quality goaldefinition. Quality goals may be linked to productperformance, service performance, customersatisfaction, quality improvement, or cost of quality.

Having quality goals placed in the strategic businessplan, indicates to all employees that quality goals havespecial importance.



II-31 (94)

Deployment of Quality Goals

The word “deployment” means to spread out, to station,or to move in accordance with a plan. The qualitycouncil has the initial task of deploying (spreading out)the main strategic quality goals into bit-size pieces forthe lower levels of the organization. As each level of theorganization (function or team) receives its goals, it isexpected that they should review their mission,capabilities, and resources. If the function or teamrequires additional resources or training, those thingsmust be resolved to accomplish the required objective.



II-31 (95)

Resources for Control

For each goal, resources must be secured. The TQstructure must have a basic process for goal setting,goal deployment, training of personnel, goal tracking,goal evaluation and recognition of effort. Through tie-into the strategic business plan, this may indicate thatresources, in the form of additional staff help,equipment, or external staff, are required for a totalquality effort to succeed.

However, the quality manager has a vital role to play inthis structure. The resources, to aid in the total qualityeffort, may be coordinated directly by the qualitymanager. Thus, he/she can provide assistance andguidance.



II-32 (96)

Measurement of Performance

A system is in place when the quality goals containedinside the strategic business plan are agreed upon,assigned to various sections (or teams) in theorganization, and funded. The measurement ofperformance must then be addressed. Each level of theorganization will regularly review their progress againstthe goals. This means that the senior executives withquality goals are measured, just as they are measuredagainst earnings per share. At different levels of theorganization, reviews are held to measure qualityprogress. These quality reviews should be held inconjunction with the reviews of other strategic goals.



II-32 (97)

Quality Audits

The quality audit is a necessary step in the process toprovide independent and unbiased information to all ofthose who have a need to know. Top management,operating departments, and related staffs must knowwhere the system stands in relation to a performancemeasure. The scope of an audit will be determined bythe guidelines set forth by the quality council.

Quality audits can be conducted through internal teams,outside auditors, upper managers, or by the president.



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STOCKHOLDERS OR OWNERS

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MANAGEMENT AND EMPLOYEES

Stakeholder Identification

Businesses have many stakeholders includingstockholders, customers, suppliers, management,employees (and their families), the community, andsociety. Each stakeholder has unique relationships withthe business. some typical business – stakeholderrelationships are shown below:

SOCIETY

INTERNAL COMPANY

PROCESSES



II-34 (99)

Stakeholder Analysis

A project with high impact will bring about majorchanges to a system or to the entire company. Thechange can affect various people inside and outside ofthe system. Major resistance to the change candevelop. As part of the define process, attempts toremove or reduce the resistance must be made.Stakeholders can be identified as:

C Managers of the processC People in the processC Upstream people in the processC Downstream people in the processC CustomersC SuppliersC Financial areas

A communication plan should involve the stakeholdersand identify, on a scale, the level of commitment orresistance that the stakeholder is perceived to have.



II-36 (100)

Performance Measurement

Performance goals and corresponding measurementsare often established in the areas of:

C ProfitC Cycle timesC Marketplace responseC Resources

Measurement methods and reporting units must bedefined for each goal.



II-36 (101)

Profit

C Stockholder valueC Community comparisonC Capital investmentC Return on investmentC Personnel costsC Sales dollars

Profit may be short-term (6 months or less) or long-term(2 years or more).

Cycle Times

C Existing cycle timesC External benchmarksC Internal benchmarksC Reduction in cycle times

Ten fold reductions in cycle times are possible.



II-36 (102)

Marketplace Response

C Analysis of returnsC Customer lossesC Product development timesC Courtesy ratingsC Customer retention ratingsC Customer survey results

Resources

C Number of improvement projectsC Reduction in variationC Return on capital investedC Cost of quality goalsC Process capability studiesC Percent defects



II-37 (103)

Benchmarking

Benchmarking is the process of comparing the currentproject, methods, or processes with the best practicesand using this information to drive improvement ofoverall company performance. The standard forcomparison may be a competitor within the industry but,quite often, is found in unrelated business segments.



II-37 (104)

Process Benchmarking

Process benchmarking focuses on discrete workprocesses and operating systems, such as the customercomplaint process, the billing process, or the strategicplanning process. This form of benchmarking seeks toidentify the most effective operating practices frommany companies that perform similar work functions.

Performance Benchmarking

Performance benchmarking enables managers toassess their competitive positions through product andservice comparisons. This form of benchmarkingusually focuses on elements of price, technical quality,ancillary product or service features, speed, reliability,and other performance characteristics.



II-37 (105)

Project Benchmarking

Benchmarking of project management is easier thanmany business processes, because of the opportunitiesfor selection outside of the group of direct competitors.Areas such as new product introduction, construction,or new services are activities common to many types oforganizations. The projects will share the sameconstraint factors of time, costs, resources, andperformance. Project management benchmarking isuseful in selecting new techniques for planning,scheduling, and controlling the project.

Strategic Benchmarking

In general terms, strategic benchmarking examines howcompanies compete. Strategic benchmarking is seldomindustry-focused. It moves across industries seeking toidentify the winning strategies that have enabled high-performing companies to be successful in theirmarketplaces.



II-38 (106)

Benchmarking (Continued)

Benchmarking as a continuous improvement process inwhich a company. Compares its own performanceagainst:

C Best in class company performanceC Companies recognized as industry leadersC The company’s toughest competitorsC Any known superior process

C Determines how that performance was achieved C Uses that information to improveC Achieves the benchmarked performanceC Continually repeats the process



II-38 (107)

Time Time

Typical Benchmark Breakthrough Benchmark

Benchmarking (Continued)

Shown below is a comparison between a typical and abreakthrough benchmark approach.

It should be noted that organizations often choosebenchmarking partners who are not best-in-class,because they have identified the wrong partner orsimply picked someone who is handy.



II-39 (108)

Benchmarking Sequences

Benchmarking activities often follow the followingsequence:

C Determine current practices

C Select the problem areaC Identify key performance factorsC Understand your own processesC Understand the processes of othersC Select criteria based on needs and priorities

C Identify best practices

C Measure the performance within the organizationC Determine the leader(s) in the criteria areasC Find an internal or external benchmark

C Analyze best practices

C Visit the organization as a benchmark partnerC Collect benchmark information and dataC Compare current practices with the benchmarkC Note potential improvement areas



II-39 (109)

Benchmarking Sequences (Continued)

C Model best practices

C Drive changes to advance performance C Extend performance breakthroughs C Use the new information in decision makingC Share results with the benchmark partnerC Seek other benchmarks for further improvement

C Repeat the cycle

Juran presents the following examples of benchmarks(slightly modified) in an advancing order of attainment:

C The customer specificationC The actual customer desireC The current competitionC The best in related industriesC The best in the world



II-40 (110)

Project Management

A project is a series of activities and tasks with aspecified objective, starting and ending dates andresources. Resources consumed by the project includetime, money, people, and equipment. The elements ofproject management are:

C Planning - deciding what to doC Scheduling - deciding when to do itC Controlling - ensuring the desired results

Project management includes project planning andimplementation to achieve:

C Specified goals and objectivesC At the desired performance or technology levelC Within the time and cost constraintsC While utilizing the allocated resources

Well executed project plans meet all of the abovecriteria. Crashing programs to return a project to thespecified time frame is done at the expense of highercosts and resource usage. Performance is measured onresults, not effort.



II-40 (111)

Time Lines

The project time line is the most visible yardstick formeasurement of project performance. The unit ofmeasurement is time in minutes, hours, days, weeks,months, or years, and is readily understood by allparticipants on a project. The overall project hasdefinite starting and ending dates, both planned andattained.

Tasks within the project are assigned starting andending times. As a performance tool, the project timeline is updated with actual completion dates andadjustments made to compensate for early or lateperformance. From a quality viewpoint, both early andlate projects have the opportunity for poor qualitycompared to the project completed on schedule.



II-41 (112)

Resources

Allocation of resources is part of the planning process.As each project activity is broken into smaller tasks, theresources are assigned to complete those tasks.Resource conflicts are resolved according to thecircumstances in which they occur. Conflicts betweentwo different projects for resources can be settled onthe basis of priority of the project.

Resource conflicts within tasks of a project are decidedby the impact on the project completion date. If onetask has available slack time, the timing of the need forthe resource can often be adjusted.

Resource leveling is used to smooth peaks and valleysin the demand for resources and spread the use moreevenly over time.

While monitoring both time and resource use during theproject is important, the more significant performancemeasures of the project are the project completion dateand the total costs. This is the “bottom line” for theproject performance.



II-42 (113)

Methodology

Methods for planning, monitoring, and controllingprojects range from manual techniques to computerprograms.

Advantages of manual project management methodsinclude:

C Ease of use and low costC Best for monitoring schedules and timing of eventsC A hands-on feel for the project statusC Can be customized to the specific project needsC Training requirements are minimal

Disadvantages of manual project management methodsinclude:

C May not be transportableC Project status is only available at one siteC Complex projects may be difficult to displayC Activities and resource conflicts may be missedC Requires manual summarizing of the informationC It is harder to analyze final project results



II-42 (114)

Methodology (Continued)

Advantages of computer/automated projectmanagement methods include:

C Able to model alternate optionsC Presents the information in a variety of formatsC Various levels of detail can be displayedC Critical path, slack times, etc. are automaticC Project status reports are easier to generateC Some data collection activities can be automated

Disadvantages of computer/automated projectmanagement methods include:

C High learning curve for the userC Higher initial costsC Data entry and updating can be time consuming C Poor data will be accepted by the computerC The manager may lose touch with the projectC The environment may be computer friendly



II-43 (115)

Network Planning Rules

C Before an activity may begin, all activities precedingit must be completed.

C Arrows imply logical precedence only. The lengthand compass direction of the arrows have nomeaning.

C Any two events may be directly connected by onlyone activity.

C Event numbers must be unique.

C The network must start at a single event, and end ata single event.

Common applications of network planning include theProgram Evaluation and Review Technique (PERT), theCritical Path Method (CPM), and Gantt charts.



II-43 (116)

PERT

The program evaluation and review technique (PERT)requirements are:

C All individual project tasks must be included.

C Activities must be sequenced to determine thecritical path.

C Time estimates must be made for each activity inthe network, and stated as three values: optimistic,most likely, and pessimistic elapsed times.

C The critical path and slack times for the project arecalculated. The critical path is the sequence oftasks which require the greatest expected time. Theslack time, S, for an event is the latest date an eventcan occur without extending the project (TL) minusthe earliest date an event can occur (TE).

S = TL - TE

For events on the critical path, TL = TE, and S = 0.



II-44 (117)

PERT (Continued)

Advantages of using PERT include:

C The planning required to identify the taskinformation for the network and the critical pathanalysis can identify interrelationships betweentasks and problem areas.

C The probability of achieving the project deadlinescan be determined, and by development ofalternative plans, the likelihood of meeting thecompletion date is improved.

C Changes in the project can be evaluated todetermine their effects.

C A large amount of project data can be organized andpresented in a diagram for use in decision making.

C PERT can be used on unique, non-repetitiveprojects.



II-44 (118)

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PERT (Continued)

Disadvantages of using PERT include:

C The complexity of PERT increases implementationproblems.

C More data is required as network inputs.

Each starting or ending point for activities on a PERTchart is an event, and is denoted as a circle with anevent number inside. Events are connected by arrowswith a number indicating the time duration required togo between events. An event at the start of an arrowmust be completed before the event at the end of thearrow may begin. The expected time between events, teis given by:

Where: to is optimistic time, tm is most likely time, tp ispessimistic time.



II-45 (119)

PERT (Continued)

An example of a PERT chart for a company seeking ISO9001 certification is shown in the Primer. Circlesrepresent the start and end of each task. The numberswithin the circles identify the events. The arrowsrepresent tasks and the numbers along the arrows arethe task durations in weeks.



II-46 (120)

Critical Path Method (CPM)

The critical path method (CPM) is activity oriented.Unique features of CPM include:

C The emphasis is on activities

C The time and cost factors for each activity aredetermined

C Only activities on the critical path are considered

C Activities with the lowest crash cost are selectedfirst

C As an activity is crashed, it is possible for a newcritical path to develop

To complete the project in a shorter period, the activitywith the lowest incremental cost per time saved iscrashed first. The critical path is recalculated.



II-46 (121)

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CPM Example

The critical path is indicated by the thicker arrows, alongpath A-C-F-I-K-L-M.

TASK ACTIVITY DURATIONweeks

COST$

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0 ISO 9001 Certification normal crash normal crash CRASHA Planning 4 3 2000 3000 1000B Select Registrar 4 3 1000 1200 200C Write Procedures 8 6 12000 15000 1500D Contact Consultant 3 1 500 700 100E Schedule Audit 6 5 200 1000 800F Write Quality Manual 4 3 800 1200 400G Consultant Advising 12 9 9600 14400 1600H Send Manual to Auditor 1 1 100 100 -I Perform Training 6 4 9000 12000 1500J Auditor Review Manual 4 3 1000 1250 250K Internal Audits 2 1 600 750 150L ISO Audit 1 1 10000 10000 -M Corrective Action 3 2 1600 2000 40010 Certification Milestone



II-48 (122)

CPM Example (Continued)

The Primer shows the priority arrangement of crashingCPM activities, and their costs. The CPM time-costtrade-off represented graphically:

CPM Time-Cost Trade-off Example

Crashing activities beyond the activity I, increases costwithout further reduction in time.



II-49 (123)

Gantt Charts (Bar Charts)

Gantt charts (bar charts) display activities or events asa function of time. Each activity is shown as ahorizontal bar with ends positioned at the starting andending dates for the activity.

Advantages of Gantt Charts include:

C The charts are easy to understandC Each bar represents a single activityC It is simple to change the chartC The chart can be constructed with minimal dataC Program task progress versus date is shown

Disadvantages of Gantt Charts include:

C They do not show interdependencies of activitiesC The effects of early or late activities are not shown

(Note to rotate the chart on the following page, press:<Shft><Ctrl>+ in Adobe Reader 7)

(To return the orientation to portrait, press:<Shft><Ctrl>- in Adobe Reader 7)



II-50 (124)

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II-51 (125)

Quality Information Systems

A quality information system (QIS) is an organizedmethod of collecting, storing, analyzing and reportinginformation on quality to assist decision makers at alllevels. The purpose of an effective QIS is to achievetimely corrective action. The following is a limitedoutline of QIS.

I. Introduction and scope: In the quality field, the onlyproduct is information.

II. Plan the quality information system:

C Define and publish the scope and objectivesC Define outputs and their usesC Identify data inputsC Flow chart the systemC Determine processing/analysis requirementsC Document the systemC Plan the training required for system usage



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Quality Information Systems (Continued)

III. How a quality information system works:

C Data can be obtained from:

C Market researchC Product design evaluation and test dataC Purchased parts and materialsC Process dataC Final inspection dataC Field performance informationC Audit results

C Internal process information:

C Is often the principle source of QIS dataC Collected by quality information equipmentC Adjustments can be manual or automatic

C Data storage can be:

C On formsC In filesC In a computer memoryC In computer external storage system



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C Data can be analyzed or processed by:

C SortingC CalculationsC Manipulation

C Quality data is often displayed in the followingways:

C Historical (where we've been)C Current (where we are)C By simulation (for predict)

C The results of the quality analysis should bereported to management for decision making.



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IV. Considerations when establishing a qualityinformation system:

C Determine the need for quality feedback:

C What is inspected?C Did the process or product meet specifications?C What were the statistically significant variations?

C Evaluate the need for an information system usinggood management rules:

C Compare cost of data required with the value ofthe information obtainable

C Determine the type of system required:

C ManualC Computer (offering faster retrieval and analysis)C Combination



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Quality Information Systems (Continued)V.For computerized systems, consider the following:

C Software is the instruction to the computer to:

C Store C Retrieve C AnalyzeC Report information

C Software is QIS documentation including:

C Procedures and formsC Design and data packagesC Logistics and training packages

C Computer system availability can be via:

C Central systems located elsewhereC Batch processed internal systemsC On-line internal systemsC Combinations

C Good form design provides:

C Easier readability, usage, and filingC Error avoidanceC Economy - faster input and sorting



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VI. For continued use, a quality information systemshould:

C Have data inputs that aretimely and accurate

C Have systems that allow for security and retrieval

C Provide data analysis that is valid and reliable

C Be audited periodically

C Provide reports and outputs that are:

C Accurate (as to facts)C Timely (for decision making)C Valid (as to information portrayal)C Reliable (must meet user needs)

C Generate report formats which will typically:

C Show trends (via charts or graphs)C Compare performance (to a desired standard)C Compare information (to other bases or indexes)C Identify the vital few problems (Pareto)C Highlight exceptions to the desired results


II. MANAGEMENT & LEADERSHIPASQ CODE OF ETHICS

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ASQ Code of Ethics

Fundamental Principles

ASQ requires its members and certification holders toconduct themselves ethically by:

I. Being honest and impartial in serving the public,their employers, customers and clients.

II. Striving to increase the competence and prestige ofthe quality profession, and

III. Using their knowledge and skill for theenhancement of human welfare.

Relations with the Public

Article 1 - Hold paramount the safety, health, andwelfare of the public in the performance of theirprofessional duties.

Relations With Employers and Clients

Article 2 - Perform services only in their areas ofcompetence.



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ASQ Code of Ethics (Continued)

Article 3 - Continue their professional developmentthroughout their careers and provide opportunities forthe professional and ethical development of others.

Article 4 - Act in a professional manner in dealingswith ASQ staff and each employer, customer, or client.

Article 5 - Act as faithful agents or trustees and avoidconflict of interest and the appearance of conflicts ofinterest.

Relations With Peers

Article 6 - Build their professional reputation on themerit of their services and not compete unfairly withothers.

Article 7 - Assure that credit for the work of others isgiven to those to whom it is due.



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Professional Conduct and Ethics

A professional code of ethics guides individuals towardactions that produce the greatest good for all. A qualityprofessional must possess high standards of ethicalconduct. ASQ’s Code of Ethics is a guide for achievingthis objective. Professional ethics take into account:

C Relations between professionals and societyC Relations between professionals and their clientsC Relations among professionalsC Relations between an employer and employee

The ASQ certification programs are established toupgrade the technical knowledge and competence ofprofessionals through an examination andrecertification process. This is one way to addressArticle 3 of the ASQ Code.



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Professional Conduct and Ethics (Cont’d)

Quality professionals should be aware of situations inwhich a conflict of interest could develop. Examples ofpotential conflicts of interest include:

C Providing recommendations on the purchase ofproducts while owning stock in that company.

C Presenting results of an ISO 9001 pre-assessmentto a client with a recommendation to use consultingservices provided by your company.

C Participating in the awarding of a contract to aprivate company founded by a close family member.

A professional cannot expect any code of ethics to becomplete, consistent, and correct for all situations. Aquality professional must also develop and use aninternal sense of ethics to resolve the conflicts that arepresented in their personal and professional lives.


II. MANAGEMENT & LEADERSHIPLEADERSHIP PRINCIPLES

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Leadership Skills and Conduct

Traditionally, leadership pertains, in great part, to thevertical chain of command. However, quality managersand engineers may make their greatest contributions byestablishing and maintaining good relations withpersonnel outside their direct chain of command.

There are numerous attributes with which qualityprofessionals should possess if they are to be trulysuccessful. The following skills are essential:

C Motivating subordinates. The quality professionalmust inspire and encourage employees, reconcilingtheir individual needs with the objectives of theorganization.

C Developing and maintaining peer relationships. Theability of the quality professional to maintain goodpeer relations usually determines theireffectiveness.



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Leadership Skills and Conduct (Cont’d)

C Establishing networks for the dissemination ofinformation. Quality professionals spend a largeportion of their time on activities devoted to thetransmission of information.

C Carrying out negotiations. Quality managers andengineers will also spend a great deal of time innegotiations; they work with customers inidentifying and meeting their needs, negotiatequality problems, work with marketing, etc.

C Resolving conflicts. Although most qualityprofessionals are in a decision making capacity,they also must handle disputes.

C Securing and allocating resources. To ensure anadequate operating budget, quality professionalsmust not only be negotiators, but they must alsohave good general knowledge of the operatingexpenses of their departments.



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C Making decisions. The essential attribute that asuccessful quality professional must have is theability to use good judgment to make decisions.

C Making effective use of time. Time is one of themost precious commodities of a qualityprofessional. Time thieves include:

C IndecisionC Failure to delegateC Lack of confidence in the organizationC Devoting time to trivial mattersC Permitting a desire to weaken a principal purposeC Dwelling on the negative rather than the positive



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The qualities that make a successful leader are oftendifficult to measure. There is no complete list ofleadership attributes upon which authorities completelyagree. Some good fundamental attributes are listedbelow:

C CongenialityC CreativityC PatienceC FairnessC PersistenceC HonestyC Decisiveness

C Communication skillsC ResourcefulnessC Strength of characterC Knowledge and wisdomC Good healthC CompassionC Enthusiasm

Quality professionals have discovered that in order toeffectively motivate others, they must use a variety ofleadership styles. Different styles must be used withemployees at different times, depending on theconditions and circumstances.



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Leadership Principles

The phrase best used to collectively describe howquality goals and efficiencies are best obtained is“through the processes of leadership.” Leadership isprimarily a human relations activity. It may be definedas the art of motivating, guiding, and directing people.

Motivation

Certainly the most challenging managementresponsibility is how to both sustain and increaseinternal motivation in the work group. The qualityprofessional should recognize that people do havecertain needs in common, which may often be met inbasically the same way.

Communication

Important factors present in motivating subordinates areverbal and written communication skills.



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Team Introduction

A participative style of management is the bestapproach to ensure employee involvement in theimprovement process. Many workers have highereducational backgrounds and are eager to participate inthe decision making process that affects them. There isno better way of motivating employees than to providethem with challenging jobs which make use of theirtalents and abilities.

Improvement teams:

C Can usually tackle larger issues than individualsworking alone

C Can build a fuller understanding of the processneeding improvement

C Can have immediate access to the skills andknowledge of all members

C Can rely on the support and cooperation of teammembers



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Team Empowerment

Team empowerment is derived from the organization’smanagement authority. A team is empowered by virtueof that power granted to it by management. A teamcharter is a very useful tool for helping a team andmanagement understand just exactly what the team isempowered to do.



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Team Objectives

The team process can be a highly effective, people-building, potential-releasing, goal-achieving socialsystem that is characterized by:

C A climate of high supportC An open communication processC Organizational goal achievementC Creative problem-solvingC Individual achievementC Commitment

The fundamental purpose of establishing teams is toimprove the internal and external efficiencies of thecompany. If teams are properly functioning, they will:

C Improve employee moraleC Remove areas of conflictC Develop creative skills of membersC Improve communication skills of membersC Develop problem solving techniquesC Improve attitudes of all partiesC Indicate to members that management will listenC Demonstrate that employees have good ideasC Improve management/employee relationships



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Team Objectives (Continued)

Listed below are some of the reasons that teams havebeen successful:

C If management has sanctioned teams in thecompany, this means that management will be moreapt to listen to employees and believe they haveideas worthy of implementation.

C The team procedure allows all team members tocommunicate and exercise creative expression.

C The concept of teams is supported by modernmotivational theories:

C Maslow’s higher level of human needs

C McGregor’s Theory Y, which recognizes the worthof an individual

C Herzberg’s theory that true motivation is found inthe work itself



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Company Team Benefits

Usually team members have diverse skills andexperience and may represent various departments andfunctions within the organization. What they share incommon is their involvement in the problem to beaddressed. The benefits of a team approach arenumerous. The most significant gains are usuallyachieved by teams – groups of individuals pooling theirtalents and expertise.



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Team Member Benefits

Teamwork offers some obvious benefits to teammembers, including:

C An opportunity for understanding of work issuesC A chance to be creative and share ideasC The opportunity to forge stronger relationshipsC The opportunity to learn new skillsC A chance to work on a project with full supportC The satisfaction of solving a problem

Team members must:

C Have a reason to work togetherC Accept an interdependent relationshipC Commit to team values



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Team Building Activities

Three key characteristics of effective team building aremutual trust, respect, and support. Team members needto be coached in the need to trust and support eachother. Support involves actively keeping an eye on theother team members and demonstrating a willingness tohelp each other out when help is needed--even when itmight not be requested. Team members encourageeach other to stretch beyond their comfort zone byoffering advice or assistance when asked or when it isobvious that the fellow team member needs it.



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Team Resources

The development of productive teams will useconsiderable resources. Resources are time, talents,money, information, and materials. Management mustoptimize the resources available to teams. The teamcharter is the best place to establish the team’sexpectations concerning available resources.

The Project Charter

A team or project charter will help:

C To eliminate any confusionC To define the subject boundariesC To identify areas which should not be addressedC To identify the deliverable productC To provide a basis for team goal setting



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Management Support

Management must give more than passive team support.This means that management, and especially mid-management, must be educated to the degree that theyare enthusiastic about the team concept. In order forteams to be successful, management must recognizethat there will be additional work created by their efforts.Leaders, facilitators, and team members should bethoroughly trained.

Management supports the team process by:

C Ensuring a constancy of purposeC Reinforcing positive resultsC Sharing business resultsC Giving people a sense of missionC Developing a realistic and integrated planC Providing direction and support



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Types of Teams

The following types of teams are used by industriesthroughout the world today:

Six Sigma Teams

The structure and functional roles of six sigma teamsclosely follow the description of project and ad hocteams, with the addition of black belt support. Problemsolving techniques, ranging from basic to sophisticated,are required.

Improvement Teams

A group belonging to any department chooses to solvea quality/productivity problem. It will continue until areasonable solution is found and implemented. Theproblem may be management selected, but the solutionis team directed. For a process improvement team,employees may be drawn from more than onedepartment.



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Project Teams/Ad Hoc Teams

Members are selected based on their experience anddirected by management to look into specific areas suchas the modernization of a piece of equipment or solutionto a customer complaint. These teams are generally adhoc and disband upon the completion of theirassignments.

Cross Functional Teams

Cross functional teams are made up of individuals whorepresent different departments or functional areas inthe organization. Individuals who represent adepartment or functional area should be subject matterexperts. That is, they should be very knowledgeableabout the practices of their functional areas.



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Self Directed Teams

This type of team operates with minimal day-to-daydirection from management. Self directed teams areasked to accomplish objectives within time frames thatare truly stretch objectives. Management must give theteam the maximum latitude possible for achieving theirobjectives.

Quality Circles

The concept of circles originated in Japan after WW II.They were so successful in Japan that many managersin the United States tried to duplicate them. The circleis a means of allowing and encouraging people on theproduction floor to participate in decisions that willimprove quality and/or reduce manufacturing costs.Department members voluntarily participate to improvedepartmental performance. Since membership isvoluntary, people are highly motivated to continue theimprovement process.



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Quality Teams

The quality circle approach has been on the decline inthe U.S. for some time. The fundamental purpose ofestablishing quality teams is to improve the internalefficiencies of the company and both internal andexternal products and service quality. This is donethrough the efforts of the team members to improvequality, methods, and/or productivity.

Natural Work Teams

Natural work team leadership is usually given to the areasupervisor. Members of teams come from thesupervisor’s work force. Outside members, fromspecialist organizations, can be included in themembership, either as active members or ascontributing guests. Often, a facilitator is an importantperson in this team’s organizational structure. He orshe is specifically trained to coordinate multiple teamactivities, oversee team progress, document results, andtrain team members.



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Synopsis of Team ApplicationsTeam Type Structure Best Applications

ImprovementTeams

May be 8 to 10members from asingle department

Can work on quality or productivityissues. A process improvement teamcan consist of multi-departmentmembership and focus on processflow and product issues.

Quality Teams May be 8 to 10members from asingle department

May initially work on quality topics oroverall department performance. Canevolve into self directed teams.

Project Teams Can have broad orspecific memberselection and mayconsist of all orpart management.

Works on specific projects such as theinstallation of a conveyor system. Canalso focus on material related itemslike an improved inventory controlsystem. Usually disbands upon thecompletion of a project.

Six SigmaTeams

Generally 8 to 12members withblack belt ormaster black beltsupport

Works on specific process orcustomer based projects ofimportance. Usually disbands uponproject completion.

CrossFunctionalTeams

8 to 12 membersfrom differentareas,departments, ordisciplines

Members are carefully selected.Knowledgeable people are required.Very similar to project teams. Tends todeal more with policies, practices andoperations.

Self DirectedTeams

6 to 15 members. Generally anatural work areateam and mayneed staff support

Requires considerable training andexposure. Can be given objectives ordevelop their own. Some companiesselect people with co-operative skillsto help with success.



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The Leader Role

Some teams have both leaders and facilitators. This iscommon for manufacturing line teams. As a generalrule, the team leader focuses on the team product (theresults) and the facilitator is most concerned with theteam process. The team leader will:

C Provide direction and suggest assignmentsC Act as a communication hub and liaisonC Handle administrative detailsC Ensure that individual needs are consideredC Recommends agendas and conducts meetingsC Assess group progress to plan and initiate actionC Take the steps necessary to ensure successC Possess an ability to encourage participationC Be genuinely concerned about peopleC Be encouraging and supportiveC Be accepting and tolerant of mistakesC Work with, not over participantsC Stick to the task at handC Be a good listener



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The Team Member Role

Each team member is responsible for:

C Participating in training to become effective C Attending team meetings, as requiredC Completing assignments between meetingsC Participating actively during meetingsC Encouraging participation by other team membersC Benefitting from the expertise of othersC Applying the steps of the improvement process



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The Recorder Role

The recorder/secretary is normally a full-fledged teammember. The recorder maintains the team’s minutesand agendas. The recorder also coordinates thepreparation and distribution of letters, reports, and otherdocuments. Often, this duty is rotated.

The Timekeeper Role

The timekeeper’s role is an optional responsibility. Thisfunction sometimes becomes the responsibility of thefacilitator. The timekeeper:

C Advises team of the remaining meeting timeC Enforces any time “norms” of the team



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Initial Project Selection

Many improvement and self directed teams have thelatitude to select their own projects. The followingfactors should be considered when selecting an initialproject:

C It should have appeal to members and management

C It should be fairly simple - but not trivial

C It should show some quick benefit (3/4 months)

C It should be within the group’s control

C It should consider time and resource constraints

C The two major activities are project resolution andlearning teamwork.

Management may define the project.



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Selecting Team Members

When selecting a team, upper management identifiesthose parts of the organization that are associated mostclosely with the problem. There are four places to look:

C Where the problem is observedC Where causes of the problem might be foundC Among those with special knowledgeC In areas that can help develop the remedy

Often a cross functional team is assembled toaccomplish significant results in a short period of time.The best and brightest people the organization has tooffer should be chosen.



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Team Size

A team can consist of members from only one area orcan be made up of a group of representatives fromdifferent parts of the organization. It is usuallyimpractical to include every person who could beinvolved. Conventional wisdom is that teams over 20people become too unwieldy and lose the activeparticipation of all team members. Teams of 4 people orless may not generate enough ideas.

Team Diversity

To achieve optimum performance a team often needsdiversity in the orientation of its individual teammembers. Some team members are needed who areprimarily oriented towards task and target dateaccomplishment. Other team members will be neededwho hold process, planning, organization, and methodsin the highest regard. Teams also need members whonurture, encourage, and communicate well. Teams willcertainly need some members who are creative andinnovative.



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Typical Team Operating Guidelines

Teamagenda

Who sets? When published? Inputinvited?, etc. Recorder to publish?

Attendance Excused absences only? How are latecomers handled? What membership isrequired to conduct business?

Meetings Time, frequency, place?

Decisionprocess

Consensus, collaborative, majority?Can one person remove an item?

Minutes and reports

Select a recorder. How are minutesapproved? Where posted? Who types?How distributed? Is the recorder avolunteer?

Leader role How defined? How selected?Expectations?

Behavioralnorms

Interruptions; beepers, radios, and cellphones off; no smoking; breaks calledat members discretion; empatheticlistening; constructive feedback.



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Team Operating Guidelines (Continued)

Confi-dentiality

What can be discussed outside thegroup?

Guests How invited? How excused?

Audits How frequent? Who is responsible?

Facilitator How selected? Expectations? How willthis role differ from the leader?

Conflict Expected? How managed?

Recom-mendations

How initiated? How routed? Who isinformed?

Commit-ments

Follow through on commitments,analysis, word processing, etc.



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Team Meeting Structure

Any effective team meeting needs logical structure.Listed below is an example format.

1. Develop an agenda2. Distribute the agenda in advance3. Start on time4. Appoint a recorder to record minutes5. Use visual aids liberally6. Reinforce participation and consensus7. Summarize and repeat key points throughout8. Put unfinished items on next agenda9. Review assignments and completion dates

10. Finish on time11. Distribute minutes promptly12. Critique meeting effectiveness periodically



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Sample Meeting Forms

Some simplified team meeting forms are shown in thePrimer.



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Team StagesMost teams go through four development stages beforethey become productive: forming, storming, norming,and performing.

Forming

Forming is the beginning of team life. Expectations areunclear. Members test the water. Interactions aresuperficial. This is the honeymoon stage. When a teamforms, its members typically start out by exploring theboundaries of acceptable group behavior. Memberslooks to the team leader (or facilitator) for guidance asto his or her role and responsibilities.

Storming

The second phase consists of conflict and resistance tothe group’s task and structure. There are healthy andunhealthy types of storming. Conflict often occurs inthe following major areas: authority issues, vision andvalues dissonance, and personality and culturaldifferences. However, if dealt with appropriately, thesestumbling blocks can be turned into performance later.This is the most difficult stage for any team to workthrough. Teams realize feel overwhelmed. They wantthe project to move forward but are not yet proficient atteam improvement skills.



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Team Stages (Continued)

Norming

During the third phase, a sense of group cohesiondevelops. Team members use more energy on datacollection and analysis as they begin to test theoriesand identify root causes. Members accept other teammembers and develop norms for resolving conflicts,making decisions, and completing assignments.Conflicts are no longer as frequent and no longer throwthe team off course. Scheduled team meetings give asense of predictability and orientation. Norming iscultivated through team-building events and activities.Norming is a necessary transition stage. A team can’tperform if it doesn’t norm.

Performing

This is the payoff stage. The group has developed itsrelationships, structure, and purpose. The team beginsto tackle the tasks at hand. The team begins to workeffectively and cohesively. During this stage, the teammay still have its ups and downs. Occasionally, feelingsthat surfaced during the storming stage may recur.



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Time

FormingMembers are:inexperiencedexcitedanxiousproud

StormingMembers:have confrontationthink individuallyare learning roleshave divided loyalties

NormingMembers:cooperatetalk things outfocus on objectiveshave fewer conflicts

PerformingMembers:show maturityfocus on the processachieve goalsoperate smoothly

Team Stages (Continued)

Adjourning

At the end of some projects the team disbands. Thisstep is called adjourning to rhyme with the four otherteam stages. Adjourning is also a very commonpractice for project teams, and ad hoc teams.



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Team Life Cycle Characteristics

Shown below is another representation of teamdevelopment stages.

Build Phase (Forming/Storming)

C Group will be uncertainC Group lacks cohesivenessC Group will not easily develop consensusC Leader exhibits a high task/ high relationship style



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Team Life Cycle Characteristics (Cont’d)

Develop Phase (Norming)

C Task related work is assumed by the groupC The group must involve non-participating membersC Leader exhibits a low task/high relationship styleC Team focuses on tasks, and relationships

Optimize Phase (Performing)

C Members prioritize and perform tasksC Members work out decisions in a caring wayC Conflict is accepted, but cooperation is preferredC Team leader is a delegatorC Team exhibits a high task/high relationship style



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Well Functioning Teams

Environmental Factors

C Team members meet regularlyC Adequate skills and authority levels are presentC The team has management and worker support

Goal Factors

C Team members help set objectivesC Objectives are understood by all membersC Objectives are set and met realistically

Role Factors

C There is strong leadership with clear responsibilitiesC Roles are understood and supported by allC Members work as a team



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Well Functioning Teams (Continued)

Relationship Factors

C There is a team identityC There is an emphasis on conflict resolutionC Conflict is open; there is growth and learningC Team members support each otherC Members enjoy each other

Process Factors

C Decisions are made by consensusC Meetings are efficient and task orientedC All members participate in discussions and meetingsC Members are kept informed C Minutes are keptC There is feedback regarding performanceC Members listen well



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Team OppositionIn spite of the potential benefits, some people areskeptical of the long-term success of teams. Thesepeople point out that the traditional style of managementin the typical American industry carries with it suchmomentum that the team approach will have littleappreciable long-term effect.

Additional Team Problem AreasThe following team problem areas must be addressed byleaders, facilitators, sponsors, and management:

C There is waning management support. C There is inadequate meeting documentationC There is inadequate time or training allottedC Exposed problems may threaten mid-managementC Facilitators and leaders controversies can develop C Good facilitation skills may be hard to findC Suggestion programs may add complications C Labor unions may be resistance to team involvementC Teams may tackle problems outside their areasC Crisis management creates team scheduling problemsC A company’s reward system may be inconsistentC Unproductive competition and conflict may occur C Idea evaluation occurs too soonC Facts and opinions are not distinguishedC There is a failure to assign member responsibilities


II. MANAGEMENT & LEADERSHIPFACILITATION TECHNIQUES

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Team Facilitation

Many companies find facilitators useful both for teamstart-ups and for a variety of other team arrangements.

Facilitators are useful in assisting a group in thefollowing ways:

C Identifying members of the group that need trainingC Avoiding team impassesC Providing feedback on group effectivenessC Summarizing points made by the groupC Balancing group member activityC Helping to secure resources that the team needsC Providing an outside neutral perspectiveC Clarifying points of view on issuesC Keeping the team on track with the processC Helping with interpersonal difficulties that may ariseC Focusing on progressC Assessing the change processC Assessing cultural barriers (attitudes, personalities)C Assessing group accomplishmentsC Asking for feelings on sensitive issuesC Helping the leader to do his/her job more easilyC Coaching the leader and participants



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Team Facilitation (Continued)

If there is no facilitator, the team leader, or an assignedcoach, must assume many facilitator duties.

The facilitator must avoid:

C Being judgmental of team members or their ideas,comments, opinions

C Taking sides or becoming caught up in the subjectmatter

C Dominating the group discussions

C Solving a problem or giving an answer

C Making suggestions on the task instead of on theprocess



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Team Facilitation (Continued)

Facilitation and leadership requirements often diminishas leadership capability is developed within the team.Refer to the diagram below:



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Common Team ProblemsProblem Examples How to Fix

Floundering C Team direction is unclearC Members seem overwhelmedC Decisions are postponed

C Leader must provide clarityC Review the team purposeC Ask “How can we proceed?”

DominantParticipants

C Members interrupt othersC Members dominate the conversation

C Promote equal participationC Structure the discussion

OverbearingParticipants

C A member has excessive influenceC A member has legitimate authorityC A member is an “expert”

C Reinforce team conceptsC Ask the expert to lead the groupC Have a private discussion with “expert”

NegativeNellies

C Members say “we tried that already”C Members defend their turfC Members are negative of suggestions

C Reinforce the positiveC Ask for other points of viewC Separate idea generation from criticism

Opinions asFacts

C Members present opinions as factsC Members make unfounded assumptionsC Self assurance seen as unquestionable

C Ask for support dataC Question opinions and assumptionsC See groupthink discussion

Shy Members C Members are reluctant to speakC Members afraid of making mistakes

C Structure group participationC Direct conversation their way

Jump toSolutions

C Members rush to accomplish somethingC Members avoid data collection and analysisC Members want immediate decisions

C Reinforce the need for data analysisC Ask for alternate solutionsC Slow the process down

Attributions C Members make casual inferencesC Members don’t seek real explanationsC Members make psychological judgments

C Challenge assumptionsC Challenge judgmentsC Ask for data to support conclusions

Put-downs(Discounts &Plops)

C A member’s comments are ignoredC Members are not listeningC The meaning of a suggestion is missedC Sarcasm is noted

C Encourage active listeningC Encourage equal participationC Talk to parties privatelyC Promote uniform idea consideration

Wanderlust(Tangents &Digressions)

C Conversations stray from the main topicC Sensitive issues are avoidedC Group pursues tangents

C Follow a written agendaC Reinforce team operating guidelinesC Redirect the discussion

Feuding C Win-lose hostilities emergeC The team takes entrenched sidesC Some members become spectators

C Confront the adversaries aloneC Reinforce team operating guidelinesC Replace the guilty parties if necessary

Risky-Shift C Expansive and expensive remedies aresuggested (using company money)

C Ask “If this were my personal moneywould I still spend it?”

All of the above problem areas can be minimized withproper team training and awareness.



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Facilitation Techniques

A number of additional techniques are reviewed in thefollowing material.

Brainstorming

Brainstorming is an intentionally uninhibited techniquefor generating creative ideas when the best solution isnot obvious. A facilitator or group leader is necessaryfor this activity. Some of the key aspects ofbrainstorming are discussed below:

C Generate a large number of ideas: Don’t inhibitanyone. Just let the ideas out. The important thingis quantity, but record the ideas one at a time.

C Free-wheeling is encouraged: Even though an ideamay seem half-baked or silly, it has value. It mayprovoke thoughts from others.

C Don’t criticize: There will be ample time after thesession to sift through the ideas for the good ones.During the session, do not criticize ideas becausethat might inhibit others.



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Brainstorming (Continued)

C Encourage everyone to participate: Everyone thinksand has ideas. So allow everyone to speak up.Speaking in turn helps.

C Record all the ideas: Appoint a recorder to writedown everything suggested. Don’t edit the ideas,just jot them down as they are mentioned. Keep apermanent record that can be read later.

C Let ideas incubate: Allow the subconscious mind tobe creative. Give it time. Don’t discontinuebrainstorming sessions too soon. Consider addingto the list at another meeting.

C Select an appropriate meeting place: A place that iscomfortable, casual, and the right size will greatlyenhance a brainstorming session.

C Group size: The ideal group size is 4-10 people.

Brainstorming does not necessarily solve problems orcreate a corrective action plan. It can be effectivelyused with other techniques such as multivoting to arriveat a consensus as to an appropriate course of action.



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Nominal Group Technique

The nominal group technique (NGT) brings peopletogether to solve problems, but limits initial interactionamong them. The concept is to prevent peer or socialpressures from influencing the generation of ideas.Hence, the term “nominal” is used to describe thelimiting of communications. To conduct a NGT problemsolving meeting:

C A facilitator or moderator leads the discussion

C A group of five to nine individuals are assembled

C A problem is presented

C Before any discussion, all members create ideassilently and individually. Usually they are noted on asheet of paper.

C The facilitator then requests an idea from eachmember in sequence. Each idea is recorded untilideas are exhausted.



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Nominal Group Technique (Continued)

C Like brainstorming, no discussion is allowed at thispoint

C The clarification, support, and evaluation of ideas isthen permitted. Expanding on the ideas of others isencouraged.

C Voting for the best solution idea is then conducted(rank ordering, priority ratings, etc.). Several roundsof voting may be needed.

The facilitator should allow about 60 to 90 minutes for aproblem solving session. As with brainstormingsessions, the facilitator should avoid trying to influencethe problem solving process. The advantage of thistechnique is that the group meets formally, and yetencourages independent thinking.



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Multivoting

Multivoting is a popular way to select the most popularor potentially most important items from a previouslygenerated list. Often, there are too many items for ateam to work on at a single time. It is often worthwhileto narrow the field to a few items worthy of immediateattention.

Multivoting is useful for this objective and consists ofthe following steps:

1. Generate and number a list of items

2. Combine similar items, if the group agrees

3. If necessary, renumber the list

4. Allow members to choose several items that theyfeel are most important. Each member might havea number of choices equal to one-third of the totalitems on the list.



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Multivoting (Continued)

5. Members may make their initial choices silentlyand then the votes are tallied. This is usually doneby a show of hands as each item is announced.

6. To reduce the list, eliminate those items with thefewest votes. Group size will affect the results.Items receiving 0-4 votes might be eliminatedaltogether.

It should be noted that most problem solving teams canonly work on two or three items at a time. The itemsreceiving the largest number of votes are usuallyworked on or implemented first. The original list shouldbe saved for future reference and/or action.



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Force Field Analysis

A useful tool for problem identification and resolution isforce field analysis. Eitington provides a description ofthe process used to perform a force field analysis:

1. The process starts with a desire to understand theforces acting on a goal

2. Determine the forces favoring the desired goal(driving forces)

3. Determine the opposing forces to the desired goal(restraining forces)

4. Add to the driving forces to overwhelm therestraining forces, or

5. Remove or weaken the restraining forces, or

6. Do both (strengthen driving forces and weakenrestraining forces)



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Force Field Analysis (Continued)

Consider an example of a force field analysis onreducing student smoking:

Driving forces Restraining forcesparental pressure free timepeer pressure peer pressurefear of addiction addictionfear of cancer exam timeother bad effects habittaxes on smoking partiesfire hazards in dorms social statusadvertising advertising

On the driving forces side, the government is forcinghigher taxes on smoking. Tobacco advertisement hasbeen severely restricted. Several high profile courtcases have gone against the cigarette industry.

On the restraining forces side, cigarettes advertisementon television, billboards, racing, or almost everywhereelse is being banned.



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Conflict Resolution

Conflict is the result of mutually exclusive objectives orviews, manifested by emotional responses such asanger, fear, frustration and elation. Some conflicts areinevitable in human relationships. When one’s actionsmay be controlled by the actions of another, there isopportunity for conflict. Common causes of conflictinclude:

• Organizational structure• Value differences• Role pressures• Perceptual differences• Divergent goals• Status threats• Personality clashes• Differences in ideals• Changes in procedures• Discrepancies in priorities



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Conflict Resolution (Continued)

Conflicts may be categorized as to the relationshipbetween the parties involved in the conflict. The relativepower or influence between parties is a factor both inthe cause and the resolution of the conflict. Categoriesof conflicts are:

• Intrapersonal - within an individual• Interpersonal - between any two people• Intragroup - within a group• Intergroup - between groups• Interdepartmental - between departments• Intercompany - between companies

The results of conflicts may be positive in someinstances, negative in some, and irrelevant in others.Irrelevant conflicts occur when the outcome has neitherpositive nor negative effects for either party.



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Positive conflicts result in:

• A combined desire to unite and improve• Win - win situations• Creative ideas brought forth• Better understanding of tasks, problems• Better understanding of other’s views• Wider selection of alternatives• Increased employee interest and participation• Increased motivation and energy

Negative conflicts result in:

• Hostile, impulsive drives to destroy• Win - lose situations• Lose - lose situations• Undesirable consequences• Isolation• Loss of productivity



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Individuals may use a number of ways to deal withconflicts depending upon the circumstances and therelationships involved. Whether a conflict resolutionmethod is appropriate or effective will also depend onthe situation. Conflict resolution can be depicted in atwo dimensional model, adapted from the Thomas-Kilmann Conflict Mode Instrument:



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• Avoiding is unassertive and uncooperative - theindividual withdraws from the situation. (You lose,I lose).

• Accommodating is unassertive but cooperative - theindividual yields to the wishes of others. (You win,I lose).

• Competing is assertive and uncooperative - theindividual tries to win, even at the expense of others.(You lose, I win).

• Collaborating is assertive but cooperative - theindividual wants things done their way, but is willingto explore solutions which satisfy the other person’sneeds as well. (You win, I win).

• Compromising is intermediate in both assertivenessand cooperativeness - the individual is willing topartially give in to reach a middle position, splittingthe differences, and partially satisfying both parties.(Neither win or lose).

There is no specific right or wrong method for handlingconflicts. The method that works best depends uponthe situation.


II. MANAGEMENT & LEADERSHIPCOMMUNICATION SKILLS

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Communication Skills

An effective quality professional must be a“communicator,” or must learn to be one. Motivatingand collaborating with people are essentialresponsibilities. At the manager level, a professionalwill be the information hub for his/her department orteam. The manager will operate as a:

C Monitor of external information from peers or expertsC Monitor of internal information from subordinatesC Disseminator or distributor of informationC Spokesperson to outsidersC Decision maker from gathered information



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Communication Skills (Continued)

A manager, or group leader, will have manyopportunities to process, receive, and pass oninformation. The four basic purposes of suchcommunications are:

C To influence employees to work for the organization

C To inform employees by providing necessaryinformation for job performance

C To control the organization’s progress toward theobjectives

C To inspire employees through displays of values,attitudes, or modeling



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Downward Flow of Communications

Managers must relay information and give orders anddirectives to the lower levels. There are normally fivetypes of information sent down through the channels:

C Instructions for subordinatesC Rationale for the instructionsC The vision and mission of the companyC Policies and procedures of the companyC Performance feedback to the employees

It has been stated that information overload can be aproblem for many employees. There is too much of it,and thus, the information is not retained. Furthermore,the lack of openness between managers and employeescan be damaging. It takes time for the manager to keepsubordinates informed.

Another detractor in downward communications is thefiltering process. A message from the highest officer ofthe company will be distorted greatly if it goes throughmultiple organizational layers.



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Upward Flow of Communications

Upward communication consists of information relayedfrom the lower levels to the higher levels of thecompany. This gives the higher levels a chance to learnabout what is happening in the lower levels.

To encourage more reliable upward communications,top level managers can have open door policies,surveys, questionnaires, suggestion systems, breakfastmeetings, shift meetings, and the like.

Misleading information has many origins and causes.There are three important reasons why a manager maynot receive accurate and complete information:

C Subordinates may withhold information that tends todiscredit them.

C There may be a tendency to tell a supervisor, whathe or she wants to hear

C An incumbent manager is not always surrounded byallies.



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Horizontal Communications

Horizontal communication refers to the sharing ofinformation across the same level of the organization.The production engineer shares information withproduction planning. The planning group, in turn,shares information with manufacturing. This is a veryimportant part of the communications process.

Formal and Informal Communications

Formal communications are official companysanctioned methods of communicating to theemployees. Formal methods can occur up, down, oracross the organization. The informal communicationlink in a company is the grapevine. This rumor mill canbe either valuable or detrimental to communication flow.It is generally advisable to avoid it.



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Special Communication Roles

Gatekeepers are described as individuals who are at thecrossroads of communications channels. They arecenters of information, normally because of their jobs.Boundary spanners are individuals who have positionsthat link them with others outside of their work units.

Communication Forms

The spoken word via the telephone, face-to-facediscussions, formal briefings, videotapes, and even theinternet are forms of verbal communications. Examplesof written communications include letters, reports,computer messages and e-mail. The written forms canbe described as one-way channels.

There are some forms of verbal communications thatcould be one-way, not two-way. This can occur with ahighly directive boss. Face-to-face meetings generallyallow for immediate feedback from the receiver to thesender.



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Communication Forms (Continued)

There are a variety of nonverbal communication signalsfrom people that the manager might be able to pick upon from a face-to-face or group meeting. The nonverbalsignals include:

C Hand movements C Use of interpersonal space C Eye contact C Head movementsC Body posture C Leg positions

In the use of interpersonal space, certain cultures arecomfortable with a set spacing. Note that not all verbalsignals really mean what others claim them to mean. Although nonverbal signals can be spontaneous, somenonverbal signals are conscious and deliberate.

The ability to explain and to clarify details have longbeen recognized as important abilities. Speaking andwriting abilities are also essential for leadershipsuccess. Listening, the other half of the communicationconcept, has received far too little attention. Effectivequality professionals have learned the art of listening.



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Communication Effectiveness

Communication effectiveness includes:

C StrategiesC Media choicesC Appropriate vehicles for different situationsC Open-ended and closed-response questioningC Listening strategies

Media Choices

The methods used to communicate ideas are:

C Verbal communication: in face-to-face discussions,meetings, phone conversations, speeches, etc.

C Written communications: reports, memos, e-mail,letters, etc.



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Vehicles for Different Situations

Reprimanding an employee should be done in privateand is typically done verbally. Second or third offensesshould be done in person with the employee anddocumented in writing with a copy given to theemployee. Business agreements may be made verbally,but must always be followed with a letter to assure bothparties have the same understanding of the agreement.



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Open-Ended and Closed-Responses

Skillful questioning is of great value to the manager.Scholtes provides an initial framework of questions:

C What is the purpose of the project or job?C How do you know that you are making a difference?C What methods are you using?

The use of open-ended questions will allow for somediscussion and probing rather than just a simple “yes”or “no” answer. Examples are as follows:

C Why? Ask “why” five times.C What is the purpose?C What will it take to accomplish the project?C Will someone care?C What is your theory on the subject?C What data do you have?C Where did your data come from?



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Listening Strategies

Active listening is defined as helping find the source ofproblems or meanings. A passive listener will respondin a manner that will discourage the message senderfrom saying more, except defensively. Ten tips for goodlistening:

1. Stop talking2. Put the message sender at ease3. Show that you want to listen4. Remove listening distractions5. Empathize with the person6. Be patient with your response7. Hold your own temper8. Avoid argument and criticism9. Ask questions

10. Stop talking

Most people would rather hear themselves speak asopposed to listening to someone else. The good news islistening skills can be learned.



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Communications in a Global Economy

In today’s global economy there is an ever increasingneed to communicate with customers, suppliers, andcolleagues abroad. It has been stated, in a businesssense, the world is no longer round (spherical), it is flat.The major advance in this area is the increased use ofthe high speed internet.

Language Issues

Other than an abundance of national and local tariffs,there is no greater restriction on international businessthan language. The following precautions should beconsidered for correspondence:

C Avoid words that have multiple meaningsC Maintain consistency of terminologyC Stick to a logical sequence of eventsC Do not use complex or compound sentencesC Do use simple direct sentencesC Avoid abbreviations, acronyms, and contractionsC Avoid puns, slang, and idiomatic expressionsC Be especially careful with contract languageC Avoid Latin abbreviations (e.g., i.e., etc.)



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Time Zones

For virtual team meetings, hand-off internationalbusiness activities, and synchronous on-linediscussions, time can be especially critical. Even withcertain asynchronous e-mail correspondence, anawareness of time (or timing) can be critical. Routine e-mail transmission between the U.S. and Korea or Indiacan easily delay shipments by two days.

The best advice is to maintain consistency in responsetimes. In the case of international work teams workingon the same or similar service or manufacturingfunctions, this can entail a pre-set, transition time.

In certain selected areas such as finance, stock trading,and commodity futures, speed can be an overwhelmingcompetitive advantage. Time, in this case, relates towhen markets are open.



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Cultural Considerations

E-business or B2B commerce must be aware of culturaldifferences. Certainly any form of prejudice ordiscrimination must be avoided. Some considerations:

C There can be wide differences in syntax anddiscourse patterns.

C Technology can vary in availability and acceptance.

C Charts and videos can be useful.

C Making language and intentions visible helps.

C There are worldwide differences in food, drink, andfashion. In some cases these should be consideredand in other cases they should be avoided.

C Religion and human rights issues are often sensitiveareas and should be avoided.

C Cultural considerations can have an impact on bothtiming issues and business practices.

C Many companies design programs to helpemployees bridge the cultural gap with co-workers.


II. MANAGEMENT & LEADERSHIPCUSTOMER RELATIONS

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Customer Relations

Everything starts and ends with customers. Customersdefine quality and set expectations. They rightfullyexpect performance, reliability, competitive prices, on-time delivery, service, and clear and accuratetransactions.

To succeed, a business must identify their appropriatemarket focus. They can do this best by identifying theircustomers and determining their requirements.

There are two main types of customers: external andinternal. The relationship that management can developwith either basic type will affect the company’s ability tobe effective in delivering customer satisfaction.



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Internal Customers

An internal customer can be defined as anyone in thecompany who is affected by the product or service as itis being generated. The internal customer is sometimesforgotten. Research has shown that managementpractices which relate to employee satisfaction, will alsoimpact customer satisfaction. Internal employeecommunications can be improved through the followingoptions:

C Company newsletters: Corporate newsC Story boards: A board display, memos, letters, etc.C Team meetings: Share business newsC Posting customer lettersC Staff meetings: Share the informationC Display of goals, progress charts, etc.C Quality awards from suppliers

To stay competitive in this environment, training of theentire workforce is required. Employee surveys canserve as a tool for overall improvement.



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External Customers

External customers include three types: end users,intermediate customers, and other impacted parties.External customers may be segmented in many ways inan attempt to better understand their requirements andidentify possible market niches.

Once a customer purchases a service or a product fromthe company, the work should start to retain them forfurther purchases. The value of a loyal customer is notmeasured on the basis of one gigantic purchase, butrather on his/her lifetime worth.

Listening to the customer results in information oncustomer expectations, priorities of expectations, andneeds.



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External Customers (Continued)

The customer’s expectations of the product can bedescribed through an analogy similar to Maslow’shierarchy of human needs.

C Basic: The bare essential attributes of the productor service should be present.

C Expected: Some additional attributes will beprovided as a part of the product.

C Desired: These are attributes that are worthwhile tohave, but not necessarily provided as part of thepackage.

C Unanticipated: These are surprise attributes that gobeyond what the customer expects from a purchase.



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External Customers (Continued)

Customer needs are not stable, and continually change.A product or service that satisfied a certain need maygenerate new needs for the customer. As the customerobtains a suitable product or service, the basic needsare fulfilled, and they will look for new attributes. Juranlists customer needs as follows:

C Stated needs: What the customers say they want (acar)

C Real needs: What the customer really wants(transportation)

C Perceived needs: What the customer thinks isdesired (a new car)

C Cultural needs: Status of the product (a BMW)

C Unintended needs: The customer uses the productin an unintended manner. (a BMW used to haulconcrete blocks)



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Instruments to Gather Customer Data

Some of the instruments available for the purpose ofcollecting customer information are described below:

C Surveys: A properly designed questionnaire gathersdata using a consistent set of standardizedquestions. Usually, a sample is selected for use.

C Focus groups: A small group (3 to 12 typically) ofindividuals is assembled to explore specific topicsand questions. A time of 1 to 2 hours is normal.

C Face-to-face interviews: Individual interviews of 30to 60 minutes in length may be used.

C Satisfaction/complaint cards: The return of a cardprompts a reaction by the company.

C Dissatisfaction sources: Some methods that voicedissatisfaction include: complaints, claims, refunds,recalls, returns, litigation, replacements,downgrades, warranty work, misshipments, etc.

C Competitive shopper: Shoppers evaluate thecompany and competitors. CEOs may call their ownoffices to measure the ease of customer access.



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Customer Surveys

Research on customer satisfaction can be worthwhile inhelping the company efforts. The objectives ofcustomer research vary, but a few major themes arenoted below:

C To determine what quality isC To find out what competitors are doingC To define quality performance measures C To identify factors to give a competitive edgeC To identify urgent problems

Surveys can be developed in questionnaire form. Anadequate number would range from 25 to 30 questions.



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Customer Surveys (Continued)

For an L-Type matrix survey, the use of a numericalscale from 1 (very dissatisfied) to 10 (very satisfied) canmake it easier to quantify the results

Customer SatisfactionVery Dissatisfied Very Satisfied

Task 1 2 3 4 5 6 7 8 9 10On Schedule

GoodProductFriendlyPrompt

Scores from survey forms can be accumulated using avariety of Likert scales. If a number can be ascribed toa product or service, then that attribute can be evaluatedfor changes and trends. A well designed and properlyexecuted survey can be a help to the company.



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Customer Surveys (Continued)

There can be problems in the use of surveys:

C Improper survey form design or poorly definedissues

C Sampling errors or poor sampling techniques

C Ignoring nonresponses

C Using incorrect analysis methods

C Failing to ask the right questions

C Ignoring the results or using them incorrectly

C Using too many questions (25 to 30 questions aretypical)



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Customer Data Analysis

Comparing customer attitudes over time or betweengroupings can provide insights into market niches andchanges. The results of customer feedback datacollection can be analyzed using a variety of tools:

C Statistical tests

C Line graphs

C Control charts

C Matrix diagrams

C Pareto analysis



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Quality Function Deployment

Quality function deployment is a tool that is sometimesreferred to as the “voice of the customer,” or as the“house of quality.” Quality function deployment (QFD)has been described as a process to ensure thatcustomers’ wants and needs are heard and translatedinto technical characteristics. This activity should focusthe product or service on satisfying customerrequirements. QFD is a tool for the entire organizationto use. It is flexible and customized for each case andworks well for manufactured products and in the serviceindustry.

QFD provides a graphic method of expressingrelationships between customer wants and designfeatures. It is a matrix that lists the attributes acustomer wants and compares it to the design features(services that satisfy customer wants).

The collection of customer wants and expectations areexpressed through the methods available to most anyorganization: surveys, focus groups, interviews, tradeshows, hot lines, etc.



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Quality Function Deployment (Continued)

The construction of the house follows:

C The left side of the house has the customer needsC The ceiling has the features and requirementsC The right side contains the customer priorities C The foundation contains the target valuesC The roof contains design feature relationships



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The possible benefits for using the QFD process are:

C Creates a customer driven environmentC Reduces the cycle time for new productsC Uses concurrent engineering methodsC Reduces design to manufacture costsC Increases communications through teamworkC Creates data for proper engineering documentationC Establishes priority requirements C Improves quality



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A Hypothetical CQE Primer Example

The house of quality is flexible and customized to eachsituation. However, the basics of QFD will remain thesame: to hear the voice of the customer and to beproactive in its design.


II. MANAGEMENT & LEADERSHIPSUPPLIER MANAGEMENT

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Supplier Selection

The quality of materials and supplies determines thequality of the end product in many instances. Acompany can no longer buy from the lowest biddersolely on price, and then inspect and stage the materialfor processing approval. Today, companies areintensifying pressure to reduce idle inventory andmaintain product quality. Increased cooperationbetween supplier and the end user is required.

Suppliers may be selected by either an internal ratingsystem or by use of an external certification model orsome composite of the two. Juran describes theprocess of supplier evaluation as:

C The evaluation of product samplesC The evaluation of the supplier’s processes

Evaluation of the Supplier Through Samples

In this stage, the customer requests product samplesfrom the supplier. Customer approval stages arise ateach phase of the production process.



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Evaluation of the Supplier’s Processes

There are three possible manufacturing processevaluation vehicles:

C Prior product performanceC Process capability analysisC Quality system review

Prior product performance assumes that the bestpredictor of future product quality is past performance.

A process capability analysis can be performed onvarious products to verify that the process is capable ofmeeting the specifications.

A quality system review may require a visit to thesupplier’s site. An on-site survey is dependent on thesize and resources of the customer and on the dollarvolume of the supplier.



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Supplier Communications

There are many ways that a producer or supplier candisappoint a customer. Planning meetings, contractmeetings, and communications which review bothrequirements and performance are steps that can betaken to prevent supplier disappointment. Juran statesthat joint quality planning requires detailed discussionbetween customer and supplier covering three majorareas:

C EconomicC TechnologicalC Managerial

All three of these areas are important and are part of theup-front stated supplier expectations.



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Joint Economic Planning Meetings

The economic aspects of customer-supplierconversations should concentrate on the following keyelements:

C Value rather than conformance to specificationC Optimizing overall quality costs



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Joint Technological Planning Meetings

The following are typical of the issues covered for afairly sophisticated product:

C Agreement on specification detailsC Agreement on the performance requirementsC Qualification of reliability requirementsC Standardization of test methods and conditionsC Establishment of a system of timely responsesC Establishment of lot identification and traceabilityC Establishment of acceptable quality levels



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Joint Managerial Planning Meetings

The prior two issues are certainly of managerialconcern. Additionally, the following items fit more firmlyinto the conventional concepts of managerial control:

C Definitions of mutual responsibilitiesC Documented reporting requirementsC The formalization of communication channelsC A formal written contractC Buyer/supplier management requirementsC Action expected of the supplier (testing, records)



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Communications During the Contract

Obviously there is a need for continuing buyer andsupplier cooperation and communication during theexecution phase of a contract.

For standard commodities, most communications arechanneled through the buyer purchasing agents and thesupplier sales personnel. For complex engineeredproducts, there may be multiple communicationchannels.



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Supplier Performance Assessment

Supplier assessment and feedback is an essentialelement to both supplier and customer alike. Bothobjective and subjective data must be collected andanalyzed to determine if corrective action is necessary.Customer ratings encourage a supplier to solve qualityproblems because they can:

C Demonstrate the effects of poor quality on costsC Move the supplier to probationary statusC Disqualify the supplier from further business

Supplier rating systems cover the spectrum from simpleto complex. A wide assortment of measurements areused to provide supplier feedback:

C Quality metricsC Timeliness metricsC Delivery metricsC Cost metricsC Compliance metricsC Subjective rating metrics

Suppliers can be rated and analyzed using many of thesame techniques presented earlier for customers.



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Supplier Ratings

Bhote lists 5 generic types of supplier rating systems:

1. No rating: the rationale is that purchasing andquality know which companies are good or bad.Therefore, a formal rating system is not needed.

2. Quality rating only: a rating based on the incominginspection statistics.

3. Quality and delivery rating: graphic method. Aquality rating charted against the delivery rating.

4. Quality and delivery rating: cost index method.Use of a rating system based on a fixed dollarpenalty of nonconformances.

5. Comprehensive method: the measuring and ratingof agreed on variables such as: quality, cost,delivery, service, etc.



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Supplier Ratings (Continued)

Juran identifies how supplier ratings can be beneficial:

C To provide objective, quantitative measurement ofsupplier performance

C To provide purchasing with information in desiredcategories

C To provide the customer and supplier with the samegrading information

C To avoid drastic actions with a “special cause”supplier problem

C To identify troublesome areas that require action



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Supplier Feedback Reports

Most of the objective and subjective supplier feedbackinformation can be provided in a variety of formats.

Traditionally, at higher corporate levels, less detail isreported. Management reporting generally focuses onthe economic factors (plus a few other key categories).The following items are representative:

C Total dollar value purchasedC Percent defect dollar to dollar value purchasedC Percent defect dollar recovered (for each supplier)C Percent of lots or product rejectedC Corrective action activity (highlights or results)C Composite supplier rating score (when applicable)

The above items are more easily digested in trend chartformat. Obviously, where performance evaluations orrankings indicate, supplier meetings and correctiveaction planning may be required.



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Supplier Improvement Strategies

In the past, companies bought from the lowest costsupplier, period. Financial concern is still important, butis mainly directed at the total cost, not just the price tag.Companies have found that it is mutually beneficial todevelop supportive long-term relationships with theirsuppliers. The new trend is one of interdependencebetween vendor and purchaser. Vendors are selectedbased on quality, delivery, technology, life-cycle-cost,and management philosophy.



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Supplier Surveillance

In many cases, a contract may require the supplier topresent both a written plan for controlling quality andproof that the plan has been followed. There are twomajor surveillance approaches. One involves programauditing. The second approach is in-processsurveillance which consists of monitoring themanufacturing process of the supplier, and can involveseveral of the following steps:

C Witnessing key events, such as operations,inspections and tests

C Critical characteristic inspection by witnessing orperforming

C Joint troubleshooting of mutual quality relatedissues (Juran, 1999)



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Supplier Partnerships and Alliances

The purpose of a partnership between customer andsupplier is to mutually improve each other's operationsin the areas of quality, costs, delivery, cycle time,response time, and other areas to ensure a mutuallycompetitive advantage. The following definitions areimportant:

C Strategic alliances: The development of anassociation (partnership) with one or morecompanies. Alliances allow partners to be biggerthan their parts and benefit both parties.

C Partners: These are joint parties in a commonbusiness or purpose. The parties are on the sameteam, with equal rights.

C Business partnering: There is a pooling of resourcesin a trusting environment focused on mutualimprovement.

(Poirier, 1993)



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Supplier Certification Programs

The certification process comes after supplier selectionand approval. It starts after the supplier beginsshipment of the product. The certification process hasbeen described by the Customer/Supplier TechnicalCommittee of ASQ, in the following criteria:

1. The customer and supplier shall have agreed uponspecifications that are mutually developed,justifiable, and clear.

2. The supplier shall have no product-related lotrejection for a significant period of time, say, oneyear, or significant number of lots, say 20.

3. The supplier shall have no nonproduct-relatedrejections for a stated period of time, say, threemonths, or number of lots, say, five. Nonproduct-related nonconformities like wrong counts are notas serious as product-related ones.

4. The supplier shall have no negative nonproduct-related incidents for a stated period, say, sixmonths, or number of lots, say, ten.



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Supplier Certification Programs (Cont’d)

5. The supplier shall have a fully documented qualitysystem. ISO 9001 is an excellent model.

6. The supplier shall have successfully passed an on-site system evaluation.

7. The supplier must conduct inspections and tests.Laboratory results are used for batch processes,and SPC is used for piece part production.

8. The suppliers shall have the ability to providetimely inspection and test data. Thisdocumentation is necessary when the productarrives. (Besterfield, 1999)

Occasionally, it may be necessary to decertify a supplieras a result of a major problem. The number of supplierscan be reduced to a manageable level, thus furtherreducing costs.



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Supply Chain Management

Traditional customer/supplier relationships haveinvolved some assessment of incoming quality viasource or incoming inspection. Obviously, there wouldhave been some preliminary selection requirements,criteria, communications, and performance assessmentactivities. However, the point remained that thesupplier’s quality was not to be totally trusted and mustbe monitored. The results of this traditional approachwere inefficient use of human resources, the latediscovery of problems, inflated inventories, lengthycycle times, etc.



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Ship-To-Stock

The disadvantages of traditional procurement methodshave provided strong logic for ship-to-stock (STS)activities. A typical STS program can be divided intothree phases (Bossert, 1988):

1. Candidacy2. Qualification3. Maintenance

STS offers many of the following advantages:

C Mutual purchaser/supplier trustC Reduced inventory levelsC Reduced purchaser testing time and expenseC Reduced incoming rejectsC A replacement of inspection activities with auditsC Enhanced supplier quality responsibilityC A supplier quality reputation that can be broadened



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Just-In-Time

STS is often a forerunner to just-in-time (JIT)procurement. If all of the controls are in place forsuccessful STS activities, then a transition to JIT ispossible. JIT consists of two principle elements:procurement and inventory. Procurement involvesscheduling and receiving purchased product in afashion that the purchased product is maintained at anear zero level. JIT procurement would focus on thesame elements as STS, but with the addition of rigid:

C Forecasting

C Inventory cost control

C Scheduling

C Freight expense controls


II. MANAGEMENT & LEADERSHIPBARRIERS TO QUALITY IMPROVEMENT

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Barriers to Quality Improvement

The following are difficulties in many organizations:

C Concern about “Who gets the credit?”

C Difficulty in answering the question: “What savingswill be made with the proposed improvements thatwill not be made without them?”

C The need to recognize that changes in onedepartment may cause increased expenditures inanother department.

C The inability to estimate the costs of a proposedquality improvement

C NIH: “Not Invented Here”; therefore the idea has nomerit

C A reluctance to increase training expenditures

C Worker errors due to inadequate training or skills



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Barriers to Quality Improvement (Cont’d)

C Functional departments wanting to optimize theirown organizations

C Separate departments competing for limitedbudgeted dollars

C Poorly designed incentive and reward systems

C Reluctance to design and install a team basedapproach

C Management’s avoidance of the need for statisticalthinking

C Failure to make planned periodic improvements anintegral part of the system

C Failure to establish corrective and preventive actionsystems

C Failure to identify needed improvements via auditsor other means

C Failure to keep adequate records



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Overcoming Improvement Barriers

Almost all organizational weaknesses are systemsbased and must, therefore, be addressed by topmanagement. Some considerations include:

C The current organizational status should beassessed both internally and independently

C A management steering committee should beestablished to direct quality and other key initiatives

C An atmosphere of supportive employeeempowerment must be developed

C Senior management must be role models by:

C Recognizing employee accomplishmentsC Providing adequate trainingC Providing support and facilitationC Responding to worthy recommendations

C Some form of continuous improvement methodologyshould be adopted



II-112 (239)

Overcoming Improvement Barriers

C Some form of corrective and preventative actionsystem should be established

C Use improvement teams to research, assess, andcorrect problems and exploit opportunities. shouldbe a major consideration

C The pulse of both internal and external customersmust be measured

C Lasting relationships and communication links withkey suppliers is a must

C The determination and reporting of quality costs willprovide an economic measurement system

C Standard operating procedures and workinstructions should be adapted and audited

C Efforts should be undertaken to break down barriersbetween departments and groups


II. MANAGEMENT & LEADERSHIPQUESTIONS

II-117 (240)

2.1. A thorough review of the works of the major quality gurus wouldindicate which of the following to be the most effective way to createquality?

a. Effective problem solvingb. Benchmarking the best competitive practicesc. Continuous process improvementd. Modern statistical control techniques

2.6. For employee involvement efforts to succeed, what may be needed?

a. Increased employee incentivesb. Increased basic training companywidec. Employee understanding of how they can make a differenced. The initiation of pilot projects

2.7. Consider the following network, with events marked within the circlesand durations in weeks:

The critical path is:

a. 1-3-6-8-10b. 1-3-6-9-10c. 1-4-6-8-10d. 1-4-6-9-10

Answers: 2.1. c, 2.6. c, 2.7. c



II-118 (241)

2.11. Which of the following techniques are especially beneficial for thegeneration of ideas when solving quality and productivityproblems?

a. Poka - yokeb. Stormingc. NGTd. PERT

2.13. The most desirable method of evaluating a supplier is:

a. A history evaluationb. A survey evaluationc. A questionnaired. Discussion with the quality manager on the phone

2.18. What is a major distinction between the CPM and PERT methods inthe evaluation of project performance?

a. Only the PERT method can be displayed on a Gantt chartb. The PERT technique allows for easier crashing of project timec. The PERT technique permits network relationships but CPM does notd. The PERT technique is event oriented, while CPM is activity centered

Answers: 2.11. c, 2.13. a, 2.18. d



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2.21. A key characteristic of a business partnership is:

a. Sharing of critical business informationb. Limited access to human resourcesc. Special company audits are performedd. Only plant managers agree on agendas

2.24. Which of the following items describe well functioning improvementteams?

a. Members listen to what others say in the meetingb. Members often act without interdependencyc. Members often have covert agendasd. Members set unrealistic objectives

2.25. The "next process is your customer" refers to:

a. "Do it right" for the next operationb. Desire for better cooperation among departmentsc. "Zero defects" for the next processd. Process efficiency is very important

Answers: 2.21. a, 2.24. a, 2.25. b



II-120 (243)

2.36. A critical path in a project means that:

a. The project is important to the profits of the organizationb. Slack times can be used to delay the ending date of the projectc. Events on this path have no slack timed. The arrows and project path are always in bold print

2.37. Technical service to suppliers is:

a. A great public relations gesture when personnel are availableb. A greater benefit to the company than it is to the supplierc. A support feature for which suppliers are normally chargedd. An optional luxury which is not a company responsibility

2.38. In planning for quality, an important consideration at the start is:

a. The relation of the total cost of quality to the net salesb. The establishment of a company quality policy or objectivec. Deciding precisely how much money should be spent on qualityd. The selling of the quality program to top management

Answers: 2.36. c, 2.37. b, 2.38. b


III. QUALITY SYSTEMS

III-1 (244)

OUR PLANS MISCARRYBECAUSE THEY HAVE NO AIM.WHEN A MAN DOES NOTKNOW WHAT HARBOR HE ISMAKING FOR, NO WIND IS THERIGHT WIND.

SENECA (4 B.C. - 65 A.D.)


III. QUALITY SYSTEMSQUALITY SYSTEM ELEMENTS

III-2 (245)

Quality Systems

Quality Systems is presented in the following topicareas:

C Quality system elementsC System documentationC Quality standards and guidelinesC Quality auditsC Cost of qualityC Quality training



III-2 (246)

Historical Context

Over the last sixty years there has been a tremendousshift in the way that companies in the U.S. must operate.Due to the huge vacuum of industrial production afterWorld War II, the unscathed U.S. industrial base wasable to become the world’s best. Goods could not bemade fast enough. Our management style (the Taylorsystem) was examined and copied in many instances.

The rise of big U.S. corporations began in the 1950s andcontinued to the early 1970s. During this period, acertain big business mind-set and management styledeveloped. Running a big business became a numbersgame. During this period, foreign competitors began toeat our lunch in a large number of technical andmanufacturing areas.

Since the mid 1970s, many U.S. companies have startedto revive. They reeled from the initial shock of lostmarkets and responded. Challenges to U.S. companiesabound in the areas of quality, productivity, reliability,communications, responsiveness, technology, costs,and customer satisfaction.



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The Quality Function

The quality department has a basic function in anorganization: to coordinate the quality efforts.

The quality department, in most organizations, plans,measures, analyzes and reports quality. It is a stafffunction which supports other departments in thecontinuous improvement of products and services. Thecommon functions of a quality organization include:

Quality control. A management function that is intendedto control or regulate the process in order to preventdefective products from being made.

Quality assurance. A planned and systematic action toprovide adequate confidence that a product will conformto requirements.

Inspection. An appraisal activity where products areinspected (or tested) to determine whether they conformto requirements.

Reliability. A function to determine the probability of aproduct performing its intended function for a specifiedtime interval under stated conditions.



III-3 (248)

The Quality Function (Continued)

Often under the quality assurance organization, thereare five additional functions:

Quality engineering. The main planning function ofquality assurance.

Quality audit. An independent evaluation of variousaspects of quality performance.

Procurement quality. Assures that new materials andpurchased parts are acceptable prior to release.

Metrology measurement. Assures that equipment iscalibrated via standards traceable to the NationalInstitute of Standards and Technology.

Administration. Originates the reports, procedures andpolicies used to support other functions in the company.This is often a valuable feedback loop.



III-4 (249)

Systems

From an organizational standpoint, a system is definedas a series of actions, activities, elements, components,departments, or processes that work together for adefinite purpose. Business systems are made up of avariety of processes.

Quality Systems

A quality system entails all of the activities that areundertaken to assure that a product or service meetsrequired standards. Sometimes the systems are formal(written), and sometimes they are informal (assumed).Some of the main elements of a quality system for amanufactured product are:

C Management responsibilityC Raw material purchasing and controlC Incoming inspection of raw materialsC Process controlC Final inspectionC Control of nonconforming productC Calibration controlC Document controlC RecordsC Corrective/preventive actions



III-5 (250)

Quality Systems (Continued)

Generally, any large group will require a formal,documented quality system. It is simply not possible tokeep everyone informed of the correct procedures andmanagement philosophy.

One definition of a quality system is:

The organizational structure, responsibilities,procedures, processes, and resources forimplementing quality management.

ANSI/ISO/ASQ Q9000-2000 has expanded the term“quality system,” to “quality management system.” ThisStandard states:

“The quality management system is that part of theorganization’s management system that focuses onthe achievement of results, in relation to the qualityobjectives, to satisfy the needs, expectations andrequirements of interested parties, as appropriate.”



III-5 (251)

Quality Systems (Continued)

The keys to a proper quality system, then, are:

C It is companywide

C It provides an operating work structure

C It contains documented technical and managerialprocedures

C It guides the coordinated actions of people,machinery and information

C It assures customer quality satisfaction andeconomical costs



III-5 (252)

Elements of a Quality System

All elements of a quality system flow from topmanagement, to the product, through a number ofelements. These major elements are discussed below:

Quality Policy

The top management of a company establishes theintention and direction of a company to meet customer’sneeds through the quality policy. The quality policystates how they intend to satisfy the customer. Thequality policy is the foundation of the total qualityhierarchy



III-6 (253)

Elements of a Quality System (Continued)

Quality Management

Quality management is that portion of management thatimplements the quality policy. In many enlightenedorganizations, the implementation of the quality policyis the function of all management and employees.

Quality System

The quality system is the total organizational structure,directed by quality management to fulfill the qualitypolicy. The quality system consists of employees andother resources directed through procedures.



III-6 (254)

Elements of a Quality System (Continued)

Quality Assurance

Quality assurance is planned and systematic actionsthat provide confidence that a product or service willsatisfy given requirements for quality. Some typical quality assurance activities are:

C Establish customer needs/expectationsC Convert customer needs to specificationsC Control of incoming materialsC Monitor processes and proceduresC Final testing of product or serviceC Warranty or service support of product or service

Quality Control

Quality control operations are those techniques andactivities that monitor and control quality. Typicalquality control techniques and activities are:

C Receiving inspectionC In-process inspectionC Final inspectionC Internal auditC Supplier control



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TOP MANAGEMENT

QUALITYMANAGEMENT

QUALITY SYSTEM

QUALITYASSURANCE

QUALITYCONTROL

PRODUCT/SERVICE

QUALITY POLICYThe quality policy is established by topmanagement. It is the overall quality intentions anddirections of an organization regarding quality.

Quality management is the management functionthat determines and implements the quality policy.

The quality system is the organizational structure,responsibilities, procedures, processes andresources for implementing quality management.

Quality assurance is all of the planned and systematicactions to provide adequate confidence that a productor service will satisfy given requirements for quality.

Quality control is the operations, techniques andactivities of quality assurance that are used to fulfillrequirements for quality of the product or service.

Quality System Flow


III. QUALITY SYSTEMSQUALITY SYSTEM DOCUMENTATION

III-8 (256)

Documentation of the Quality System

The document set that comprises the quality system canbe organized in many different ways. Most organize thequality documentation into a hierarchy.

The top of the pyramid is the quality manual. Thequality manual records management’s quality policy andcontains information on how the company will meet therequirements of ISO or any other standard.

Tier two represents the quality procedures. Theseprocedures are the focal point of the system, since theydescribe the responsibilities of the various personneland the administrative system used to accomplish thetasks. Thus, the quality manual details what is to bedone, the quality procedures describe who will do it.

Finally, tier three illustrates the work instructions thatdescribe how to do the tasks. The work instructionsdetail the specific steps to accomplish the goals definedin the quality manual and the quality procedures. Somecompanies use four tiers with the last level representingthe required forms and records.



III-8 (257)

Quality Documentation Pyramid



III-9 (258)

Quality System Components

The documented portion of the quality system shouldcontain the following four components:

C Quality policy: The quality policy should be aprominent part of the quality system so that theemployees are informed of management’s directionand “vision.”

C Responsibilities: The documented system alsoshould describe and define the responsibilities ofeveryone in the organization responsible for quality.

C “How to do it”: The documented quality systemshould describe how the various tasks are to beperformed.

C Verification: The documented quality systemshould also describe how the quality of the productis verified.

One of the purposes of a formal quality system is todocument and freeze the operations of the company. Itis important to make sure that the formalized systemsare the best.



III-10 (259)

Types of Documents

A formal quality system is characterized by formalinstructional documents. These documents providedirection to the employees on how to accomplish a task,who is responsible for performing those tasks, or howthe company systems work. There are various namesfor these documents. Some of the names are:

C Standard operating proceduresC ProceduresC Work instructionsC Manuals

Many companies have spent considerable amounts ofeffort and money to develop these documents. This isbecause good documentation is useful, and, in fact,necessary to the continued success of a company.



III-11 (260)

Types of Documents (Continued)

The formal quality system contains procedures orinstructions that define and operate the system. Thereare several types of documents that are used in qualitysystems. These are shown in Table below.

Document Type CommonName

Policy documents: Documents thatdescribe the overall company qualitypolicy, commitment to quality andquality system managementorganization.

Qualitymanual

“Ways of doing business”documents: Documents thatdescribe how the company qualitymanagement system operates.

Qualityprocedures

Technical documents: Documentsthat describe how to do specifictasks such as equipment operation,administrative steps, etc.

Workinstructions



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General Characteristics of Documents

All documents used in the quality system havesimilarities. The basic content of any good qualityprocedure or instruction should include:

C Purpose of the document

C Basis of the document

C Scope of the document

In addition, the documents should contain theinformation necessary to convey the intended message.Each document has a goal, according to the type. Thedocuments should be generated so that the goal isaccomplished in the least amount of effort.



III-12 (262)

Quality Manual

The quality manual is a policy document generatedprincipally by upper management to outline how thecompany is to operate. The goal of the quality manualis to inform company employees and customers of themanagement vision and approach to operating thebusiness. It should define how management intends tosatisfy the customer for continued business success.The key elements of the quality manual are:

C Policy statementC General descriptions of policy implementationC Correlation of policy and implementation to

applicable quality standards

The quality manual is most frequently organized alongthe outline of ISO 9001:2000 or other applicablestandard(s).



III-12 (263)

Quality Procedures

Quality procedures are “ways of doing business”documents. Sometimes these are called standardoperating procedures (SOPs). Quality proceduresshould define management or administrative processesin a manner that supports the company policy. Thequality procedures should:

C Be consistent with company policyC Describe the functional organizationC Outline responsibilities of personnelC Be implementedC Be understood by all employees

Quality procedures are the real focal point of thedocument system. They define the companyorganization, and how the company quality policy will beimplemented to best satisfy the customer. Procedurestell the operating entities what they are supposed to do,and describe their interfaces.



III-12 (264)

Documentation Systems

A documentation system can be divided into two majorcomponents:

C Configuration management (for design)C Document control (for design and other companies)

Configuration Management

Juran (1999) describes configuration management as:“The collection of activities needed to define, identify,manage, record, or approve the hardware and softwarecharacteristics of a product.”

Configuration management can be described via twoquestions:

C What constitutes the product at any point in time?C What changes have been made to the product?



III-13 (265)

Configuration Management (Continued)

According to Cox (1995), configuration managementconsists of four basic elements:

C Configuration identification: the process of definingand identifying every element of the product.

C Configuration control: to manage the change orderprocess from design to implementation.

C Configuration accounting: the documenting of theapproved configuration identification, and theimplementation status of the changes.

C Configuration audits: a comparison of the productagainst the engineering specifications in order todetermine compliance.



III-14 (266)

Configuration Identification

The starting point for a configuration is called thebaseline. There are three levels to a baseline:

C Functional baseline: general requirements of theproduct

C Allocated baseline: defines the generalrequirements for a subsystem in the overall product

C Product baseline: defines the detailed requirementsof the system or item

The baseline documents are very detailed. They willinclude all of the original drawings, specifications, tests,procedures, parts, materials, etc.

Configuration Control

Once the product baseline has been approved (orcreated), changes to the design will fall underconfiguration control. Ideally, there will be establishedprocedures for coordination of the change order. Anychanges may have to go through the project engineer,with signatures from other key departments.



III-14 (267)

Configuration Accounting

Configuration accounting is the tracking of all proposedchanges and the implementation status of everyapproved change. The details of every change arerecorded and reviewed for existing and futurecompatibility. A department, perhaps the qualitydepartment, will have the responsibility of verifying thatthe changes have been implemented and thatdocumentation is completed.

Configuration Audits

This could consist of audits of the documentationsystem for completeness and accuracy, or audits of theproduct to verify engineering specification accuracy.



III-15 (268)

Documentation Control

The information required under configurationmanagement could be immense. Information could beavailable from all parts of the organization including:

C Contracts design input C Design specifications C Process details C Engineering changes C Inspection and test data C Supplier dataC Final inspection dataC Field dataC Failure data scrapC Warranty charges, etc.

Configuration management of procedures, forms, andrecords often requires the documentation to be inwritten form. Thus, a method for filing, storing, andretrieving the documents is needed. Even an electronicsoftware documentation system requires organization.



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Revision Control

Keeping track of revisions, and ensuring theiravailability are two of the more challenging tasks of aquality system. They are challenging because theyrequire attention to minor details. The first step ofrevision control is deciding how to mark the documents.There are two principle methods of revision marking:

C Revision control by sectionsC Revision control by total document

Revisions of longer documents, like the quality manual,are usually maintained section by section. That is, asingle quality manual may have a number of sections,each with a different revision date.

Total document revision control is frequently used forquality procedures and work instructions. This meansthat a single change requires the generation anddistribution of the total document.



III-16 (270)

Marking Changes

ISO 9001:2000 (paragraph 4.2.3c) requires that changesto the quality system documents be identified along withthe revision level. Change markings can occurthroughout the document. A common change markingis to underline additions and strike-out words/phrasesthat have been eliminated. Most word processors willdo this automatically.

ISO 9001:2000 allows documentation to be in any formor medium (paragraph 4.2.1, Note 3). Many companiesare now using computer network systems to distributeand control the documents. Computer distribution hasone danger. Employees have a habit of printing thedocument and keeping that version handy. This meansthat revision control can be lost.



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Document Formats

The formats of all quality system documents should beconsistent. This allows employees and auditors to knowwhere items are found, without confusion. In addition,constant formats make a quality system lookprofessional. Format consideration includes the majorheadings. These headings should be consistent withinthe same document type.



III-17 (272)

Correlation Matrix of Documents

Some companies choose to have a correlation matrix totrack requirements. In the event a company is ISO9001:2000 certified, every requirement of the standardshould be identified and “broken-out.” The sequencecan go as follows:

Specific ISO 9001:2000 Requirement

Addressed in which section of the qualitymanual, including who is responsible?

Correlated to any necessary proceduresincluding equipment, records andresponsibilities?

Connected to any specific work instruction,providing adequate details to perform thework, record information, etc.?



III-18 (273)

ISO 9001:2000 Records

A listing of required ISO 9001:200 records is shown onPrimer page III - 18.


III. QUALITY SYSTEMSQUALITY STANDARDS

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Quality Standards and Other Guidelines

Standards are measures of excellence against whichcomparisons are made. Quality standards can begovernment or industry endorsed descriptions ofessential characteristics for an item or activity. Qualitystandards may be product specific, user specific, orgeneric and are approved by a recognized authority.Examples of standards include:

C ISO 9001:2000 Quality Management Systems -Requirements

C ISO/TS 16949 Quality Management Systems -Particular requirements for the application of ISO9001:2000 for automotive production and relevantservice part organizations

Although adherence to quality standards has becomevery widespread, a large amount of business isconducted using only requirements and specifications.



III-19 (275)

Requirements

A requirement is a formal statement of a need and themandatory and expected way to attain it. It can alsorepresent an accomplishment level to achieve specificobjectives for given conditions. A requirement can bea contractually binding technical prerequisite stated inapproved specifications. Note that registration to aquality standard may also be a requirement to conductbusiness with a company.

Specifications

A specification is a mandatory requirement. Aspecification clearly and accurately describes essentialtechnical requirements and verification procedures foritems, materials and services. When invoked by apurchase order or contract, it is legally enforceable andits requirements are binding.



III-20 (276)

Industry Standards

Industry standards are numerous. Some industrieshave several associations that publish standards.Industry standards are developed to rationalize andsimplify the design, manufacturing, service and use ofthat industry’s output. For consistency, industrystandards should be based on international or nationalmodels. However, they are often not presented in aformat that is consistent from industry-to-industry.

Some examples explaining the character of industrystandards:

C Many industries have accepted the ISO 9000 seriesstandards

C The automotive industry has modified ISO 9001(ISO/TS 16949)

C The steel industry has standardized alloycompositions and properties

C Most industries accept the test methods of ASTM



III-20 (277)

International/Industry Standards

ISO/TS 16949 is an example of an international standardthat has been modified and adopted as an automotiveindustry standard. ISO/TS 16949 is ISO 9001:2000 in itsentirety with significant additions to many elements.This Standard replaces QS-9000 (1998). Additionally, sixother documents may be required by Chrysler, Ford,General Motors, and other OEMs:

C Quality System AssessmentC APQP Reference ManualC PFMEA Reference ManualC Production Part Approval Process ManualC Measurement System Analysis Reference ManualC Fundamental SPC Reference Manual



III-21 (278)

Industry/National Standards

American National Standards Institute (ANSI) andAmerican Society of Mechanical Engineers (ASME) haveestablished and executed a quality assurance standardfor the design, construction, and operation of nuclearpower plants. This Standard, ANSI/ASME NQA-1, is anexample of a national standard that is also an industrystandard.

Other Standards

Each organization must determine which standard(s) areapplicable to their business. Included in the decisionare both regulatory and customer requirements. Theorganization must also determine whether it will:

C Ignore the quality system requirements

C Comply with some or all of the requirements

C Comply with the requirements and obtain third-partyregistration or accreditation verifying that they meetthe requirements

There are many other quality system standards whichapply to specific industries.



III-21 (279)

ISO 9000:2000

The ISO 9000 Quality Management Standards wererevised and published by ISO in December, 2000. Thethree new ISO Standards are:

ISO 9000:2000, Quality Management Systems –Fundamentals and Vocabulary

ISO 9001:2000, Quality Management Systems –Requirements

ISO 9004:2000, Quality Management Systems –Guidelines for Performance Improvements



III-22 (280)

ISO 9001:2000 Summary1 Scope

1.1 General1.2 Application

2 Normative reference3 Terms and definitions4 Quality management system

4.1 General requirements4.2 Documentation requirements

5 Management responsibility5.1 Management commitment5.2 Customer focus5.3 Quality policy5.4 Planning5.5 Responsibility, authority and communication5.6 Management review

6 Resource management6.1 Provision of resources6.2 Human resources6.3 Infrastructure6.4 Work environment

7 Product realization7.1 Planning of product realization7.2 Customer-related processes7.3 Design and development7.4 Purchasing7.5 Production and service provision7.6 Control of monitoring and measuring devices

8 Measurement, analysis and improvement8.1 General8.2 Monitoring and measurement8.3 Control of nonconforming product8.4 Analysis of data8.5 Improvement



III-23 (281)

ISO 9001: 2000 Summary

ISO 9001:2000 is summarized on Primer pages III - 23through III - 30.



III-31 (282)

Malcolm Baldrige National Quality Award

The Malcolm Baldrige National Quality Award wasmodeled after the Deming Prize in Japan and focuses onorganizational excellence. The systems model is nowcalled the Baldrige National Quality Program (BNQP) butthe presented award is still called the MBNQA. Corevalues and concepts are based on:

C Visionary Leadership: Senior leaders set directions,create a customer focus, create methods forachieving excellence, and build knowledge andcapabilities.

C Customer Driven Focus: Understanding today’scustomer desires and anticipating future customerdesires and marketplace offerings.

C Organizational and Personal Learning: Adopting awell-executed approach to learning includingcontinuous improvement and adaptation to change.

C Valuing Employees and Partners: Committing toemployee satisfaction, development, and well-being.Building internal and external partnerships to betterachieve overall goals.



III-32 (283)

MBNQA (Continued)

C Agility: Creating a capacity for rapid change andflexibility.

C Focus on the Future: A strong future orientation andwillingness to make long-term commitments to keystakeholders. Seeking opportunities for innovation.

C Managing for Innovation: Making meaningfulchanges to improve products, services, andprocesses. Creating new value for stakeholders.

C Management by Fact: Measurement and analysis ofperformance, critical data, key processes, outputs,and results.

C Public Responsibility and Citizenship: Adopting apractice of good citizenship, business ethics andprotection of health, safety, and the environment.

C Focus on Results and Creating Value: Developingperformance measurements that focus on keyresults and create value for all stakeholders.

C Systems Perspective: Managing the wholeenterprise, to achieve performance improvement.



III-32 (284)

MBNQA (Continued)

The Criteria for the MBNQA includes voluntarycompliance as well as customer or organizationalmandatory compliance requirements. Organizations areincreasingly seeking compliance with these models asa result of not only client driven motivations but fororganizational prestige and improvement.

The purposes of the Criteria include:

C To provide a basis for organizational self-assessments

C To actually achieve the Baldrige award

C To provide feedback to applicants

C To help improve organizational performancepractices and capabilities

C To facilitate information sharing of the best U.S.practices

C To serve as a working tool for understanding andmanaging performance

C To serve as a guide for planning and training



III-32 (285)

MBNQA (Continued)

The criteria are designed to help organizations use anintegrated approach to organizational performancemanagement that results in:

• Ever-improving value to customers, contributing tomarketplace success

• Improvement of overall organizational effectivenessand capabilities

C Organizational and personal learning

The Baldrige award eligibility categories now include:

C Manufacturing businessesC Service businessesC Small businessesC Education institutionsC Health care organizations



III-33 (286)

MBNQA (Continued)

The Malcolm Baldrige 2006 categories, items, and pointvalues. are shown in the table below.

2006 Categories/ Items Point Values1 Leadership 120

1.11.2

Senior LeadershipGovernance and Social Responsibility

7050

2 Strategic Planning 852.12.2

Strategy DevelopmentStrategy Deployment

4045

3 Customer and Market Focus 853.13.2

Customer and Market KnowledgeCustomer Relationships and Satisfaction

4045

4 Measurement, Analysis, and Knowledge Management 904.1

4.2

Measurement, Analysis, and Review of OrganizationalPerformanceInformation and Knowledge Management

40

455 Human Resource Focus 85

5.15.25.3

Work SystemsEmployee Learning and MotivationEmployee Well-Being and Satisfaction

352525

6 Process Management 856.16.2

Value Creation ProcessesSupport Processes and Operational Planning

4540

7 Results 4507.17.27.37.47.57.6

Product and Service OutcomesCustomer-Focused OutcomesFinancial and Market OutcomesHuman Resource OutcomesOrganizational Effectiveness OutcomesLeadership and Social Responsibility Outcomes

100 70 70 70 70 70

Total Points 1000



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Baldrige and ISO 9001 ComparisonsSelected Criticisms for ISO 9001 and MBNQA

ISO 9001 MBNQA1. Does not assure world class

performance1. Past winners have not solved all

business problems2. Narrow quality documentation

focus2. Quality documentation

requirements are not spelled out3. Minimal effort to improve company

efficiencies3. Winning the award may displace

more important objectives4. Not helpful for high-tech

companies4. Can create an internal strain on

resources5. Automotive industries require

additional ISO/TS 16949registration

5. The sharing requirement costsmoney and might aid competitors

6. Products produced may notcapture customer desires

6. A winning company’s productsmay not be superior to competitors

7. Registration costs may be high($150-200,000)

7. Award costs can be staggering($500,000 and up)

Requirement Comparisons for ISO 9001 and MBNQA

ISO 9001 MBNQA1. Adequate quality systems 1. Best-of-the-best quality systems2. Objective evidence of meeting

requirements2. Clear evidence of product quality

3. Completely controlled and currentdocumentation

3. Clear evidence of customer’sperception of company superiority

4. Periodic surveillance audits thatverify compliance

4. Historic trends must support asingle audit

(Juran, 1999)


III. QUALITY SYSTEMSQUALITY AUDITS

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Audit Purpose and Benefits

The purpose of quality auditing is to examine theeffectiveness of management directed control programs.The philosophy of quality assurance programs is basedon prevention rather than detection of problems. Whereproblems do occur, emphasis is on:

C Early detection of the problemC The depth of the problemC Discovery of the root cause of the problem

Management implements control programs to:

C Prevent problemsC Identify problemsC Prevent the reoccurrence of problems

Quality problems result in:

C Customer dissatisfactionC Lost profitsC Loss of employee morale



III-35 (289)

Audit Purpose and Benefits (Cont’d)

Quality auditing provides management with objectivefeedback based on facts, enabling management to makeinformed decisions. The primary directive of an audit isto be beneficial to the function being audited. Examplesof specific auditing purposes are to determine that:

C Products are fit for useC Adequate written procedures exist and are utilizedC There is adherence to regulatory requirementsC Product or system deficiencies are identifiedC There is conformance to specificationC Remedial action is taken and the result is effectiveC Information is obtained to identify and reduce risksC There is effective use of company resourcesC Standardized organizational practices exist



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Audit Philosophy

Quality audits are formal, systematic, and independent.The results of the audit are based on facts. Theeffectiveness and integrity of an audit depend heavilyupon the skills and training of the auditor(s). The newaudit philosophy is centered around two main themes:

C Auditors must be fact-finders, not fault-finders

C Audits should not be conducted in a covert manner;avoid secrecy



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Types of Audits

Quality auditing is concerned with three general types ofaudits. The system audit, the process audit, and theproduct audit. Each of these general categories ofaudits will be discussed in more detail on the followingpages of this Section.

SYSTEM AUDIT

PROCESS AUDIT

PRODUCT AUDIT



III-37 (292)

System AuditsA system audit is the largest and most extensive ofaudits. System audits are conducted to verify, throughobjective evidence, whether or not the qualitymanagement systems and organizational plans areindeed carried out to the requirements set forth. Systemaudits may be external (supplier) or internal (in-house).

Process Audits

A large and significant portion of the system audit isdevoted to the process audit. One or more processesmay be audited during the systems audit. The processaudit, conducted by itself, is a convenient audit, oftenyielding swift results. Process audits:

C Are less extensive than system auditsC Usually concentrate only on specific processesC May be performed internally or externallyC Require less planning than the system auditC Can be very helpful in improving a process



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Product Audits

The product audit is an assessment of the final productor service and its “fitness for use” evaluated against theintent of the purpose of the product or service. Productaudits are customer oriented (from the customer's pointof view). Product audits may be performed by as few asone auditor or by as much as a large team (or evenmany teams) of auditors. Product audits may beperformed internally or externally.

Internal Audits

An internal audit is performed within an organization tomeasure its own performance, strengths, andweaknesses against its own established procedures andsystems. An internal audit may be performed by in-house personnel. An internal audit is considered to bea first-party audit.



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External Audits

An external audit is an audit by company directive andperformed on an outside source, such as a supplier.The external audit may be performed by companyrepresentatives; or the company may hire outsideauditors to conduct the supplier audit. However,product knowledge, contracts, purchase agreements,and secrecy agreements make it more common for thecompany conducting the audit to send personnel fromit's own auditing staff to perform an external audit.

Third Party Audits

A third-party audit is when an outside source, or a third-party, is used to conduct the audit. The third-party auditis used to obtain a more independent and objectiveassessment or achieve certification to a recognizedstandard.



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Specific Objective Audits

Some examples of specific objectives audits follow:

Assessment: Sometimes used to indicate a less formalmeans of measuring and reporting than the normalaudit. An assessment is usually limited in scope.

Compliance: This is a type of audit which verifieswhether or not the audit systems, processes, orproducts, satisfy the requirements as set forth in thecontractual agreements and standards.

Pre-Award Survey: A system audit may be conducted asa condition of accepting a new supplier prior to contractaward.

Procedural Audit: A procedural audit is a form of thecompliance audit which verifies documented and formalprocedures.

Quality System Review: System audits resulting fromsignificant changes affecting product quality. This typeof audit may be necessary if product quality declines orthere are critical changes in management.



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General Audit Matrix

Audit NameAudit Type

Process Product System

Compliance Audit C NA C

Corporate Audit C C X

External Audit C C X

Extrinsic Audit C C X

Full Scope Audit C C X

Informal Audit C C C

Internal Audit C C C

Management Audit C C X

Pre-award Survey C C X

Procedure Audit C NA X

Process Audit X NA NA

Product Audit NA X NA

Quality Audit C C X

Quality Program Evaluation C C X

Self Audit C C C

Supplier Audit C C C

Surveillance Audit C X X

Systems Audit NA NA X

Third-Party Audit C C C

Unannounced Audit NA NA NA

X = Normal Audit Type C = Audit Possibility NA = Not Applicable



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System Audit Matrix

Type Subject Application

Extrinsic A company is the subject ofa customer audit

External

VendorSurvey

Supplier External

Pre-awardSurvey

Potential supplier External

Systems orManagement

Audit

In-depth qualitymanagement systems andcompliance

Internal orExternal

AssessmentAudit

More limited in-depth thanthe system audit

Internal orExternal

Appraisal Total quality programeffectiveness.

Internal orExternal

ComplianceReview

Verification of effectivenessof quality managementsystem

Internal orExternal

Full Audit Entire company or productfrom design developmentto end of product life

Internal orExternal



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Audit Program Administration

Top management has the responsibility for establishingand authorizing the organizational auditing program.The audit authority (or audit manager) should establishclear objectives for the audit program and for thespecific audit types. Audit manager duties include:

C Establish the objectives of the audit program

C Establish the responsibilities and procedures

C Ensure adequate resources

C Ensure the implementation of the audit program

C Ensure that audit program records are maintained

C Monitor, review, and improve the audit program

The audit program should be periodically reviewed andevaluated by management.



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Auditing Standards

ISO 19011:2002

ISO 19011:2002 combines criteria for both quality andenvironmental systems auditing. The following topicsare addressed in ISO 19011:2002:

C Standards - to be used in the audit processC Auditors - criteria for an auditor skill levelsC Monitoring / maintenance of auditor performance C A code of ethics

ISO 9001:2000

ISO 9001:2000 quality standards provide internationalrequirements as to what elements are to be audited.ISO 9001:2000, Section 8.2.2, identifies the requirementto perform internal audits and addresses the followingelements:

C Requirements for documented internal audit plansC Records of the results of internal auditsC Evidence of review of the resultsC Identification of corrective actions and follow up



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Lead Auditor Responsibilities

C Assisting in the selection of other team membersC Maintaining the ethics of the audit teamC Defining the requirements of each audit assignmentC Complying with applicable auditing requirementsC Preparing the audit planC Preparing working documents C Briefing the other auditorsC Representing the audit team with the auditee C Reviewing documentationC Reporting critical nonconformitiesC Reporting obstacles in performing the auditC Submitting the audit report



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Auditor Responsibilities

C Complying with the applicable audit requirementsC Communicating and clarifying audit requirementsC Carrying out assigned responsibilities effectively C Maintaining objectivity and confidentialityC Remaining within the audit scopeC Cooperating with and supporting the lead auditorC Acting in an ethical mannerC Collecting and analyzing evidenceC Retaining and safeguarding documentsC Documenting any observationsC Noting areas more extensive auditingC Answering relevant questionsC Verifying the effectiveness of corrective actionsC Reporting the audit results



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Client Responsibilities

C Determines the audit need, scope, and purpose

C Initiates the audit

C Determines the auditing organization

C Receives the audit report

C Determines follow-up action



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Auditee's Responsibilities

C Informing employees about the auditC Appointing staff to accompany the audit teamC Providing resources needed by the audit teamC Cooperating with the auditorsC Providing access to the facilities and materialC Determining and initiating corrective actions

Audit Scope

The client makes the final decisions on the scope anddepth of the audit, which quality system elements,physical locations, and organizational activities are tobe audited within a specified time frame. The resourcescommitted to the audit should be sufficient to meet itsintended scope and depth.

Audit Frequency

The need to perform an audit is determined by the client,taking into consideration changes in management,organization, policies, techniques, technologies, as wellas changes to the system itself, and the results of otherrecent audits. Within an organization, internal auditsmay be organized on a regular basis for management orbusiness purposes.



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Preparing the Audit

The audit plan should:

C Be approved by the clientC Be communicated to the auditors and auditeeC Be designed to be flexible (permitting changes)C Define the place and date of the auditC Include the audit objectives and scopeC Stipulate reference documentsC Identify audit team members and assign tasksC Define the language of the auditC Define the duration of the auditC Provide an anticipated auditee meeting scheduleC Identify confidentiality requirementsC Stipulate audit report distribution and date

The working documents, facilitating the audit, mayinclude:

C Flow chartsC Checklists and reporting forms



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Flow Chart Usage

The starting point for a system or major process audit isan important decision. If there is sufficient audit time, agood place to start is at the beginning. If the finalresults are of more importance and the auditor alreadyhas some knowledge of the activities, beginning at theend may be desirable. These widely used and highlyeffective forms of field investigative activities are calledtracing (or tracking).

The use of flow charts is often helpful with either traceforward or trace backward audits. If the needed flowcharts exist, they can be requested and followed foraccuracy and compliance. If they do not exist, theauditor may find it very helpful to create one during thetracing process. A flow chart is an effective documentfor evidence of compliance or adequacy. A comparisontable of auditing approaches is shown in the Primer.



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Checklists

A checklist is one of the distinguishing features betweenan audit and other less formal methods of performancemonitoring. The checklist serves as a guide to eachmember of the audit team, in order to ensure that the fullscope of the audit is adequately covered. It alsoprovides a place for recording data collected during thefield work. Checklist questions are not open endedquestions to be discussed in the field; rather they arethe individual facts necessary to form conclusions.Checklist questions must be precise, measurable, andfactual.



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Executing the Audit

The Opening Meeting

C Introduces the audit team to the auditee'sC Reviews the scope and the objectives of the auditC Summarizes the methods and proceduresC Establishes communication linksC Discusses the resources and facilities neededC Sets the time and date for the closing meetingC Clarifies any unclear details of the audit plan

Evidence Collection

C InterviewsC Physical evidenceC Examination of documents and recordsC Observation of activities and conditions



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Executing the Audit (Continued)

Interviews

Most of the information obtained during the audit will beby questioning auditee personnel. The auditor shoulddetermine not only compliance, but also how adequatethe compliance is. Most of the questions should allowfor some discussion and probing rather than just asimple “yes” or “no” response. This gives the auditeethe opportunity to elaborate and possibly provide othersupporting documentation or evidence.



III-47 (309)


Physical Evidence

Verification of formal controls such as methods,practices, procedures, policies and documentation isdone through field work. The auditor(s), accompaniedby the designated auditee representative, physically goto the facility or location where the production or serviceis occurring (plant floor, department, or customerservice area). The act of verification by the auditor isthe most important aspect in the performance of theaudit.



III-47 (310)


Verifying Documents and Records

In the performance of the audit, any supporting auditeedocumentation should be noted beneath thecorresponding checklist question. The auditor mayreview the documentation at the time it is presented. Itis best if supporting documentation has been previouslyobtained and reviewed during the audit planning phase.When recording document data, the following itemsshould be included:

C Location of the document sampledC Identification of the record or documentC The time and dateC Any observations which may affect the document



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Observation Techniques

Audit observation is the act of recognizing andconfirming a fact or occurrence by some objective orsubjective measurement. Particular attention should begiven to the recording of details that may potentiallyresult in either positive or negative audit findings.These observations should be traceable to time, locationand conditions under which they were made. Wheneverpossible, the auditor should obtain an acknowledgmentfrom the auditee escort

All audit observations should be:

C Documented and reviewedC Clear and conciseC Supported by evidenceC Identified in terms of the specific requirementsC Reviewed by the lead auditor with the auditeeC Acknowledged by the auditee’s management



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Closing Meeting with Auditee

At the end of the audit, prior to preparing the auditreport, a meeting with the auditee's senior managementshould be held, to present audit observations to thesenior management in such a manner that they clearlyunderstand the results. The lead auditor should presentobservations and the audit team's conclusions.Records of the closing meeting should be kept.



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Audit Report Preparation

The lead auditor is responsible for the accuracy andcompleteness of the audit report. The audit reportshould:

C Reflect both the tone and content of the auditC Be dated and signed by the lead auditorC Contain the scope and objectives of the auditC Contain details of the audit planC Identify the audit teamC Identify the auditee's representativeC List audit datesC Identify the specific organization auditedC Identify the reference documentsC Describe observations of nonconformitiesC Express a judgment of the extent of compliance

Report Distribution

The audit report should be sent to the client by the leadauditor. It is the client's responsibility to provide theauditee's senior management with a copy.



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Audit Completion

The audit is completed upon submission of the auditreport to the client.

Corrective Action Follow-up

The auditee is responsible for determining and initiatingthe corrective action needed to correct the cause of anonconformity.

Corrective action, and subsequent follow-up audits,should be completed within a time period agreed to bythe client and the auditee, in consultation with theauditing organization.

Record Retention

Audit documents should be retained according to theagreement between the client, the auditing organizationand the auditee, and in accordance with any regulatoryrequirements.



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Glossary of Audit Terms

Appraisal: A form of the quality system audit, normallyconducted to examine the total quality programeffectiveness and implementation.

Assessment: Another term for the quality audit,sometimes used to indicate a less formal means ofmeasuring and reporting than the full audit.

Audit: An independent, structured, and documentedevaluation of the adequacy and implementation of anactivity to specified requirements.

Auditee: The organization to be audited. The auditeemay be another group within the firm, or it may be anentirely separate organization.

Auditor: A person who is qualified and authorized toperform all or part of an audit.



III-50 (316)

Glossary of Audit Terms (Continued)

Client: The person or organization requesting orsponsoring an audit.

Examination: A measurement of goods or services todetermine conformance to some specified requirement.

Finding: An audit conclusion which identifies acondition having a significant adverse effect on thequality of the goods or services produced.

Follow-up audit: A subsequent audit which verifies thatsome corrective action has been performed asscheduled, and determining that the action waseffective.

Lead auditor: A person who is qualified and authorizedto direct an audit.

Objective evidence: Qualitative or quantitativeinformation, records, or statements of fact which arebased on observations, measurements, or tests that canbe verified.



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Glossary of Audit Terms (Continued)

Observation: An audit observation identifies a conditionwhich is not yet causing a serious degradation ofquality.

Process audit: The evaluation of a process operationagainst established instructions and standards. It alsomeasures the effectiveness of process instructions.

Product audit: The examination, inspection, or testingof a product which has been accepted previously for thecharacteristics being audited.

Quality system audit: A structured activity performed toverify that one or more portions of a quality program areappropriate and being implemented effectively.

Quality (system) survey: An activity conducted prior toa contract award and used to evaluate the overall qualitycapability of a prospective supplier or contractor.

Verification: The act of reviewing, inspecting, testing,checking, auditing, or otherwise establishing anddocumenting whether items, processes, services ordocuments conform to specified requirements.


III. QUALITY SYSTEMSCOST OF QUALITY

III-52 (318)

Selling Costs

General andAdministrative Costs

Profit

Fixed andMiscellaneous Expenses

Indirect Labor

Indirect Materials

Direct Labor

Direct Materials

Area ofConcentration of a QualityCost Program

Revenues

Overhead Cost

Prime Cost

Cost of GoodsProduced

Cost ofGoods Sold

Traditional Cost Concept

Most companies utilize financial reports which comparethe actual costs to the budgeted costs. The differenceis called a variance and, if significant, may promptmanagement action. Shown below is a schematic of atraditional corporate financial structure which indicatesareas where a quality cost program will operate.



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Origin of Quality Cost Measurements

In the 1950s and 1960s, some enlightened companiesbegan to evaluate and report quality costs for a varietyof reasons.

What resulted was a method of defining and measuringquality costs and reporting them on a regular basis(monthly or quarterly). The quality cost reports becamea vehicle to:

C Determine the status of cost control efforts, and

C Identify additional opportunities for reducing thecost of quality by systematic improvements

Since the costs of quality are high (some authorities say15% to 25% of total costs), the opportunity forimprovement should easily capture the attention ofmanagement.



III-54 (320)

Quality Cost Categories

Prevention costs: The costs of activities specificallydesigned to prevent poor quality in products orservices.

Appraisal costs: The costs associated with measuring,evaluating, or auditing products or services to assureconformance to quality standards and performancerequirements.

Failure costs: The costs resulting from products orservices not conforming to requirements orcustomer/user needs.

C Internal failure costs: Failure costs which occurprior to delivery or shipment of the product, or thefurnishing of a service, to the customer.

C External failure costs: Failure costs which occurafter deliver or shipment of the product, or during orafter furnishing of a service, to the customer.



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Three Levels of Product Costs



III-56 (322)

Costs Category Examples

Listings of prevention, appraisal, and failure costs areshown on Primer pages III - 56/57.



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Optimum Quality Costs

The total quality curve is depicted in the theoreticalmodel below (Juran, 1999). The minimum level of totalquality costs occurs when the quality of conformance is100%. The model illustrates that as prevention andappraisal costs increase, the failure costs will decreaseuntil an optimum point is reached.

Most companies initially find that they are woefully tothe left of the optimum quality cost point.



III-58 (324)

Optimum Quality Costs (Continued)

Listed below are some typical quality cost ratios forAmerican companies.

Cost Category Percent of TotalPreventionAppraisal

Internal FailureExternal Failure

0 - 510 - 5020 - 4020 - 40



III-58 (325)

Total Cost of Quality

Total Failure

Appraisal

Prevention

Program Start

Sales

Time

1 2 3 4 5 6 7 8 9 1002468

1012141618202224262830

Internal

Failure

Optimum Quality Costs (Continued)

Hypothetical Quality Costs Trends Over Time

The implementation of preventative measures to controlquality often take time. Appraisal measures are initiallyundertaken which cause internal failures to increase butexternal failures (and total failures) to decrease.However, a small increase in prevention methods willnormally create a large decrease in total quality costs.



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Quality Cost Improvement

C Define the company quality goals and objectives:

C The relative position desired among competitorsC The type of long-term quality reputation desired

C Translate the quality goals into quality requirementswhich represent the real workplace.

C Develop realistic programs and projects consistentwith the company goals

C Set up quality cost categories of prevention,appraisal, and failure to accumulate costs

C Arrange for accounting to collect and presentquality costs

C Analyze the quality cost data for major improvementcandidates

C Utilize the Pareto principle to isolate specific vitalareas for investigation.



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Quality Cost Comparison Bases

Quality costs should be related to two or threecomparisons bases. Some examples are:

C Labor bases:C Total direct labor (worked)C Standard labor (planned)

C Manufacturing cost bases:C Shop cost of outputC Direct laborC Direct materialC Indirect costs

C Manufacturing cost of outputC Including the total shop cost of output C Production engineering costs and expensesC Provision for complaintsC Packing and shipping

C Sales bases:C Net sales billedC Contributed value

C Unit bases:C Quality costs, dollars per unit of production

C Quality costs related to production



III-61 (328)

Typical Quality Cost ReportQuality Cost Report for September 2006

Dollars ($) Percent of TotalPrevention Costs

Quality Control Administration 5250 2.1Quality Control Engineering 14600 5.9Other Quality Planning 1250 0.5Training 2875 1.2

Total Prevention 23975 9.7Appraisal Costs

Inspection 55300 22.3Test 23800 9.6Vendor Control 1700 0.7Measurement Control 1950 0.8Materials Consumed 375 0.2Product Quality Audits 800 0.3

Total Appraisal 83925 33.8Internal Failure Costs

Scrap 66500 26.8Repair, Rework 1900 0.8Vendor Losses 2500 1.0Failure Analysis 4000 1.6

Total Internal 74900 30.1External Failure Costs

Failures - Manufacturing 14500 5.8Failures - Engineering 7350 3.0Failures - Sales 4430 1.8Warranty Charges 31750 12.8Failure Analysis 7600 3.1

Total External 65630 26.4Total Quality Costs 248430 100.0Bases

Direct Labor 94900 8.1Conversion Cost 476700 40.8Sales 1169082 100.0

RatiosInternal Failure Costs to Direct Labor 78.9Internal Failure Costs to Conversion 15.7Total Quality Costs to Sales 21.3



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Advantages of a Quality Cost System

C Provides a single overview of qualityC Aligns quality and company goalsC Provides a problem prioritization systemC Provides a way to distribute quality costsC Improves the effective use of resourcesC Provides emphasis for doing the job rightC Helps to establish new product processes



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Limitations of a Quality Cost System

C Cost measurement does not solve quality problemsC Quality cost reports do not suggest specific actionsC Quality costs are susceptible to mismanagementC It is difficult to match effort and accomplishmentsC Important costs may be omitted from cost reportsC Inappropriate costs may be included in cost reportsC Many costs are susceptible to measurement errors



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Other Quality Cost Pitfalls

C Perfectionism in the numbers

C Other data pitfalls

C Inclusion of non-quality costs

C Implications of reducing quality costs to zero

C Reducing quality costs but increasing totalcompany costs

C Understatement of quality cost

C Inconsistency of measurement



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1.8

1.2 1

0.2

0.8

0.5 0.2

3

3.4

8.59

8

7

6

4

5

3

2

1

0

Pareto Analysis of Quality Costs

Pareto analysis is widely used to analyze quality costs;particularly failure costs. Corrective action, in the formof problem solving techniques and prevention methods,is undertaken on the major defect categories first.

Problem Categories

Pareto Analysis of Cylinder Block Scrap



III-65 (333)

AllBad All

GoodAll

Bad

LSL USL

Traditional Concept Y

L

Target

LSL USL

Taguchi Concept

Taguchi's Loss Function

Taguchi contends, as product characteristics deviatefrom the normal aim, losses increase according to aparabolic function.

Traditional and Taguchi Loss Concepts

Formula: L = K (Y - T)2

Where: L = loss in dollars T = target value K = cost coefficient Y = actual quality value


III. QUALITY SYSTEMSQUALITY TRAINING

III-66 (334)

Quality Training

Management must be aware of the importance of havingthoroughly trained employees to perform operationswhere product and service quality are at stake. Goodtraining is a planned and ordered process where thetrainee is guided along a path of learning. This meansthat a supervisor must ensure that those who are totrain new employees are themselves clear about dutiesand that the process of training is properly supervised.

The quality engineer may be involved in eitherdepartmental development training or training for theentire plant workforce. The need for training may arisefrom direct management requests, self perceived needs,or from workforce performance.



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Training to Reduce Defects

When employees attempt to perform tasks for whichthey have not been adequately trained, qualityobjectives cannot be economically reached. Propertraining reduces both errors and costs. There are threegeneral conditions that lead to workmanship defects:lack of skill or training, misunderstanding instructions,and carelessness.



III-67 (336)

Training for Customer Interface

Elements of a good program include:

C Teach skills that are distinctive to the companyC All employees are treated as career employeesC Regular retraining is requiredC Time and money are allocated for trainingC Provide on the job trainingC Teach new skillsC Use training for strategic changesC Training is not cut when times are toughC The customer interface level is involvedC Training is used to teach vision and values



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Training Needs Assessment

Delineation of training needs must come before thepreparation of course content, the selection of materialsand aids, the teaching methods, and even before anyother training program planning. A formal trainingneeds analysis (TNA) should be conducted to assessthe gaps in current performance and ideal performance.The TNA will collect information for evaluation on:

C Current activities and performanceC Future activities and ideal performance

If a gap in performance exists, the decision should bemade to:

C Provide for trainingC Select the proper subject content for trainingC Allocate the necessary resources for trainingC Determine the number of employees to be trainedC Determine the amount of training to be providedC Collect information on the effectiveness of training

(Smith, 1987)



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Training Needs Assessment (Continued)

The procedures and the amount of information for eachTNA can vary substantially. Smith (1987) has developeda three step TNA procedure:

C Surveillance: This is having one’s “ears” to theground by using a variety of documents on the stateof the company.

C Investigation: Some of the data gatheringtechniques in this step are:

C Personal observationsC Interviews: group, individualC Questionnaires: checklists, ratingsC Records of activitiesC Work samplesC Performance appraisalsC Work studiesC Psychological tests

C Analysis: This is the detailed analysis of the datacollected.



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Training Guidelines

There are several broad guidelines that should beconsidered in developing an industrial training program.

C Continuously educate all organizational levels in theskill, knowledge, and attitudes needed to do qualitywork.

C Place a great emphasis on teaching skills such asthe ability to cooperate, to share a mutualunderstanding, to work together, and other basicsocial skills.

C Provide for continuous learning. Training is nevercomplete.

C Include all levels of personnel from the janitor to thepresident. If the training involves managementcommitment, start there first.



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Training Principles

Training is the primary method used by management todevelop increased capability in job performance. Thereare some underlying principles which can be used toenhance the effectiveness of training.

C Objectives should be expressed in performanceterms as much as possible.

C Learners should receive immediate feedback inunderstandable terms about the correctness of theirresponses.

C Training programs must be audited and validated,then modified if they do not achieve their objectives.

C Training programs must be adapted to theindividual as much as possible.

C Learners must be involved by having the materialexpressed in ways that are directly relevant.



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Training EffectivenessTraining employees is a costly venture for any company.In addition to the dollar costs of the training consultant,the per person cost of the employee must beconsidered. For a two day in-house training program,the costs include:

Trainer: Workshop cost per day, includingtransportation, lodging, and expenses

Employees: The daily salary or hourly base for eachemployee at the workshop

Temps: The cost to provide a replacement for a regularemployee who is at the workshop

Room: Cost of the room, including refreshments

Preparation time: Costs of salary and hourly employeesin preparing for the workshop

TNA costs: The costs involved in conducting the TNAwhich led to the workshop. These costs should includematerials and travel.

Juran (1993) states, “The ultimate measure of the valueof training is the degree of success in applying theconcepts.”



III-72 (342)

Training Effectiveness (Continued)

There are several simple evaluations of trainingeffectiveness that are frequently used:

C “Smile” evaluations provide a reaction to thetrainer’s impact, but with little guarantee thatlearning can be transferred to the job.

C A post test exam of the workshop tests a number ofobjectives at the end of the workshop.

C A third simple method to test for effectivenesswould be to have a pre-test and a post-test. Thepre-test is conducted at the start of the workshop,with the post-test conducted at the end of theworkshop. The difference in test scores would bean indication of effectiveness.



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Training Deterrents

Many people have a resistance to learning new thingsand training specialists need to be aware of thistendency. Trainee attitudes are extremely important inlearning ability and speed. Employees are sometimesreticent about asking questions because of fear ofappearing dumb. Fear and anxiety are ever presentdeterrents to learning and can freeze performance.

Sympathetic and supportive relationships betweeninstructors and learners are essential to reduce fear andanxiety. Such relationships should include aconstructive tolerance for mistakes.


III. QUALITY SYSTEMSQUESTIONS

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3.2. Quality policies are principally issued by management to:

a. State the position of the company on qualityb. Ensure people are reminded about qualityc. Provide detailed instructions in regard to qualityd. Ensure customer satisfaction

3.5. Which of the following is the best definition of configurationmanagement?

a. The collection of all product related information and activitiesb. A documentation systemc. A record keeping system for order change d. A product production management plan

3.7. The percentages of total quality cost are distributed as follows:prevention 12%; appraisal 28%; internal failure 40%; and externalfailure 20%. One would conclude:

a. More money should be invested in preventionb. Expenditures for failure are excessivec. The amount spent for appraisal seems about rightd. Nothing

Answers: 3.2. a, 3.5. a, 3.7. d



III-76 (345)

3.10. When an auditor or group independent of the company, thecompany's customer, suppliers or any party involved with thecompany conducts an audit, that audit is called which of thefollowing?

a. An internal auditb. An external auditc. A system auditd. A third-party audit

3.11. The short-term effect of a dramatic increase in prevention costswould be:

a. An increase in total quality costsb. A decrease in appraisal costsc. An increase in external failure costsd. A decrease in internal failure costs

3.17. The follow-up on the need for corrective action, identified in an auditreport, is most clearly the responsibility of which of the following?

a. The client's upper managementb. The auditee's upper managementc. The lead auditord. The operating area in which finding was made

Answers: 3.10. d, 3.11. a, 3.17. b



III-77 (346)

3.21. A checklist will often permit the audit team to achieve which of thefollowing?

a. A flexible audit formatb. The identification of noncritical processesc. The effective use of timed. The determination of corrective action steps

3.23. Which of the following is the best method for developing materials fora training program on the gaps in performance?

a. Secure a workshop trainerb. Review a record of activitiesc. Set up a one shot case studyd. Allocate employees for training

3.26. The purpose of a quality manual is to:

a. Use it as a basis for every quality decisionb. Standardize the quality methods and decisions of a companyc. Provide a written basis for rejection of lotsd. Make it possible to handle every situation in exactly the same manner

Answers: 3.21. c, 3.23. b, 3.26. b



III-78 (347)

3.35. In order to evaluate the internal effectiveness of the customer orderplanning function, which of the following audits is most appropriate?

a. Product auditb. Process auditc. Management auditd. System audit

3.36. Which of the following elements are NOT a basic part of configurationmanagement?

a. Configuration controlb. Configuration auditsc. Configuration accountingd. Configuration design

3.37. If shop floor employees are exposed to new assembly techniques, thebest instructional proficiency evaluation would be:

a. Observation of performance resultsb. Testing of assembled productsc. Oral and written testing of the operatorsd. Training evaluation by the instructed employees

Answers: 3.35. b, 3.36. d, 3.37. a


IV. PRODUCT AND PROCESS DESIGN

IV-1 (348)

THERE IS NO SUCH THING ASABSOLUTE CERTAINTY, BUTTHERE IS ASSURANCESUFFIC IENT FOR THEPURPOSE OF HUMAN LIFE.

JOHN STUART MILL 1859


IV. PRODUCT AND PROCESS DESIGNQUALITY CHARACTERISTICS

IV-2 (349)

Product and Process Design

Product and Process Design is presented in thefollowing topic areas:

C Quality characteristicsC Design reviewC Technical drawingsC Design verificationC Reliability and maintainability



IV-2 (350)

Classification of Quality Characteristics

Quality characteristics are the desired customer-basedproperties for a product or service. Companies also usequality characteristics to define, for the consumer, theproduct or service a company is offering. Qualitycharacteristics are used to establish productdifferentiation in the marketplace. Often, these qualitycharacteristics define the company as well as theproduct.

C Products: Reliability, safety, ease of use, aesthetics,performance, and durability.

C Service: Promptness, knowledge, credibility,access, satisfaction, and accuracy.

Companies use quality characteristics to define theirstrategic vision with their customers.



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Product Quality Characteristics

Topic ExampleReliability Mercedes BenzSafety BMW/VolvoEase of use Voice activated cellular phones Aesthetics Lincoln - What a luxury car should bePerformance Pontiac - We build excitementDurability Maytag - World’s loneliest repair man

Service Quality Characteristics

Topic ExamplePromptness Roto-Rooter - 1 hour emergency serviceKnowledge Most law firm adsCredibility A spokesperson with integrity

Over 100 years experienceAccess H&R Block (25 zillion offices)Satisfaction Hotels (100% satisfaction guarantee)

Burger King - Have it your wayAccuracy First time, every time

Initial quality characteristics come from two sources.One source is from the company's strategic plan orvision. The second source is the customer.



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Product and Process Characteristics

Quality characteristics are used to develop product andprocess characteristics. Quality characteristics aremost often too fuzzy to provide direct input into thedesign process. Product and process designers needwell-defined criteria to proceed with a design project.Changing quality characteristics into product andprocess characteristics is known as developing thedesign specification. Examples are illustrated below:

Product /ProcessCharacteristic

Design Specification

C Timeliness/PromptnessC Normal serviceC Emergency service

24 hours a dayEvery day of the yearService within 1 hour

C PortabilityC LightweightC Fits in pocket

less than 8 pounds5 ounces1 x 3 x 4 inches



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Characteristic Classifications

Often, product features are graded or evaluated at ornear the time of design as to relative importance. Thesecharacteristics may be measured by attribute or variabletechniques and may be somewhat independent of defectcategories.

This system requires a determination of the importanceof individual features or properties of a product orservice. The distinction can be as simple as satisfactoryor not satisfactory. It can also be as complex as anumber of classes of seriousness such as: critical,major, minor, or incidental.



IV-5 (354)

Characteristic Classifications (Cont’d)

Consider the following matrix.

Characteristic Critical Major Minor Incidental

Current to BOK UAligned to BOK U< 3 minor errors/Section UCorrect answers to questions URing metal opens easily UDurability of binder UConsistency of font size U

According to Gryna (2001), quality characteristics mayalso include sensory characteristics. One importantportion of this application are visual characteristics.Some approaches to define limits in this area include:

C Photographs of acceptable limitsC Physical standards for assigned limitsC Assigned inspection conditions


IV. PRODUCT AND PROCESS DESIGNDESIGN REVIEW

IV-6 (355)

Design Inputs

It is important to recognize that a design is intended tosatisfy customer needs. The customer is a mixture ofboth internal and external users. The internal customerprovides the strategic and product requirements of thecompany and the external customer provides theirspecific product requirements.

Examples of internal customers and their requirementsare detailed below:

Internal Customer RequirementsSales Cost and quantityQuality Reliability and quality

levelsTop management Profit and gross marginManufacturing Manufacturability

requirementsService Serviceability

requirements



IV-6 (356)

Design Inputs (Continued)

Examples of external customers and their requirementsare illustrated below:

External Customer RequirementsEnd user Quality characteristicsDealers, distributors Service, storage, and

deliveryRegulatory agencies Safety, emissions

The early process/product definition phase is oftenreferred to as the design concept phase. During thisphase, quality characteristics (ideas) are turned intowritten process or product design specifications. Onequality tool used to translate customer ideas into designspecifications is quality function deployment (QFD).



IV-7 (357)


Both ISO 9001:2000 and ISO/TS 16949:2002 require acompany to control design inputs related to theproduct., including applicable statutory and regulatoryrequirements.

It would be impractical (as well as almost impossible) forthe design procedure to provide all details in developingthe design specification. Usually, the design procedureincludes a design input checklist.

Example Design Input Checklist

Customer drawingsCustomer contractMarket research resultsTooling, gages, fixtures, facilitiesQuality system requirements Training requirementsSales (volume) projectionsManufacturability requirementsSafety requirementsProduct performance requirementsQuality requirementsPrice, cost, gross marginWarranty, repair, return history



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Each area of the checklist is reviewed to develop thedesign specification. An essential success factor isensuring that the design specifications are quantifiedwith a tolerance. An inability to quantify a designspecification usually means that the requirements arenot well understood. Additionally, some areas may needto be determined later. Both of these issues create risksin the design process.



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Design Review

Design specifications may be developed with aniterative approach, in phase, or in stages. An exampleof the sequence of design specifications developmentis:

C SystemC SubsystemC Module (printed circuit board, software, etc.)C Component or material

Once the design specification phase starts to takeshape, a design review should take place. A designreview is usually considered mandatory when thedesign specification (concept phase) is complete, orcomplete enough to assign engineers to the task ofmaking the design specifications real prototypes.



IV-8 (360)

Design Review (Continued)

A design review is a documented, comprehensive, andsystematic examination of the design progress toensure it is capable of fulfilling the design inputs andthe design specification. The review communicatesdesign project status, progress, results, and changes,and also identifies potential and real areas of risk. Thedesign review process is established by managementpolicy or customer specifications, or both.

Often a product design requires trade-offs betweenconflicting aspects of reliability, maintainability, cost,weight, ease of manufacture and performance. The finaldecision on a product design, therefore, dependsheavily upon the experience of members of the designteam.



IV-9 (361)


The membership and responsibilities of a typical designreview committee are shown below:

Member Review Phase Responsibility

I II III IV V

Chairperson (of designfunction) X X X X X Calls and conducts reviews;

issues all reports

Design engineer (of thisproduct) X X X X Prepares and presents the design

approach

Independent designengineer X X X X Reviews and verifies adequacy of

design

Customer or marketingrepresentative X X X X X Ensures that the customer's

viewpoint is represented

Reliability manager orengineer X X X X X Evaluates the design for reliability

Materials/stress engineer X Verifies stress calculations andmaterial usage

Human factors/safetyengineer X X Ensures product safety in use

and manufacture

Manufacturing engineer X X X Ensures cost effectivemanufacture

Quality engineer or qualityrepresentative X X X X Reviews inspection and test

capabilities

Test engineer X X Presents test procedures andresults

Others As required



IV-10 (362)


Each review committee has a designated chairperson(not the design engineer) who has general managementexperience, design understanding, and technicalknowledge of the various disciplines involved. Thedesign review considers all important factors in thecreation of a mature product design.

C Are customer performance requirements met?C Is the design as simple as possible?C Are proven components and configurations used?C Are manufacturing tolerances adequate?C Is the manufacturing process capable?C Are approved parts used in all practical cases?C Are environmental requirements met?C Are operational conditions considered?C Are maintainability features present?C Are there provisions for testing and inspection?C Have potential failure modes been analyzed?C Has a worst-case analysis been conducted?



IV-10 (363)


The design process goes through several phases.Examples of typical design phases and purposes are:

Design Phase PurposeConcept Acquire and document design

inputs Design Convert design inputs into

documented specificationsPrototype Convert design specifications into

hardwarePre-production Pilot runs, capability analysis

studies and confirmationDeployment Full production Final Determine the success of meeting

the design inputs

Design reviews should be conducted at the end of eachphase. It is important that relevant stakeholders attendthe design review. There should be a consensus amongthe relevant stakeholders, that each phase has beensuccessfully completed, and the project is ready tomove forward to the next step. A major component ofdesign reviews is the qualification process, which fallsinto two general categories, verification and validation.



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Design for Six Sigma (DFSS)

Design for six sigma (DFSS) is the suggested method tobring order to product design. Hockman (2001) and Suh(1990) noted that 70% to 80% of all quality problems aredesign related. Emphasis on the manufacturing sidealone will concentrate at the tail end of the problemsolving process. The emphasis should be at the frontend. Problem solving at the downstream end is morecostly and time consuming than fixing it at the source.



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Design for Six Sigma (Continued)

One of the ways to increase revenues must includeintroducing more new products to sell to customers.Cooper (1993) states that new products account for alarge percentage of company sales (40%), and profits(46%). Of course, not every new product will survive.Two studies provide some statistics.

Development Items Study A Study BNew product ideas 7 11Products entering

development4 3

Products launched 1.5 1.3Successful products 1 1

The table indicates that a large amount of ideas areneeded. These ideas are sorted, screened, andevaluated in order to obtain the most feasible options toenter the development stage, pass into the launch stage,and become successful products.



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Cooper (1996) provides more details of how winningproducts are obtained:

1. A unique, superior product: This is a product withbenefits and value for the customer.

2. A strong market orientation: An understanding ofcustomer needs and wants exists.

3. Predevelopment work: Up front activities such asscreening, market analysis, technical assessment,market research, and business analysis are vital.

4. Good product definition: A company must havegood product and project definition.

5. Quality of execution: The development processmust be executed with the proper amount ofcorrectness.

6. Team effort: Product development is a team effortthat includes R&D, marketing, and operations.

7. Proper project selection: Poor projects must bekilled at the proper time.



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8. Prepare for the launch: A good product launch isimportant and resources must be available forfuture launches.

9. Top management leadership: Management mustprovide guidance, resources, and leadership.

10. Speed to market: Product development speed isthe weapon of choice, but sound managementpractices should be maintained.

11. A new product process: This is a screening(stage gate) process for new products.

12. An attractive market: An attractive market makesit easier to have a successful product.

13. Strength of company abilities: The new productprovides a synergy between the company andinternal abilities.



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There are many product development processes tochoose from. Rosenau (1996) suggests that the former“relay race” process (passing the product frommarketing to engineering to manufacturing and backthrough the loop) is obsolete. Multi-functional teamactivities involving all departments are necessary foreffectiveness and speed to market. The process iscomprised of 2 parts: a “fuzzy front end” (ideageneration and sorting) and new product development.



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The complete NPD process includes 5 activities:

C Concept study: A study is needed to uncoverunknowns about the market, the technology, or themanufacturing process.

C Feasibility investigations: There is a need todetermine the limitations of the concept. Find out ifthe unknowns are resolvable.

C Development of the new product: This is the startof the NPD process. This includes thespecifications, needs of the customer, targetmarkets, and determination of key stage gates.

C Maintenance: These are the post delivery activitiesassociated with product development.

C Continuous learning: Project status reports andevaluations are needed to permit learning.



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A stage gate process is used by many companies toscreen and pass projects as they progress throughdevelopment stages. The gate is a management reviewof the particular stage in question. It is at the variousgates that management should make the “kill” decision.Too many projects are allowed to live beyond theiruseful lives and clog the system.



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In the area of new product management, Crawford (1997)and Cooper (1993) describe some commonly acceptednew product terms:

1. New-to-the-world products: These are inventions,and discoveries like camera phones, and laserprinters.

2. New category entries: These are company productsthat are new to the company.

3. Additions to product lines: These are extensions ofthe organization’s existing product line.

4. Product improvements: Current products madebetter.

5. Repositionings: Products that are retargeted for abrooder use.

6. Cost reductions: New products are designed toreplace existing products, but at a lower cost.



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Treffs (2001) presents a four step design model:

C Identify: Use team charter, voice of customer, QFD,FMEA, and benchmarking

C Design: Emphasize CTQs, identify functionalrequirements, develop alternatives, evaluate andselect

C Optimize: Use process capability information, astatistical tolerancing approach, robust design, andvarious six sigma tools

C Validate: Test and validate the design



IV-15 (373)


Simon (2000) provides a 5 step DMADV process for sixsigma design. The DMADV method for the creation of anew product consists of the following steps:

C Define: Define the project goals and customerneeds

C Measure: Measure and determine customer needsand specifications

C Analyze: Determine the process options

C Design: Develop the details for producing to meetthe customers’ needs

C Verify: Verify and validate the design



IV-16 (374)

Need Statement of Problem

Conceptual Design

Selected Schemes

Embodiment of Schemes Detailing Working

Drawings, etc

Analysis of Problem


The design engineer will select a design process. Atypical design process is depicted from Cross (1994):

The French Design Model

The designer will capture the needs, provide analysis,and produce a statement of the problem. Theconceptual design will generate a variety of solutions tothe problem. This brings together the elements ofengineering, science, practical knowledge, productionmethods, and practices. The detailing step consolidatesand coordinates the fine points of producing a product.

The use of six sigma tools and techniques must beintroduced in a well-thought-out manner at variousphases of the project.



IV-17 (375)

Design Using QFD

Quality function deployment is a tool that is sometimesreferred to as the “voice of the customer,” or as the“house of quality.”

By describing the product in the language of theengineer, along the top of the house of quality, thedesign team lists those engineering characteristics thatare likely to affect one or more of the customerattributes.

Hauser (1988) states, “by comparing weightedcharacteristics to actual component costs, creativedesign teams set priorities for improving components.”It is important to focus on customer satisfaction valueswhen considering engineering characteristics.Increasing one engineering characteristic may have anegative impact on another engineering characteristic.



IV-17 (376)

Design Using QFD (Continued)

The house of quality’s distinctive roof matrix helpsengineers specify various engineering features thathave to be improved collaterally,” (Hauser, 1988).

The foundation of the house contains the benchmarkingor target values. The values indicate “how much” foreach of the measures.

The right-hand wall of the house in indicates thecustomer competitive assessment, and other factorsaffecting the customer. The competition comparisonshows graphically the relative weights.

The elements which are included in the house arecustomized to the particular product or service beingdescribed. When reviewing a completed house, theeasiest method is to look at each area separately.



IV-18 (377)


An Expanded Example of QFD



IV-19 (378)

Engineeringcharacteristics

Productionrequ irements

Key processoperations

Partscharacteristics

House ofquality

Productionplanning

Processplanning

Partsdeployment


After setting the primary design characteristics, Hauser(1988) suggests using the “hows” from the house ofquality as the “whats” of another house that depictsdetailed product design. This process is repeated witha process planning house and then production planninghouse. In this way, the voice of the customer is carriedthrough from design to manufacturing.

Linked House of Quality Example



IV-20 (379)

A Robust Design Example

In 1953, a mid-size Japanese tile manufacturingcompany was having a serious problem with their $2mkiln. The problem was extreme variation in tiledimensions. The stacked tiles were baked inside atunnel kiln as shown below. Tiles on the outside of thestack tended to have a different dimension and exhibitedmore variation than those on the inside of the stack.

Figure 4.1 A Schematic of a Tile Tunnel Kiln

The cause of variation was readily understandable.There was an uneven temperature profile inside the kiln.To correct the cause, the company would have toredesign the kiln. This company's budget didn't allowfor such costly action, but the kiln was creating atremendous financial loss.



IV-20 (380)

A Robust Design Example (Continued)

Although temperature was an important factor, it wastreated as a noise factor. This meant that temperaturewas a necessary evil and all other factors would bevaried to see if the dimensional variation could be madeinsensitive to temperature. People having knowledgeabout the process were brought together. Theyidentified seven major controllable factors which theythought could affect the tile dimension.

After testing the seven factors over specified levelsusing an orthogonal design, the experimentersdiscovered that limestone content was the mostsignificant factor. It was found that by increasing thelimestone content from 1% to 2% with slightly betterlevels for other factors, the percent warpage could bereduced from 30% to less than 1%. Limestone was thecheapest material in the tile mix. Moreover, they foundthrough the experimentation that they could use asmaller amount of amalgamate (the most expensivematerial) without adversely affecting the tile dimension.This is a classic example of improving quality, reducingcost, and drastically reducing the number of defectivesat the same time.



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Robust Design

The United States has coined the term “TaguchiMethods” to describe Dr. Taguchi’s system ofrobustness for the evaluation and improvement of theproduct development.

Robust design processes are one of the more importantdevelopments in design processes in recent years. Thisprocess can produce extremely reliable designs bothduring manufacture and in use. Robust design uses theconcept of parameter control to place the design in aposition where random “noise” does not cause failure.



IV-21 (382)

Products/Procedures

Noise Factors

ResponseSignal Factor

Control Factors

Robust Design (Continued)

The diagram below describes the process of robustdesign.

The concept is that a product or process is controlled bya number of factors to produce the desired response.The signal factor is the signal used for the intendedresponse. The success of obtaining the response isdependent on control factors and noise factors.



IV-22 (383)


Control factors are those parameters that arecontrollable by the designer.

Control factors are sometimes separated into thosewhich add no cost to the product or process and thosethat do add cost. Since factors that add cost arefrequently associated with selection of the tolerance ofthe components, these are called tolerance factors.Factors that don’t add cost are simply control factors.

Noise factors are parameters or events that are notcontrollable by the designer. These are generallyrandom, in that only the mean and variance can bepredicted. Noise factors in furnace design might be:

C Line voltage variationsC Outside temperatureC Parallax errors in dial setting

The function of the designer is to select control factorsso that the impact of noise factors on the response areminimized while maximizing the response to signalfactors. This adjustment of factors is best done usingSDE.



IV-22 (384)


Phadke (1989) describes some key robust designprinciples:

C Concept design: Concept design is the selection ofthe process or product architecture based ontechnology, cost, customer, or other importantconsiderations. This step depends heavily on theabilities and creativity of the designer.

C Parameter design: During the parameter designstage the design is established using the lowestcost components and manufacturing techniques.The response is then optimized for control andminimized for noise.

C Tolerance design: If the design doesn’t meetrequirements, the designer must consider moreexpensive components or processes that reducethe tolerances. The tolerances are reduced until thedesign requirements are met.



IV-23 (385)

Concept DesignIn the development of a new product, the productplanning department must determine the functionsrequired. The designer will have a set of requirementsthat a new product must possess. The designer willdevelop various concepts, embodiments, or systemsthat will satisfy the customer’s requirements.

All possible alternative systems should be considered.The criteria for selection of a design will be based on thequality level and development costs, that will enable theproduct to survive in the highly competitivemarketplace.

The product design must be “functionally robust,”which implies that it must withstand variation in inputconditions and still achieve desired performancecapabilities. The designer has two objectives:

C Develop a product that can perform the desiredfunctions and be robust under various operating orexposure conditions

C Have the product manufactured at the lowestpossible cost

The nominal values and tolerance parameters of the newsystem must be determined.



IV-23 (386)

Parameter Design

Parameter designs improve the functional robustness ofthe process so that the desired dimensions or qualitycharacteristics are obtained. The process is consideredfunctionally robust if it produces the desired part for awide variety of part dimensions. The steps to obtain thisrobustness would be:

1. Determine the signal factors and the uncontrollablenoise factors and their ranges.

2. Choose as many controllable factors as possible,select levels for these factors, and assign theselevels to an appropriate SDE. Controllable factorscan be adjusted to improve the functionalrobustness of the process.



IV-24 (387)

e10

N

s - V1 = S/N = -10 logr V

β⎛ ⎞η ⎜ ⎟

⎝ ⎠

Parameter Design (Continued)

3. Calculate S/N ratios from the experimental data.

4. Determine the optimal conditions for the process.The optimal conditions are derived from theexperimental data. The maximum average S/N ofeach level of controllable factors will be used for theoptimal settings. Additional experiments will beconducted for verification of the settings.

5. Conduct actual production runs.



IV-24 (388)

2i

10

y = S/N = -10 logn

⎛ ⎞η ⎜ ⎟⎝ ⎠∑

2i

10

1y = S/N = -10 log

n

⎛ ⎞⎜ ⎟⎜ ⎟η⎜ ⎟⎜ ⎟⎝ ⎠

∑

Signal-to-Noise Ratios

A signal-to-noise ratio (S/N) is used to evaluate systemperformance. In assessing the result of experiments,the S/N ratio is calculated at each design point. Thecombinations of the design variables that maximize theS/N ratio are selected for consideration as product orprocess parameter settings. There are 3 cases of S/Nratios:

Case 1: S/N ratio for “smaller-is-better”:

Where: S/N = -10 log(mean-squared response). Thisvalue would be used for minimizing the wear, shrinkage,deterioration, etc. of a product or process.

Case 2: S/N ratio for “larger-is-better”:

Where: S/N = -10log(mean-squared of the reciprocalresponse).



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Signal-to-Noise Ratios (Continued)

Suppose a plot of S/N ratio looks like the following forone of the factors in a three level experiment:

S/N ratio (dB)

Levels of the Controllable Factor

In the above figure, the input (controllable) factor shouldbe chosen between the medium and high levels, sinceinput variation will cause little output variation. S/Nratios for Case 2 will seek the highest values for itemslike strength, life, fuel efficiency, etc.



IV-25 (390)

2 2

10 10 2

mean y = S/N = 10 log = 10 logvariance S

⎛ ⎞ ⎛ ⎞η ⎜ ⎟ ⎜ ⎟⎝ ⎠ ⎝ ⎠

Signal-to-Noise Ratios (Continued)

Case 3: S/N ratio for “nominal-is-best”:

This S/N ratio is applicable for dimensions, clearances,weights, viscosities, etc.



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Tolerance Design

The tolerances for all system components must bedetermined. This includes the types of materials used.In tolerance design, there is a balance between a givenquality level and cost of the design. The measurementcriteria is quality losses. Quality losses are estimatedby the functional deviation of the products from theirtarget values plus the cost due to the malfunction ofthese products.

Tolerances are usually established by using engineeringexperience, considering the uncertainty of design andproduction factors. Taguchi states that a safety factorof 4 is typically used in the United States. This safetyfactor will vary across industry. The defense andcommunications sectors may require much largervalues. The shipping specifications for a productcharacteristic is said to be on a higher-level in relationto the subsystem and parts.



IV-26 (392)

Function LimitTolerance Specification = Safety Limit

0ALoss when exceeding functional limit = = Loss when exceeding tolerance specifications A

φ

Tolerance Design (Continued)

The functional limit )0 must be determined by methodslike experimentation and testing. Taguchi (1993) uses aLD50 point as a guide to establish the upper and lowerfunctional limits. The LD50 point is where the productwill fail 50% of the time.

The formulas for tolerance specifications, the functionallimit, and safety factors are as follows:

Functional Limit: 0ii

i

A = (i = 1, 2)Δφ

Commonly 0= ΔΔφ

The economical safety factor N is determined as follows:



IV-27 (393)

Taguchi’s Quality Imperatives

The following is a paraphrase of Taguchi’s robustdesign principles:

C Robustness is a function of product design. Themanufacturing process and on-line quality controlcannot do much to change that. Quality losses area loss to society.

C Robust products have a strong signal with lowinternal noise. The design change of increasing thesignal-to-noise ratio will improve the robustness ofthe product.

C For new products, use planned experiments varyingvalues, stresses, and conditions to seek out theparameter targets. Orthogonal arrays arerecommended.

C To build robust products, use customer-useconditions.

C Tolerances are set before going to manufacturing.The quality loss function can be measured.



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Taguchi’s Quality Imperatives (Cont’d)

C Products that barely meet the standard are onlyslightly better than products that fail thespecifications. The aim should be the target value.

C The factory must manufacture products that areconsistent. Reduced variation is needed forconsistency.

C Reducing product failure in the field will reduce thenumber of defectives in the factory. Part variationreduction decreases system variation.

C Proposals for capital equipment for on-line qualityefforts should have the average quality loss (qualityloss function) added to the proposal.

The use of engineering techniques using robust designwill improve customer satisfaction, reduce costs, andshorten the development time.



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Design for X (DFX)

Design for X (DFX) is defined as a knowledge-basedapproach for designing products to have as manydesirable characteristics as possible. These include:quality, reliability, serviceability, safety, userfriendliness, etc. This approach goes beyond thetraditional quality aspects of function, features, andappearance of the item.

AT&T Bell Laboratories coined the term DFX to describethe process of designing a product.

The DFX toolbox has continued to grow in number fromits inception 15 years ago to include hundreds of toolstoday (Huang, 1997). The user can be overwhelmed bythe choices available. A set methodology would aid inthe following ways:

C Understanding how DFX worksC Aiding in the selection of a toolC Speeding learning of DFX toolsC Providing a platform for multiple DFX tools



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Design for X (DFX)The following material is based principally on the workof Watson (1998):

1. Design guidelines:

DFX methods are usually presented as rules of thumbwhich provides broad design rules and strategies.The design rule to increase assembly efficiencyrequires a reduction in the part count and part types.The strategy would be to verify that each part isneeded.

2. DFX analysis tools:

Each DFX tool involves some analytical procedurethat measures the effectiveness of the selected tool.A DFA (design for assembly) procedure wouldaddress the handling time, insertion time, totalassembly time, number of parts, and the assemblyefficiency. Each tool should have some method ofverifying its effectiveness.

3. Determine DFX tool structure:

A technique may require other calculations beforebeing considered complete. An independent tool willnot depend on the output of another tool.



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Design for X (Continued)

4. Tool effectiveness and context:

Each tool can be evaluated for usefulness by the user.The tool may be evaluated based on accuracy ofanalysis, reliability characteristics and/or integrity ofthe information generated.

5. The focus of activity and the development process:

Use of the DFX tools will be of benefit if the productdevelopment process is understood by the designteam. Understanding the process activities will helpdetermine when a particular tool can be used.

6. Mapping tool focus by level:

The mapping of a tool by level implies that DFXanalysis can be complex. Several levels of analysismay be involved with one individual tool. Thestructure may dictate the feasibility of tool use.



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DFX Characteristics

The following characteristics and attributes should beconsidered by DFX projects: (Bralla, 1999)

Function and performance: These factors are vital forthe product.

Safety: Design for safety requires the elimination ofpotential failure prone elements that could occur in theoperation and use of the product.

Quality: The three characteristics of quality, reliability,and durability are required and are often groupedtogether in this category.

Reliability: A reliable design has already anticipated allthat can go wrong with the product, using the laws ofprobability to predict product failure. Techniques suchas FMEA and derating of parts are considered. Parallelcritical component systems may be used.



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DFX Characteristics (Continued)

Testability: The performance attributes must be easilymeasured.

Manufacturability: The concept of design formanufacturability (DFM), includes testability, andshipability. A design must simplify the manufacture ofa product through a reduced number of parts andmanufacturing operations.

Assembly (design for assembly, DFA): DFA meanssimplifying the product so that fewer parts are involved,making the product easier to assemble.

Environment: The objective is minimal pollution duringmanufacture, use, and disposal. This could be definedas design for the environment (DFE).

Serviceability (maintainability and repairability): Aproduct should be returned to operation and use easilyafter a failure. This is sometimes directly linked tomaintainability.



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DFX Characteristics (Continued)

Maintainability: The product must perform satisfactorilythroughout its intended life with minimal expenses. Thebest approach is to ensure the reliability of components.

User friendliness or ergonomics: Because of humanfactors, engineering must match the product to the user.

Appearance (aesthetics): Attractiveness or “eye appeal”is especially necessary for consumer products.

Packaging: The best package for the product must beconsidered. The size and physical characteristics of theproduct are important. Automated packaging methodsare desirable.

Features: Features are the accessories, options, andattachments available for a product.

Time to market: The ability to have shorter cycle timesin the launch design of a product is desirable.


IV. PRODUCT AND PROCESS DESIGNTECHNICAL DRAWINGS

IV-32 (401)

Introduction to Blueprints

People who design parts and equipment mustcommunicate their ideas to other people. For thisreason, it is important to include all necessaryinformation on the drawings used to fabricate the itemin question. The information must be presented tominimize misunderstanding.

Blueprints must contain a lot of information. All thisinformation takes space. Using “technical shorthand”helps keep this space to a minimum. One example isthe use of standard abbreviations. Another is the use ofdrawing conventions. To read blueprints, theconventions and information locations must beunderstood.

Working drawings are of two different kinds, detaildrawings (drawings of individual parts) and assemblydrawings (showing how the parts fit together).Assembly drawings also include a parts list, whichidentifies all the pieces needed to build the item.



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Blueprint Information

There are numerous variations of blueprint formats. Theexample below is representative of most drawingconventions.

A Blank Drafting Sheet



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Blueprint Information

The first place to look for information on a drawing is inthe title block, located in the lower right-hand corner ofthe sheet. Although there is some variation among titleblocks used by different organizations, certaininformation is basic. The following paragraphs describethe information one will almost always find in a titleblock. The numbers before the descriptions refer to thenumbers in the previous Figure.



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Blueprint Information (Continued)

(1) Company name. The space above the title isreserved for the company address (by city andstate) of the designing or manufacturing firm.

(2) Title of drawing. This box identifies the part orassembly illustrated.

(3) Scale. The relationship between the size of theimage and the size of the actual object is calledthe scale of the drawing. Some parts are eithertoo big or too small to show conveniently at fullsize. The designer has the choice of drawing amechanical part either full size, or larger orsmaller than actual size.

When the drawing is larger or smaller than full size,the designer states the scale. Slightly differentconventions have been established by the differentgroups of people who make drawings.



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(4) Drawing size. This section gives a letterdesignation for the overall size of the sheet onwhich the drawing has been made. The followingtable lists the standard sizes with theircorresponding designations.

Letter Width HeightABCDEFJR

8.511172234283648

111722344440

anyany

Standard Blueprint Sizes



IV-34 (406)


(5) Drawing number. The drawing number is thebasic identification assigned to the drawing,which usually becomes the number of the partitself. This number is also used to file thedrawings, making it easier to locate them.

(6) Sheet number. This space is used to designatehow many sheets were used to complete thedrawing, and which one of the series thisparticular drawing happens to be.



IV-35 (407)


(7) Approvals block. This is sometimes referred toas the “sign-off block.” This area provides spacefor the signatures or initials of the personsinvolved in drafting, checking and approving thedrawing. Each person signs the document andfills in the date on the appropriate line whenhis/her portion of the work was finished orapproved.

(8) Material block. This block specifies what the partis made of - for example, the exact type of steel tobe used. This space might also designate thesize of the raw stock to be used.

(9) Tolerance block. Nothing can be to the exact sizespecified on a drawing. Normal machining andmanufacturing processes allow for slightdeviations. Many times, the amount of alloweddeviation is critical to the proper operation of thepart.



IV-35 (408)


(10) Finish block. This space gives information on howthe part is to be finished. That is, will it be buffed,plated, painted, anodized, etc. Added to thisrequirement might be the type of heat treatment tobe applied after the part has been machined.

(11) Parts list. (Used only on assembly drawings.) Thisspace is usually positioned right above the titleblock. Individual component parts, their partnumbers and the quantity required for each unit arelisted. This list is built from the bottom up.

(12) Revision block. The revision block is a separateblock positioned in the upper right-hand corner ofthe drawing. It is used to note any changes thathave been made to the drawing after its finalapproval. It is placed in a prominent position.



IV-36 (409)


(13) Detail drawing. A detail drawing is intended toprovide all the information needed to make aspecific part. See the figure below.



IV-37 (410)

Horizontal Line

VanishingPoint

Orthographic Projections

A basic problem that must be faced when constructinga drawing is that objects are three-dimensional. That is,they have height, width and depth. A drawing has onlytwo dimensions-height and width.

Designers solve this problem by using perspective.Perspective is a way of drawing things as the eye seesthem. The Figure below shows perspective.



IV-37 (411)

Orthographic Projections (Continued)

Designers have also developed a way to avoid distortionand draw the surfaces of blocks in their true size andshape. The method used is called orthographicprojection.

An orthographic projection is actually a right-angleprojection that eliminates the distortions in shape andsize caused by perspective. It does so by ignoring thefact that things farther from the eye appear smaller.



IV-38 (412)

Orthographic Projections (Continued)

An Orthographic Projection

An orthographic projection shows an object fromdifferent views. For example, the figure above shows anotched block inside an imaginary, transparent box.The shape of the block is projected out to each side ofthe box. The projection on each side shows the truesize and shape of the block as seen from that direction.



IV-39 (413)

Blueprint Lines

Notes on detail drawings convey many kinds ofinformation. Specific notes are tied by leaders directlyto specific features. The table below, shows commondrafting lines. Note that the weight and pattern of thelines indicate special significance.

thick linesObject lines - Illustrate all visible edges ofthe object drawn

medium lines

Cutting plane lines - Show where a sectionhas been taken. Arrows indicate thedirection in which section is seen inaccompanying cutaway view.

thin linesHidden lines - Show hidden features of theobject.Centerlines - Locate centers of roundfeatures (thin lines interrupted by shortdashes).Extension lines - Extend from object todimension lines.Dimension lines - Show extent of adimension.

Leaders - Like dimension lines, but usuallyhas a note at the outer end.

Phantom lines - Show position(s) of a part ofan object that moves.



IV-40 (414)

Blueprint Lines (Continued)One unique characteristic of detail drawings, asopposed to assembly drawings, is the inclusion ofdimension lines. Every measurable dimension isshown. Other lines on a blueprint include break linesas illustrated below:

Type Examples

Short Break Line

Long Break Line

Cylindrical Break Line

Cutting Plane Line

Section Lines



IV-41 (415)

1.000" ± 0.002"

+ 0.004"1.000" - 0.000"

Tolerances

Since variation exists in all manufacturing processes, itis customary to designate the permissible tolerance onblue print drawings. Listed below are examples oftolerances.

Type Illustration

1. Title block tolerance x.xxx = ± 0.002" x.xx = ± 0.01"

2. Bilateral toleranceVariation is permitted in bothdirections from a specifiedtolerance.

3. Unilateral toleranceVariation is permitted in onedirection from a specifiedtolerance.



IV-42 (416)

1.002"0.998"

1.002"Max.

Tolerances (Continued)

Type Illustration

4. Limit toleranceA tolerance which shows thehigh and low limits of adimension.

5. Single limit toleranceA tolerance specifying amaximum or minimum limitonly.

6. Positional tolerancingA feature frame shows theexact location and tolerance(allowable variation from theexact location).



IV-43 (417)

Statistical Assignment of Tolerances

The assignment of tolerances involves many factorsincluding the sigma safety level required.

There is an exercise on IV - 43 which shows that thestandard deviation of an assembly equals the squareroot of the summation of all component part variances.



IV-44 (418)

0.997"0.995"

1.000"0.998"

Shaft Hole

1.004"1.002"

1.000"0.998"

Shaft Hole

1.001"0.999"

1.000"0.998"

Shaft Hole

1.000"

1.000"

Shaft Hole

Allowances and Fits

Listed below are some major points regarding therelationship between mating parts.

Term

Clearance Fit

When two mating parts can beassembled easily (positive allowance), as shown.

Interference Fit

When two mating parts must be forcedtogether.

Transition Fit

This fit can be clearance orinterference depending upon theactual sizes of the parts.

Line To Line Fit

A fit where both parts are the samesize (considered an interference fit).

Illustration



IV-45 (419)

Parallel Running

Dimensioning

A designer must described the dimensions of featuresin order to control their locations. Some options canpermit undesirable tolerance build up.

Parallel Dimensioning

Parallel dimensioning consists of several dimensionsoriginating from a projection line. This technique is alsocalled baseline dimensioning.

Parallel and Superimposed Running Dimensioning

Superimposed running dimensions simplify paralleldimensioning in order to reduce drawing space. Thedimensions can appear above or below the arrows.



IV-45 (420)

A B C

Chain

Chain Dimensioning

Chain dimensioning should only be used if the functionof the part will not be affected by the accumulation oftolerances. In the Figure below, if A equals 2.000 ±0.005, B equals 1.000 ± 0.005 and C equals 1.000 ± 0.005,the total part dimension would be 4.000 ± 0.015.

Illustration of Chain Dimensioning

Other Dimensioning Options

In some complex parts, combined parallel and chaindimensioning options may be used. In the case of non-linear hole locations, dimensioning by coordinates (withor without an accompanying table) may be desirable.



IV-46 (421)

Nominal size

Thread per inchEnglish

Thread series

Thread class

Internal or externalAdditional data

Metric

Metric

Major diameter

Pitch

1/2 16 UNC 3A LH M 9.0 1.25x

Screw Thread Specifications

Listed below is a description of a screw thread drawingspecifications.

The definitions for common screw thread specificationsare listed on Primer pages V - 46/47.



IV-47 (422)

Pitch Width

Axis

DepthThread angle

Crest

Root

Major diameter

Pitchdiameter

Minordiameter

Screw Thread Nomenclature

Pictured in the figure below are the various parts of acommon thread profile.

The definitions for the most important screw threadparts are listed on Primer page V-47.



IV-48 (423)

Surface Texture Components

Symbol DescriptionBasic surface finish symbolSurface produced by any meansMaterial removed by machiningNo material removal permitted

MeaningLay is parallel to the line

Lay is perpendicular to the line

X Lay is angular in both directions

M Lay is multidirectional

C Lay is circular

R Lay is radial

a = roughness value Ra in micrometersb = production method, treatment, etc.c = roughness cutoff in millimetersd = directional lay keye = minimum material removal in mm



IV-49 (424)

Geometric Dimensioning and Tolerancing

Characteristics and Symbols

Type Characteristic ANSIY14.5 M

1982

ASMEY14.5 M

1994

ISO70831994

Form

Flatness

Straightness

Circularity

Cylindricity

Profile Profile of a line

Profile of asurface

Orien-tation

ParallelismAngularity

Perpendicularity

Run-out

Circular runout

Total runout

Loca-tion

Position

Symmetry

Concentricity



IV-50 (425)

Other Symbols and Terms

SymbolDescription

ANSIY14.5 M

1982

ASMEY14.5 M

1994

ISO70831994

MMC

LMC

RFS

PTZ

Tangent Plane None

Diameter

Basic Dimension

ReferenceDimension

(100) (100) (100)

Datum Feature

Between None

None

Datum Target



IV-50 (426)

Feature Control Frames with Symbols

Example 1 Example 2



IV-51 (427)

Datum Planes

When three datums are specified, reference is made tothe primary, secondary and tertiary datums. Thefollowing rules apply:

CPrimary datum. This is the supporting datum thatmust be contacted at the three highest points on thesurface.

CSecondary datum. This is an aligning datum thatmust be contacted at the two highest points on thesurface.

CTertiary datum. This is a stopping datum that mustbe contacted at the highest point on the surface.



IV-52 (428)

Shaft Hole

0.260"0.250"

0.272"0.262"

Virtual Condition

The virtual condition (virtual size) of any dimensiondepends upon its size, form and location (position).Consider the following example:

Assume that the hole size is true and parallel at adimension of 0.263". The shaft measures 0.260"maximum O.D. The two parts should, therefore, mateproperly with a clearance fit. However, if the shaft isbent, making its virtual size a maximum of 0.265", thenthe two parts will not mate.



IV-52 (429)

Virtual Condition (Continued)

Examples of violations of dimensional virtual conditionare:

Size: Oversize shaft, undersized holeForm: Tapered keyway, crooked shaft, bent pinPosition: The feature is out of location

Material Conditions

The ANSI terms for maximum material condition andleast material condition are and respectively. Thedefinitions are:

MMC The condition of a dimension where the mostmaterial allowed (by the tolerance) is still there(the maximum weight).

LMC The condition of a dimension where the mostmaterial to be removed (by the tolerance) hasbeen (the least weight).



IV-53 (430)

Shaft Hole

0.260"0.250"

0.272"0.262"

Material Conditions (Continued)

MMC is the largest shaft and the smallest hole. LMC isthe smallest shaft and the largest hole. Consider thefollowing example:

The MMC of the hole is 0.262". The MMC of the shaft is0.260". The clearance is 0.002".



IV-53 (431)

Full Indicator Movement

Many dimensions are designated as FIM, FIR or TIR.The abbreviations stand for: Full indicator movement,full indicator reading, total indicator reading,respectively.

Consider the Figure below. The feature control frameindicates that surface B is to be parallel to surface Awithin 0.004" FIM.

SURFACE PLATE

A SURFACE

B SURFACE

PART

.004 A



IV-54 (432)

Hole

Pin

Bonus Tolerancing

Bonus tolerance applications can exist when maximumor least material conditions are used. The concept isthat when mating parts are manufactured for assemblythere may be conditions where each individual part maybe slightly further away from its ideal location and stillwork. Review the Figure below.

Non-Symmetrical Part Mating



IV-54 (433)

1.000

B

1.000

.305

.295

A

A BØ .005 CM

Bonus Tolerancing Example

Consider an example using MMC. In the Figure below,assume the centerline of the hole to be exactly 1.000from both datums.

The original tolerance is 0.005 for a MMC of 0.295.Assume that the hole were actually produced at 0.301.The following would then be true:

Original tolerance 0.005+ Bonus tolerance 0.006 (0.301 - 0.295)

Total tolerance 0.011

There is now more tolerance available for clearancebetween the pin and hole.



IV-55 (434)

Blueprint DefinitionsActual Size The actual size is a measured size of a feature.

Allowance The intentional difference between the maximummaterial limits of mating parts.

ASMEY14.5M-1994

The authoritative document governing the practice ofgeometric dimensioning and tolerancing in the U.S.

ASMEY14.5M“Rule #1”

The amount of variation in size and geometric form ofa feature. The boundary between the maximum (MMC)and least (LMC) material condition.

ASMEY14.5M“Rule #2”

All RFS notations must apply to all individualgeometric tolerances and/or datum reference, when nomaterial condition applies.

Basic Size Any size from which tolerance limits may be derived.

BilateralTolerance

A bilateral tolerance permits variation in bothdirections from a specified dimension.

CircularRunout

The control requirement of circular elements of asurface during a full revolution about a datum centeror axis.

Circularity

The condition whereby all points on a surface ofrevolution (cylinder, cone, sphere) are equidistant orwithin a specified tolerance from a common center oraxis.

Clearance Fit A clearance fit has size limits such that a clearancewill always occur when mating parts are assembled.



IV-56 (435)

A or A

Blueprint Definitions (Continued)

Datum The origin from which the location or geometriccharacteristics of other part features of a part areestablished. It is a theoretically exact point, plane oraxis.

DatumFeature

An actual feature of a part used to establish a datum.

DatumFeatureSymbol

A symbol containing a datum reference letter in arectangular box.

Datum Line A line which provides a reference for functional, ormeasurement purposes.

Datum Plane A theoretically exact plane established by the outsideor contacting points of a feature or by a simulateddatum plane such as a surface plate.

DatumReference

A datum feature as referenced or specified on adrawing.

DatumReferenceFrame

The reference frame consisting of three mutuallyestablished perpendicular datum planes whichprovide a complete dimensional orientation for thedesign features of concern.

Datum Target

A specified point, line, axis or plane (identified on thedrawing with a datum target symbol) used to establisha datum.



IV-57 (436)


.003

Feature A general term used to identify a distinct portion of apart, such as a surface, pin, hole, slot, shaft, etc.

FeatureControl Frame

A feature control frame is a compartmentalized boxcontaining the geometric characteristic symbol andthe corresponding tolerance.

Feature ofSize

A feature such as a hole, shaft, pin, slot, etc. whichhas an axis, centerline or center plane when related toor described by geometric tolerances.

Fit The general term which indicates the amount oftightness or looseness which results from a specifiedcombination of tolerances in the design of matingparts. Fits are of four general types: clearance,interference, transition, and line.

FormTolerance

A statement of the permissible variation of a featurefrom a desired actual value. Form tolerance refers toflatness, straightness, circularity, and cylindricity.

Full IndicatorMovement(FIM)

The total movement observed on an indicator incontact with a part feature surface during one fullrevolution about a datum axis. FIM has replaced theterms full indicator reading (FIR) and total indicatorreading (TIR) as a standard reference.

GeometricTolerance

A general term indicating the category of tolerancesused to control form, orientation, profile, runout andlocation on a drawing.



IV-58 (437)


Least MaterialCondition(LMC)

The condition whereby a feature of size contains theleast amount of material, within the slated limits ofsize. An example is the largest permitted hole sizeand smallest permitted shaft size. LMC is identifiedby the symbol .

Limits of Size The specified maximum and minimum sizes of anyfeature.

LocationTolerance

A tolerance which states how far an actual featuremay vary from an ideal location. These tolerancesrefer to geometric characteristics containing positionand concentricity.

MaximumMaterialCondition(MMC)

The condition whereby a feature of size contains themaximum amount of material within the stated limitsof size. An example is the minimum permitted holediameter and maximum permitted shaft diameter.MMC is identified by the symbol

Modifier A modifier is a material condition symbol such asmaximum material condition (MMC) , regardless offeature size (RFS) and least material condition(LMC) .

Nominal Size The nominal size is a stated dimension used for thepurpose of general identification ( 2.050,1.310, 0.050).



IV-59 (438)


Parallelism

The condition whereby a surface, line, or axis isequidistant along its length to all points of a datumplane or axis.

PositionTolerance

A zone within which the center or axis of a feature ispermitted to vary from a true or exact position.

Profile of aLine

The tolerance (unilateral or bilateral) within which theelements of a line must lie.

Profile of aSurface

The tolerance (unilateral or bilateral) within which theelements of a surface must lie.

ProjectedToleranceZone

A tolerance zone which applies to a feature (such asa hole) into which another feature (such as a pin) is tobe inserted. The projected tolerance zone extendsfrom the surface of one part along the functionallength of a second mating part to assure properassembly.

ReferenceDimension

A provided dimension used for information purposesonly.

Runout Runout is the permissible error (or control tolerance)of a controlled feature surface during a full rotation(360°) about a datum axis. A runout tolerance may becircular or total.

Symmetry The condition whereby the median point of allopposing features are correspondingly positionedaround the axis or center plane of a datum feature.



IV-60 (439)


ToleranceZone

The total measured value within which all elements ofa surface or axis must fall.

VirtualCondition

The boundary of a feature, that represents thecollective effects of size, form and location,considered in determining the fit or clearancebetween mating parts or features. It represents themost extreme condition of assembly.


IV. PRODUCT AND PROCESS DESIGNDESIGN VERIFICATION

IV-61 (440)

Design Verification

ISO 9001:2000 requires that design and developmentsbe in a form that enables verification against inputs.Designs must be approved before release. Furthermore,design and development outputs should:

C Meet input requirements

C Provide adequate information for manufacture andservice

C Reference product acceptance criteria

C Specify any characteristics essential for safe andproper use

ISO/TS 16949:2002 requires additionally design outputs.



IV-62 (441)

Design Verification (Continued)

Verification is confirmation by examination andevaluation of objective evidence that a specific designspecification has been met. Validation is confirmationby examination and evaluation of objective evidencethat a specific intention has been met. The differencebetween these two activities entails who does them andthe nature of the acceptance criterion.

C Verification is conducted by engineering todetermine if the material, component, module,subsystem or system meets the designspecifications.

C Validation is conducted by the customer (end-user)to see if the product meets their needs. The(internal and external) customer validates theproduct against their indicated qualitycharacteristics.



IV-63 (442)

Verification Validation

CustomerRequirements

SystemSpecifications

SubsystemSpecifications

Module

Subsystem

System

Product

Validation is done by thecustomer to accept the product’s fitness of use,usually when the product iscomplete.

Verification is done byengineering to designspecifications at eachstage.

ModuleSpecifications

Component/MaterialSpecifications

Component orMaterial


Verification and Validation Relationships



IV-63 (443)


Several different qualification methods can be used forproduct verification and validation. One obviousqualification method is to use product testing todetermine if the product meets the criteria set forth inthe design specification. This tends to be the mostcommon and straight forward method.

Another qualification method is product testing using athird-party such as a nationally recognized testinglaboratory. It is common for household and electricalproducts to have safety qualification testing conductedby Underwriters Laboratories.


IV. PRODUCT AND PROCESS DESIGNRELIABILITY AND MAINTAINABILITY / INTRODUCTION

IV-64 (444)

Reliability and Maintainability

Reliability and Maintainability is presented in thefollowing topic areas:

C IntroductionC Preventive maintenanceC Reliability and maintainability indicesC Bathtub curveC Safety and hazard assessment tools


IV. PRODUCT AND PROCESS DESIGNR & M / PREVENTIVE MAINTENANCE

IV-64 (445)

Reliability Introduction

With an increase in the technical complexity ofproducts, and the advent of world-wide competition,there has been growing concern about productreliability. Simply stated, reliability is the assurance thatthe product will perform as intended. Product durabilityimplies that the product will last for a long time.

Reliability is the probability that a product will performits intended function satisfactorily for a pre-determinedperiod of time in a given environment. Note that thereare four key elements in this definition.

One might state that the reliability of an electric motor tooperate a water pump in a 35 ° to 100 °F ambienttemperature environment for five years is 0.95.



IV-65 (446)

Preventive Maintenance

In general, most pieces of equipment, machinery, orsystems are under some sort of preventive maintenanceprogram. When an item or system experiences abreakdown or failure, the item is normally repaired.Individual parts may be replaced in the system, but thebigger system is maintained.

In the operation of a plant, equipment and systems failunexpectedly. The repair of these types of failures isconsidered corrective maintenance items. Correctivemaintenance cannot be planned, but can be determinedby reliability. The mean time to repair (MTTR) isapplicable for such items. If an item cannot be repairedupon failure, it is characterized by a mean time to failure(MTTF).



IV-65 (447)

Preventive Maintenance (Continued)

The time to repair has three elements to it:

1. Preparation time: Locating people, traveling to thesite, obtaining tools, parts, and instruments.

2. Active maintenance time: Studying the charts,performing the repair, and verifying the repair. Thiscan be specified as the mean active maintenancetime (MAMT).

3. Delay time: The wait time involved in such activitiesas locating charts, waiting at the store’s counter,waiting on production to clear the area, andawaiting personnel to verify repairs.

Preventive maintenance (PM) has the function of theprevention of failures via planned or scheduled efforts.



IV-66 (448)


Ireson (1996) defines the maintenance concerns as:

C The mission profileC Availability and/or reliability requirementsC Maintenance worker constraintsC Weight and volume restrictionsC Spare parts policyC Periodic testingC Scheduled maintenanceC Geographic nature of the systemC The levels of specialized maintenance requiredC Planned types of support equipment



IV-66 (449)


To optimize maintenance costs and operating costs, itis necessary to gather information and data for themaintained part. The information would include:

1. The time-to-failure distribution parameters for themain failure modes

2. The effects of the failure modes

3. The cost of failure

4. The cost of scheduled replacement

5. The effect of maintenance on reliability

6. The increase in defects before failure

7. The cost of inspection or test(O’Connor, 1996)



IV-67 (450)


The knowledge of various hazard rates are meaningfulin that:

C Given a decreasing hazard rate, it is best to notreplace the part.

C Given a constant hazard rate, part replacement doesnot reduce failure rates.

C Given an increasing hazard rate, scheduledreplacement reduces failure rates.

C Given an almost failure-free, but increasing hazardrate, scheduled replacement will provide a near zerofailure rate.



IV-67 (451)


The collection of information on replaced or maintainedparts will provide useful information. The knowledge ofvarious hazard rates are meaningful:

Decreasing hazard rate, it isbest to not replace the part.Scheduled maintenance willreturn the part to the top ofthe curve.

Constant hazard rate, partreplacement will result in thesame probability of failure asbefore.



IV-68 (452)


Increasing hazard rate.Scheduled replacement of apart will reduce theprobability of failures.

Increasing hazard rate withnear failure free life.Scheduled maintenance willensure near failure freeprobability.


IV. PRODUCT AND PROCESS DESIGNR & M / INDICES

IV-69 (453)

Reliability and Maintainability Indices

Availability A measure of the degree to which an item is inan operable and committable state at the startof a mission when the mission is called for atan unknown (random) time.

Dependability A measure of the degree to which an item isoperable and capable of performing itsrequired function at any (random) time duringa specified mission profile, given itemavailability at the start of the mission.

Failure modeand effectsanalysis(FMEA)

A procedure by which each potential failuremode in a system is analyzed to determine theresults or effects thereof on the system, andto classify each potential failure modeaccording to its severity.

Failure rate(8)

The total number of failures within an itempopulation, divided by the total number of lifeunits expended by that population, during aparticular measurement interval under statedconditions.



IV-70 (454)

Number of items failedFailure Rate = = Total operating hours

λ

Total operating hoursMTBF = = Number of items failed

θ

1 1Failure rate = or = MTBF

λθ

Failure Rate and MTBFFor exponential data, the failure rate of a product can becalculated from test data using the formula:

For exponential data, the mean time between failures can becalculated from test data using the formula:

There is an obvious relationship between failure rate and MTBF:

Various sources denote mean time between failures (MTBF) aseither μ or θ. When a product is repairable, MTBF is used. Ifnot, MTTF is used.



IV-70 (455)

( ) ( )

( ) ( )

n

i ni = 1

x = t + n - x t

3 = 20 hr + 38 hr + 42 hr + 7 - 3 50 hr

= 0.01/hr

λ

λ

λ

∑

1 1MTBF = = = = 100 hr0.01 hr

θλ

Failure Rate and MTBF (Continued)Example: If seven items are tested for 50 hours each, and oneitem fails at 20, 38 and 42 hours respectively, what is the failurerate of the item?

Let: x = 3, n = 7, t n = 50, t 1 = 20, t 2 = 38, t 3 = 42

What is the MTBF?



IV-71 (456)

Series System ReliabilityIn a series system, the total reliability of the system isdependent on each individual component working. Thereliability of this type of system is the product of all of theindividual component reliabilities.

Example: Determine the series system reliability.

Formula: Rseries= R1 x R2 x R3

= 0.90 x 0.95 x 0.94

Answer: = 0.80



IV-71 (457)

Parallel System Reliability

In a parallel system, the reliability of the system iscalculated by subtracting the product of theunreliabilities from 1.

Example: Determine the parallel system reliability.

Formula: U1 = 1 - R1 = 0.10U2 = 1 - R2 = 0.05U3 = 1 - R3 = 0.06

Rparallel = 1 - (U1 x U2 x U3)= 1 - (0.10 x 0.05 x 0.06)= 1 - (0.0003)

Answer: Rparallel = 0.9997



IV-72 (458)

Input R1 = 0.95

R2 = 0.9

R3 = 0.9

R4 = 0.99 Output

Combination Systems

The important thing to remember in a combined systemis to solve the reliability of the parallel system first, thenuse it in series to solve the series system reliability.

Example: Determine the reliability of the combinationsystem below.

Formula: R2,3 parallel = 1 - U2 x U 3= 1 - (0.10 x 0.10)= 1 - 0.01= 0.99

Rsystem = R1 x R2,3 x R4= 0.95 x 0.99 x 0.99

Answer: = 0.93

From the calculations above, it should be clear that theparallel design offers a greater assurance ofperformance.



IV-72 (459)

Other Systems

There are a large number of system modeling formats,which are probably too complex for the CQE exam.They include:

C Active redundancy systemsC Standby parallel systemsC Shared load systemsC Bayes’ theorem applicationsC Boolean truth table methodsC Tie and cut set methods



IV-73 (460)

t

R(t)

tt --- tt t tR = e or R = e or R = eλ μθ

Exponential Distribution

The exponential distribution shown below is commonlyused for predicting the reliability of items in the constantrate failure period.

The reliability for the exponential distribution is:

Where:

Rt = Probability of failure-free operation for a time periodt = Specified period of failure-free operation

: = 2 = Mean time between failures (MTBF)8 = Failure rate (the reciprocal of :)e = Natural logarithm base = 2.71828 ...



IV-73 (461)

( ) ( )( )

- t

- t

f t eh t = = = R t e

λ

λ

λλ

Exponential Distribution (Continued)

The hazard rate for the exponential is:

The hazard rate is unchanging. Another way that this isstated is that the exponential distribution has a constantfailure rate.

The exponential distribution has the followingproperties:

C The mean and standard deviation have the samevalue.

C Approximately 63.21% of the area under the curvefalls below the mean.



IV-74 (462)

( )( )( )

- t

- (0.002/hr)(400 hr)

1 1 = = = 0.002 failures / hrMTBF 500 hr

R t = eR 400 = eR 400 = 0.449

λ

λ

Exponential Distribution (Continued)

Example: An item has an exponential failure rate and aMTBF of 500 hours. What is the reliability at 400 hours?



IV-75 (463)

Weibull Distribution

The Weibull distribution consists of many distributionalshapes rather than a single unique shape as in manydistributions. The shape of the distribution is mainly afunction of the shape parameter $. Several differentcurve shapes are shown in the Figure below. All curveshave the same scale parameter, 0.

$ < 1 Infant mortality

$ = 1 Useful life

$ > 1 Wearout

There are two common versions of the Weibulldistribution used in reliability. The two parameterWeibull and three parameter Weibull. The difference isthat the three parameter Weibull distribution has alocation parameter



IV-75 (464)

( )-1

t- t-f t = exp- for t β β

β γ γ⎛ ⎞ ⎛ ⎞≥ γ⎜ ⎟ ⎜ ⎟η η η⎝ ⎠ ⎝ ⎠

Weibull Distribution (Continued)

For the three parameter Weibull distribution:

Where: $ is the shape parameter0 is the scale parameter( is the non-zero location parameter

Note the scale parameter is the point where 63.21% ofvalues fall below this parameter. When $ is 1.0, theWeibull function reduces to the exponential and when $is about 3.5 (and 0 = 1 and ( = 0), the Weibull closelyapproximates the normal distribution.



IV-76 (465)

System Effectiveness

In many cases, individual items are assembled into sub-systems and then into systems. As systems becomemore complex, the probability of individual items failingbecomes greater. It becomes important in manyinstances that the failure.

System effectiveness, then, is a combination of severalissues brought together to determine if a system has ahigh likelihood of achieving the mission at hand. Thethree major components of a system’s effectiveness areavailability, dependability, and capability.



IV-76 (466)

System Effectiveness (Continued)

System effectiveness: A measure of the degree towhich an item or system can be expected to achieve aset of specific mission requirements, and which may beexpressed as a function of availability, dependabilityand capability.

SE = Availability x Dependability x Capability*

The definitions of the three components are:

Availability: A measure of the degree to which an itemor system is in the operable and committable state at thestart of the mission.

Dependability: A measure of the item or systemoperating condition. It may be stated as the probabilitythat an item will (a) enter or occupy any one of itsrequired operational modes during a specified mission,and (b) perform the functions associated with thosemodes.

Capability: A measure of the ability of an item or systemto achieve mission objectives given the conditionsduring the mission.



IV-77 (467)

Maintainability

Maintainability: The measure of the ability of an item tobe retained or restored to a specified condition whenmaintenance is performed by personnel havingspecified skill levels, using prescribed procedures andresources, at each prescribed level of maintenance andrepair.

The maintenance action rate is a key component ofmaintainability. If an item fails, how long does it take toget back into service? The maintenance action rate isoften prescribed by contract and is defined as:

Maintenance action rate: The reciprocal of the meantime between maintenance actions or 1/MTBMA.



IV-77 (468)

i

MTBFA = MTBF + MTTR

Availability

Availability: A measure of the degree to which an itemis in the operable and committable state at the start of amission, when the mission is called for at an unknown(random) time. The three common measures ofavailability are:

1. Inherent availability (Ai): This is the ideal state foranalyzing availability. The only considerations are theMTBF (reliability) and the MTTR (maintainability). Thismeasure does not take into account the time forpreventive maintenance and assumes repair beginsimmediately upon failure of the system.

The measure for inherent (potential) availability (Ai) is:

Note: MTTR stands for mean time to repair.



IV-78 (469)

o

MTBMAA = MTBMA + MDT

A

MTBMAA = MTBMA + MMT

c ct p pt

c p

F M + F MMMT =

F + F

Availability (Continued)

2. Operational availability (Ao): This is what generallyoccurs in practice and takes into account that themaintenance response is not instantaneous. Themeasure of operational (actual) availability Ao is:

Where: MTBMA is the mean time between maintenanceactions both preventive and corrective and MDTis mean down time.

3. Achieved availability (AA): Achieved availability issomewhat more realistic in that it takes preventive andcorrective maintenance. The assumption is no loss oftime waiting for the maintenance action to begin. Themeasure for achieved (final) availability (AA) is:

Where: MTBMA is the mean time between maintenanceactions both preventive and corrective andMMT is the mean maintenance action time


IV. PRODUCT AND PROCESS DESIGNR & M / BATHTUB CURVE

IV-79 (470)

Bathtub Curve

The three general types of failures observed for complexproducts are illustrated with the life-history or “bathtub”curve. It should be noted that many electrical productsdo not follow this model.

Infant mortality. These failures are generally the resultof components that do not meet specifications orworkmanship that is not up to standard. These are notdesign related issues, but quality related issues. Theinfant mortality period is noted by a decreasing failurerate. The Weibull distribution is commonly used todetermine when the infant mortality period is over.

Constant failure rate. Once the failures due tocomponents and workmanship are eliminated, theconstant failure rate period is entered. This is alsocalled the random failure rate period. One can predictthe probability of a failure in a certain interval, but not aspecific failure at a specific time. The constant failurerate period is the most common time frame for makingreliability predictions. The exponential distribution isutilized.



IV-79 (471)

Bathtub Curve (Continued)

Wearout period. As components begin to fatigue orwear out, one begins to observe failures at an increasingrate. As time goes on, failures occur more and morefrequently to a point where it may no longer be practicalto continue operating the system. Several distributionsmay be appropriate to model the wearout period. Thenormal and log normal distributions are often used.

An Illustrative Life - History Curve



IV-80 (472)

Distribution of Time Between Failures

Along with concern for high failures during the infantmortality period, customers must be concerned with thelength of time that a product will run without failure.This measurement concerns the second stage of thebathtub curve known variously as the normal, chance,or random failure period. Often this failure rate isconstant with the time between failures distributedexponentially as shown below:


IV. PRODUCT AND PROCESS DESIGNR & M / HAZARD ASSESSMENT TOOLS

IV-81 (473)

FMECA

A FMECA provides the design engineer, reliabilityengineer, and others with a systematic technique toanalyze a system, subsystem, or item, for all potential orpossible failure modes. This method then places aprobability that the failure mode will actually occur andwhat effect this failure has on the rest of the system.The criticality portion of this method allows one to placea value or rating on the criticality of the failure effect onthe entire system.

A FMEA or FMECA (in some cases there is little, if any,difference) is a detailed analysis of a system down to thecomponent level. Once all of the items are classified asto the failure mode, effect of failure, and probability thatfailure will occur, they are rated as to their severity viaan index called an RPN (risk priority number). Once allcomponents or items have been analyzed and assignedan RPN value, it is common to work from the highestRPN value down.



IV-81 (474)

FMECA Process Steps

1. FMEA Number: assigned number

2. The part number, name, description

3. Design responsibility:

4. Person responsible for FMEA preparation

5. Date the FMEA was prepared and revision level

6. Subsystem part number

7. Component function

8. Potential failure mode

9. The potential effect of failure

10. The potential cause of failure

11. What current controls to prevent the failure?



IV-82 (475)

FMECA Process Steps (Continued)

Risk Assessment and RPN

The next major step is to weigh the risks associated withthe current component, effect, and cause with thecontrols that are currently in place.

12. P is the probability this failure mode will occur.Values for this index generally range from 1 to 10,with 1 being virtually no chance, and 10 being nearcertainty of occurrence.

13. S is the severity of the effect of the failure on therest of the system if the failure occurs. Thesevalues are often indexed from 1 to 10. A value of 1means the user will be unlikely to notice, with a 10meaning that the safety of the user is in jeopardy.

14. D is a measure of the effectiveness of the currentcontrols (in place) to identify the potential weaknessor failure prior to release to production. This indexmay also range from 1 to 10. A value of 1 meansthis will certainly be caught, whereas a value of 10indicates the design weakness would most certainlymake it to final production without detection.



IV-82 (476)

FMECA Process Steps (Continued)

15. RPN. The risk priority number is the product of theindices from the previous three columns.

RPN = PASAD

16. The actions then are based upon what items eitherhave the highest RPN and/or where the major safetyissues are.

17. There is a column for actions to be taken to reducethe risk, a column for who is responsible and finallya column for the revised RPN, once correctiveaction is implemented.

In summary, the FMECA provides a disciplinedapproach for the engineering team to evaluate designsto ensure that all the possible failure modes have beentaken into consideration.



IV-83 (477)

System FMECAPart No./Name: 37XT11-Lock Mech. P = Probability FMEA No. 43Project: Re-design S = Seriousness Final Design Deadline: Dec. 1, 2006Other Departments: Shop Service, etc. D = Likelihood Prepared By: RCDSubsystem Name: Quill Clamping Mechanisms RPN = Risk Priority Reviewed By: BLWSuppliers Involved: Wilton and others Number FMEA Date: Nov. 20, 2006 Rev.Design Responsibility: Bob Dovich

PARTNUMBER

NAME

FUNCTION POTENTIALFAILUREMODE(S)

POTENTIALEFFECT(S)

OF FAILUREPOTENTIAL

CAUSE(S) OFFAILURE

CURRENTCONTROLS

RISK ASSESSMENT

RECOMMENDED CORRECTIVE

ACTION(S)

ACTION(S)TAKEN

REVISED RISKASSESSMENT

RESPONSIBLEDEPT OR

INDIVIDUALP S D RPN P S D RPN

WILTONPOWERLOCK

CLAMP LEAK HOUSE-KEEPING WEAR

ACCEPTSUPPLIER'S

INFO2 4 3 24

DISCUSS WITHSUPPLIER

LOSESCLAMPING

FORCE(SHIFTING)

MACHININGPARTS

OVERSIZE

SELECTEDINADEQUATESIZE POWER

LOCK

ENG.STANDARD 2 4 4 32

PERFORM LOADTESTS

MATERIALS &WORKMAN-

SHIPSTD. Q.C. 1 4 2 8

NONE

OVERPRESSURE NONE 2 4 2 16

REVIEW NEED FORSYSTEM TO

PREVENT OVER-PRESSURIZATION

PUMPSIZING

ENG.STANDARD 1 4 2 8

REVIEW PRESSUREDELIVERED IN FIELDAND ACTUAL NEED

An Illustrative FMECA

Note that the above FMECA breakdown uses twoprobability components: The probability that the failuremode will occur (P) and the probability of detection priorto release (D).



IV-83 (478)

Risk Assessment

Risk assessment is the combination of the probability ofan event or failure and the consequence(s) of that eventor failure to a system’s operators, users, or itsenvironment. The analysis of risk of failure normallyutilizes two measures of failure:

C Severity of failure

C Probability of failure



IV-84 (479)

Risk Assessment (Continued)

The severity of failure is generally defined by the hazardseverity categories from MIL-STD-1629 (1980). Theseare shown in Table below.

Classification DescriptionI Catastrophic A failure that may cause death or

mission lossII Critical A failure that may cause severe

injury or major system damageIII Marginal A failure that may cause minor

injury or degradation in missionperformance

IV Minor A failure that does not causeinjury or system damage but mayresult in system failure andunscheduled maintenance

Hazard Severity Categories



IV-84 (480)


Another example, from Ireson (1996) uses a severityindex based on a scale from 1 to 10.

Rank Criteria1 It is unreasonable to expect that the minor

nature of this failure will degrade theperformance of the system.

2 - 3 Minor nature of failure will cause slightannoyance to the customer. Customer maynotice a slight deterioration of the systemperformance.

4 - 6 Moderate failure will cause customerdissatisfaction. Customer will notice somesystem performance deterioration.

7 - 8 High degree of customer dissatisfaction andinoperation of the system. Does not involvesafety or noncompliance to governmentregulations.

9 - 10 Very high severity ranking in terms ofsafety-related failures and nonconformanceto regulations and standards.

Commercial Severity Index (Scale 1 - 10)



IV-85 (481)


The hazard classification or severity index is generatedfor each component or subsystem by the reliabilityanalyst. This classification is based on the expectedresults of the failure of the component or subsystem.The probability of failure may also be ranked. Acommon ranking of failure probabilities is shown inbelow.

FailureProbability Level

Description Probability

A High likelihood ofoccurrence

>10-1

B Probable occurrence 10-1 to 10-2

C Occasionally occurs 10-2 to 10-3

D Remote probability 10-3 to 10-6

E Highly unlikely <10-6

A Common Failure Probability Ranking



IV-85 (482)


A number of systems are used to combine theprobability of failure and the hazard category. Thesesystems are based on accepting a degree of risk ofoccurrence with respect to the severity of the hazard.For instance, the table below shows one type of riskassessment matrix.

HazardCategory

Allowable FailureProbability Level

I Catastrophic E (Unlikely)II Critical E (Unlikely)III Marginal D (Remote)IV Minor C (Occasional)

Example Risk Assessment Matrix

* Frequently, catastrophic failure modes have additionalsafety measures, such as redundant components orfrequent inspections during service, etc. Note that nohazard category has an allowable failure probability of“frequent” or “probable.”



IV-86 (483)

Fault Tree Analysis

Fault tree analysis (FTA) is a systematic, deductivemethodology for defining a single, specific, undesirableevent, and determining all possible reasons (failures)that could cause that event to occur. The FTA is aneasier and faster method of analysis compared toFMECA because it focuses on those system failures thatcan cause a catastrophic “top” event. FMECAprogresses sequentially through all possible systemfailure modes, regardless of their severity.

When properly applied, a FTA is extremely useful duringthe initial product design phase. Other potential uses ofFTA include:

C Functional analysis of highly complex systemsC Evaluation of subsystem events on the top eventC Evaluation of safety requirementsC Evaluation of system reliabilityC Identification of design defects and safety hazardsC Evaluation of potential corrective actionsC Maintenance and troubleshooting simplificationC Logical elimination of causes



IV-86 (484)

Fault Tree Analysis

FTA is preferred over FMECA/FMEA when:

C The safety of personnel is paramountC A small number of “top events” can be identifiedC A functional profile is of critical importanceC There is a high potential for error failureC The primary concern is a quantified risk evaluationC Product functionality is highly complexC The product is not repairable once initiated

FMECA/FMEA is preferred over FTA when:

C Top events cannot be explicitly definedC Multiple successful profiles are feasibleC The identification of all failure modes is importantC Product functionally has little human intervention

(Reliability Toolkit, 1993)



IV-87 (485)

FTA Event Symbols

There are numerous symbols used in FTA, and these arebroken down into two main categories; event symbolsand gate symbols as shown below:

or Top event: Contains a description ofa system-level fault or undesiredevent.

Basic event: Usually the lowestlevel of event fault that one wishesto study. It is used as an input to alogic gate.

Undeveloped event: This is a fault atthe lowest level of examinationwhich is not expanded upon. Theundeveloped event is used as aninput to a logic gate. It may bedeveloped later.



IV-87 (486)

FTA Event Symbols (Continued)

Input event: Contains what would bean input fault into the system. Theinput fault can be an internal systemfault or a condition from a sourcethat is external to the system.

Fault event: Contains a descriptionof a lower-level fault. It can receiveinputs from or provide outputs to alogic gate.

Transfer function: A connectionbetween two or more sections of afault tree or to signify a location on aseparate sheet of the same tree.



IV-88 (487)

Logic (Gate) Symbols

“and” gate The output event occurs(series) only if all the input events

occur simultaneously.

“or” gate The output event occurs if(parallel) any one of the input events

occur.

Priority The output event occurs if,“and” gate and only if, all of the input

events occur in the orderfrom left to right.



IV-88 (488)

Logic (Gate) Symbols (Continued)

Exclusive The output occurs if one, but“or” gate not both, of the input events

occur.

m out of n The output event occurs if m(voting) gate of n input events occur.

n inputs



IV-89 (489)

CD ROMDRIVE D

AND

CD ROMDRIVE E

OR

COMPUTER FAILSTO WORK

HARD DRIVE CPU KEYBOARD MONITOR

0.010 0.010

0.001 0.015 0.020 0.015

0.0001 CALCULATED

Fault Tree Analysis Example

Fault tree analysis begins at the system level, assumingthat failure occurs. For instance, consider theprobabilities for a home computer failing to work asshown in below:



IV-89 (490)

FTA Example (Continued)

The fault tree is analyzed using the failures, instead ofthe successes. In the above case, the computer fails tooperate if CD ROM drive D and drive E fail, or the harddrive fails, or the CPU fails, or the keyboard fails, or themonitor fails. Since “and” gates multiply and “or” gatesadd, the probability of the home computer not workingcan be computed.

:system = 1 - (0.9999)(0.999)(0.985)(0.98)(0.985):system = 1 - 0.9498:system = 0.0502

The probability of a failure is 5.02%



IV-90 (491)

CD ROMDRIVE D

AND

CD ROMDRIVE E

OR

COMPUTER WILL

OPERATE

HARD DRIVE CPU KEYBOARD MONITOR

0.990 0.990

0.999 0.985 0.980 0.985

0.9999CALCULATED

Success Tree Analysis

Success tree analysis begins at the system level andassumes a successful system operation. Unlike thefault tree in which the top event is undesirable, thesuccess tree top event is a desirable goal. For instance,consider the probability of success for a home computeroperating as shown below.

The probability of the home computer working can becomputed.

Rsystem = (0.9999)(0.999)(0.985)(0.980)(0.985)Rsystem = 0.9498



IV-91 (492)

Product Safety and Liability

A company is liable for its products. The idea that theconsumer accepts all the risk as presented in the legalphrase “caveat emptor” (let the buyer beware) is nolonger valid. A company has the responsibility to makegood on any loss or damage incurred by the user of itsproduct. This is defined by the word liability.

Many liability lawsuits are won when the supplier showsdeliberate, glaring indifference for user safety.Companies with product safety programs generally neednot worry about this type of case because they cannormally demonstrate deliberate efforts to protect theuser. Unfortunately, blatant user indifference is not theonly user safety consideration.

Many concepts of law take into account a degree ofreasonableness. That is, the standards by which issuesare judged are based upon reasonable expectations,safeguards, or user responsibility. However, the presentliability standards are moving ever closer to absoluteliability. Absolute liability generally absolves the user offault and places any and all safety responsibilities uponthe designer, manufacturer, distributor, or store.



IV-91 (493)

Product Safety and Liability (Continued)

The majority of activities involved in a product safetyprogram take place before a product is placed in theuser’s hands. A human factors analysis is one tool usedto uncover risk and safety issues associated with theuser’s operation of products. The user focus helpsreveal many of these post-sale issues before productsare released to the customers. However, once a productis in the hands of users, new misuses, risks, usernegligence, or additional hazard exposures may becomeapparent.

Often users seek liability damages because a productcreates a risk that the company could not predict duringthe design and manufacturing efforts. These lawsuitsare successful because the company has theresponsibility to warn users about uncovered post-salehazards. Without the post-sale monitoring process, thecompany cannot become aware of new hazards.



IV-92 (494)


One product liability lawsuit can ruin a company. Forthis reason, many companies involve external or internallegal professionals, along with product safetyprofessionals throughout the product developmentprocess. Presented below are some milestone liabilityand product safety regulations.

Topic Regulations

Traffic safetylegislation

C Directed at the vehicle. The NHTSAinstituted passenger restraints (1966)

C Other laws directed at the motorist and theenvironment

Consumer ProductSafety Act (1972)

C Directed at a wide range of consumerproducts

C Granted powers to the Consumer ProductSafety Commission

Food and Drug,many different acts

C Pure Food and Drug Act (1906)C Medical Good Manufacturing Practices

(1978)C Medical Risk (1990)C Medical Quality System Regulation (QSR) -

Covering Manufacturing and Design (1996)



IV-92 (495)


Since products can impact human health and safety,design errors can lead to large personal injury claims.Strategies for dealing with this type of liability include:

C Paying attention to reliability and quality in productdevelopment and testing

C Releasing products that are well-tested and meetrequirements

C Establishing mechanisms for immediately notifyingcustomers of any hazards

C Arranging a quick replacement of defective units,when a critical problem is found

C Selecting a product liability insurance policy thatincludes provisions for defense of judgments

C Negotiating end-user agreements that have alimitation on all damages

C Including legal counsel in contract negotiations tobe sure the company has adequate protection



IV-93 (496)

Programs to Improve Product Safety

C Top management:

C Commits to make and sell only safe productsC Mandates formal design reviewsC Establishes guidelines for product traceabilityC Establishes claim defense guidelinesC Establishes safety performance guidelinesC Ensures compliance via audits

C Supplemental organization product safety structure:

C A product safety committeeC Safety engineersC Outside experts for advice and audits

C Other key product safety organizationalresponsibility centers include:

C Product designC ManufacturingC Quality controlC MarketingC Field service



IV-94 (497)

x yx

y y

- Safety Factor = S .F. = M O S =

μ μμμ μ

x

y

x y

y

60,000 psiS.F. = = = 1.875 = 187.5%32,000 psi

- 60,000 psi - 32,000 psiMOS = = = 0.87532,000 psi

μμ

μ μμ

Safety Factor

A design engineer concerned with mechanical loadingdevices must consider the safety factor and margin ofsafety. These are defined as:

Where :x = average strength and :y = average stress

Example: An aircraft component is being designed withan average material strength of 60,000 psi. Theexpected stress is 32,000 psi. What is the safety factor?What is the margin of safety?



IV-94 (498)

Stress-Strength Interference

In the most basic terms, an item fails when the appliedstress exceeds the strength of the item. In general,designers design for a nominal part strength andanticipated applied stress. The variability about thestress and strength nominals is also important. In theFigure below, the distribution curves for stress andstrength are far enough apart that there is littleprobability that a high stress level would interfere withan item that is on the low end of the strengthdistribution.



IV-95 (499)

( )1/22 2x-y x y x-y x y = - = + μ μ μ σ σ σ

Stress-Strength Interference (Continued)

In the Figure below, the proximity and variability of themeans for stress and strength indicate an increasedlikelihood of failure which is represented by theoverlapping shaded area.

Stress - Strength Overlap

When the stress distribution and strength distributionare independent of each other, the followingrelationships apply:



IV-95 (500)

( )x y

1/22 2x x

- Z =

+ μ μ

σ σ

( ) ( ) ( )( )x y

1/2 1/22 2 2 2x x

- 1600 lb - 1500 lbZ = = = 2.77 + 30 lb + 20 lb

μ μ

σ σ

Stress-Strength Interference (Continued)

To calculate the probability of a failure from stress-strength interference, the standard normal distributionand Z tables are utilized.

Example: If the stress distribution has a mean stress of1,500 lb with a standard deviation of 20 lb and the unit isdesigned to handle 1,600 lb with a standard deviation of30 lb Calculate Z to get the probability of failure:

From a standard normal distribution, the area above a Zvalue of 2.77 (2.77 standard deviations) is 0.0028. Theprobability of failure is 0.28%.


IV. PRODUCT AND PROCESS DESIGNQUESTIONS

IV-99 (501)

4.2. A technique whereby various product features are graded as torelative importance is called:

a. Classification of defectsb. Quality engineeringc. Classification of characteristicsd. Feature grading

4.4. Which of the following activities normally occurs after the finalcompletion of a product design?

a. Verificationb. Validationc. Apportionmentd. Prototype conversion

4.7. For complex electronic systems, the major contributor to repair timeis generally:

a. Diagnosisb. Disassembly/reassemblyc. Remove/replaced. Final checkout

Answers: 4.2. c, 4.4. b, 4.7. a



IV-100 (502)

4.14. Maintenance reduces the probability of failure when:

a. The hazard rate is constantb. The hazard rate is decreasingc. The hazard rate is increasingd. The hazard rate is unknown

4.16. In robust design, a factor that can cause unknown variability, or anerror in the response factor, is considered a:

a. Signal factorb. Control factorc. Noise factord. Response factor

4.18. In the failure rate model shown below, the part of the curve identifiedas A represents:

a. The bathtub curveb. Random and independent failures fitting a Poisson modelc. The debugging period for complex equipmentd. The wear out period

Answers: 4.14. c, 4.16. c, 4.18. c



IV-101 (503)

4.21. Failure modes and effects analysis involves what activity?

a. The determination of the probability of failure in a specified period oftime

b. The expected number of failures in a given time intervalc. The study of failure to determine how a product fails and what causes

the failured. A study of the probability of success in a given time period

4.22. The symbol means:

a. Welds placed hereb. Positionc. Total runoutd. Geometric tolerance

4.27. Maintainability is:

a. The probability of a system being restored to functional operationwithin a given period of time

b. Can be improved only by a state of the art improvementc. Probability of survival of a system for a given period of timed. Maintaining a machine in satisfactory working condition

Answers: 4.21. c, 4.22. c, 4.27. a



IV-102 (504)

4.30. For a shaft with a specification of 1.000" ± 0.005", what is the MMC?

a. 1.000" maximumb. 0.995" minimumc. 1.000" ± 0.005"d. 1.005" maximum

4.31. Reliability, maintainability, and product safety improvements are mostoften economically accomplished during which of the followingphases?

a. Design and developmentb. Prototype testc. Productiond. Field operation

4.35. The principal purpose of robust design techniques is to:

a. Make the product less sensitive to noise effectsb. Use the tools of experimental designc. Reduce the sources of variationd. Improve manufacturing quality

Answers: 4.30. d, 4.31. a, 4.35. a



IV-103 (505)

4.44. The risk priority number is used when:

a. Auditing safety hazardsb. Predicting reliabilityc. Constructing a fault treed. Completing a FMECA

4.45. A design review is conducted for the purpose of:

a. Verifying the details of all the drawingsb. Verifying the accuracy of all the specificationsc. Verifying workmanship quality of the drawingsd. Verifying the completeness and accuracy of the overall design

package

4.48. Specifying a tolerance by +0.000" -0.001", is known as:

a. Bilateral tolerancingb. Limit dimensioningc. Manufacturing limitsd. Unilateral tolerancing

Answers: 4.44. d, 4.45. d, 4.48. d



IV-104 (506)

4.53. If the average repair time for a system is 3 hours and the MTBMA is122 hours, what is the operational availability?

a. 0.975 c. 0.982b. 0.976 d. 0.997

4.56. Criminal liability involving injury cases may be invoked in all of thefollowing areas, EXCEPT:

a. Negligenceb. Fraudc. Mountebankd. Knowingly violating a law

4.60. The qualification of a sophisticated product would entail:

a. Neither verification nor validationb. Verification, but not validationc. Both verification and validationd. Validation, but not verification

Answers: 4.53. b, 4.56. c, 4.60. c


V. PRODUCT AND PROCESS CONTROL

V-1 (507)

OPPORTUNITIES ARE USUALLYDISGUISED AS HARD WORK,SO MOST PEOPLE DON’TRECOGNIZE THEM.

ANN LANDERS


V. PRODUCT AND PROCESS CONTROLTERMS

V-2 (508)

Product and Process Control

Product and Process Control is presented in thefollowing topic areas:

C Terms C Material controlC Tools C Acceptance sampling

Key Product and Process Control Terms

Control plan: A written document of the activitiescontrolling the process or product.

Qualification process: A process of demonstrating thata product or process is capable of fulfilling a statedspecification.

Quality characteristic: A characteristic of a process orproduct which defines the quality of the process orproduct.

Quality plan: A document with specific qualitypractices, resources, and sequences of activities toensure that customer requirements, needs, andexpectations are met.



V-3 (509)

Key Control Terms (Continued)

Rework:The action taken on a nonconforming item sothat it will fulfill the originally specified requirements.

Special characteristic: A customer-identified product orprocess characteristic.

Specification: Documented, detailed requirements withwhich a product or service must conform to.

Traceability: The ability to trace the history, application,or location of a product, and in some cases, service, bymeans of recorded identifications.

Validation: Confirmation by examination and provisionof objective evidence that the particular requirementsfor a specific intended use are met.

Verification: Confirmation by examination and provisionof objective evidence that specified requirements havebeen met.



V-3 (510)

Process Capability

Process capability is a measure of the inherentuniformity of the process and the ability to direct theprocess to a defined target. It is often necessary tocompare the process variation with the specificationtolerances to judge the suitability of the process.

Quality Planning Documents

Quality planning documents are designed for repetitiveuse. Customarily, they are included in the qualitymanual and detailed in quality procedures and workinstructions. This documentation provides an organizedmethodology for their perpetual use.


V. PRODUCT AND PROCESS CONTROLTOOLS

V-4 (511)

Written Procedures

A procedure is a document that specifies the way toperform an activity. For most operations, a procedurecan be created in advance by the appropriateindividual(s). Some procedures may be developed bythe quality department for use by other operatingdepartments. Generally, these departments provideinput.

Work Instructions

Procedures describe the process at a general level,while work instructions provide details and a step-by-step sequence of activities. Controlled copies of workinstructions are kept in the area where the activities areperformed. Some discretion is required in writing workinstructions, so that the level of detail included isappropriate for the background, experience, and skillsof the personnel that would typically be using them.



V-4 (512)

Process Controls

Production operations, which directly affect quality, areidentified and planned to ensure that they are carriedout under controlled conditions. Controlled conditionsinclude the following:

C The prior approval of processes and equipment

C Documented procedures defining the manner ofproduction

C The use of suitable production and servicingequipment, in an appropriate working environment

C Compliance with reference standards, codes,quality plans, and documented procedures

C The monitoring and control of suitable process andproduct characteristics

C Workmanship criteria, stated in the clearestpractical manner, must be provided

C The suitable maintenance of equipment to ensurecontinued process capability



V-5 (513)

Product and Process Control Methods

Determining product and process control methods isoften called the development of a quality plan. Qualityplanning employs the coordination of companyresources to meet customer requirements.

The first necessity is to identify all the key internal andexternal customer requirements. One should rememberto include all of the critical product and processcharacteristics uncovered throughout the completedesign process.

The second step is to identify the manufacturingprocess flow and the manufacturing support processes.

The third step is to identify the quality tools that acompany will use to control the processes.



V-6 (514)

Product and Process Control (Cont’d)

Requirements SupportProcesses

Quality Tools

Outsidediameter

Receivinginspection

Part workinstructions

Finishing Subassembly Inspectioninstructions

Packing Systemassemble

Process workinstruction

Length Final test Qualityprocedures

Material Shipping Purchase orderdata

Safety tests Purchasing SPC chartsLabeling Outside

processingTest fixtures

Identification Training Routing sheets

Examples of Product & Process Control Detail



V-6 (515)

Product and Process Control (Cont’d)

After the customer requirements, processes, and qualitytools have been identified, a control plan can bedetailed. First, one takes a customer requirement, thendecides which process step and which quality toolshould be used to satisfy the requirement. Someexamples are:

C The outside diameter is checked at subassemblyusing a part work instruction.

C The packing is completed at shipping using aprocess work instruction.

C The material is controlled by purchasing usingpurchase order data, requiring a certificate ofanalysis, and at receiving inspection using a partwork instruction.

C The length is checked at final inspection using aninspection report.

C A safety test is performed by an outside processorusing the appropriate purchase order data.



V-7 (516)

Control Plans

A control plan is a document describing the critical toquality characteristics of a part or process. Throughthis system of monitoring and control, customerrequirements will be met, and the product or processvariation will be reduced. Each part or process musthave a control plan. A group of common parts using acommon process can be covered by a single controlplan.



V-7 (517)

Control Plans (Continued)

For the automotive sector, ISO/TS 16949:2002 and theAdvanced Product Quality Planning APQP (2000)identify three control plan phases:

C PrototypeC Pre-launchC Production

A prototype control plan is used in the earlydevelopment stages when the part or process is beingdefined or configured.

A pre-launch control plan is used after the prototypephase is completed, and before full production isapproved.

A production control plan is used for the full productionof a part. It contains all of the line items for a full controlplan.



V-7 (518)


Often, an improvement team will undertake a project toimprove quality, costs, efficiencies, etc. A projectcontrol phase is then necessary in order to sustain theproject gains. The control plan must truly be a “livingdocument” (APQP, 2000) for it to remain effective.

A responsible person must be placed in charge of thecontrol plan. This ensures successful monitoring andupdating. The project leader may or may not be asuitable person for the role, as he/she may be replacedor transferred to a different position. A better selectionwould be the “process owner.”

The current process owner can be listed on the controlplan, but in reality it is a functional role that is to bepassed on to the next individual in that sameorganizational position. If the control plan is notmaintained, the benefits of the project could be slowlylost.



V-8 (519)


A blank control plan, a description of the line items inthe control plan, and a filled in example control plan areillustrated in the Primer. Customer requirements maydictate the exact form of the control plan. Often, thereis some flexibility in the construction of the forms.

Control Plan (Sample)

Control Plan for: Control number: Team members: Page:

Original date:Contact person (typically process owner): Revision date:

Part

/ Pro

cess

Subp

roce

ss s

tep

Key

Inp

ut v

aria

ble

(X)

Key

out

put v

aria

ble

Sp

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ia

l

Spec

ifica

tions

Mea

sure

men

t ga

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chni

que

Gag

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apab

ility

Sam

ple

size

Sam

ple

Freq

uenc

y

Initi

al C

pk

Pers

onR

espo

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le fo

rm

easu

rem

ent

Con

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met

hod

Rea

ctio

n pl

an

Illustrative Blank Control Plan



V-9 (520)

Description of Control Plan Line Items

1. Control plan: Provide a title for the control plan. Thecontrol plan will often be placed into anotherdocument, such as an instruction or database.

2. Control number: Provide a reference number.

3. Team members: If a cross-functional team isinvolved, provide the member’s names.

4. Contact person: This could be the person in chargeof the project. However, the name and function of theprocess owner are more important.

5. Page: Provide page numbers if required. Somecontrol plans may contain 20 pages.

6. Original date: Indicate the original date of issue.

7. Revision date: Provide the latest revision date of thecontrol plan.

8. Part/ process: List the part number or the processflow being charted.

9. Subprocess step: Indicate the subprocess step.



V-9 (521)

Control Plan Line Items (Continued)

10. Key input variable (X): Note the key input variable,when appropriate. On any line item, only the X or Yvariable is filled out, not both. This indicates whichitem is being monitored.

11. Key output variable (Y): Note the key input variable,when appropriate.

12. Special characteristics note: Indicate if a specialcharacteristic is to be monitored and controlled.

13. Specifications: For manufacturing applications, theengineering specifications should be controlled.For other applications, use the specification limitsand target values.

14. Measurement gage technique: The gage ormeasurement technique should be described.

15. Gage capability: Provide the capability of themeasurement system. Instruments may needuncertainty determinations. The MSA manual lists:

C Under 10% error as acceptableC 10% to 30% error may be acceptableC Over 30% error is not acceptable



V-10 (522)

Control Plan Line Items (Continued)

16. Sample size: Provide the sample size for eachsubgroup.

17. Sample frequency: List how often the inspection ormonitoring of the part or process is required.

18. Initial Cpk: This provides an indication of processcapability.

19. Person responsible for measurement: Indicate whowill make and record the measurement.

20. Control method: Note how this X or Y variable willbe controlled. Examples include control charts,checklists, inspections, measurements, etc.

21. Reaction plan: Describe what will happen if thevariable goes out of control.



V-11 (523)

Illustrative Control PlanControl Plan (Example)

Control Plan for: CQE PrimerControl number: CQE-001 Team members: Glenn, Wes,

Tim, Bob, Odis, BillPage: 1 of 1Original date: March 16, 2006

Contact person (typically Process Owner): Bill Revision date: August 15, 2006

Part

/ Pro

cess

Subp

roce

ss s

tep

Key

Inpu

t var

iabl

e (X

)

Key

out

put v

aria

ble

(Y)

Spec

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char

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ristic

note

Spec

ifica

tions

Mea

sure

men

t/ ga

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chni

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Gag

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Sam

ple

size

Sam

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freq

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Initi

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pk

Pers

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Con

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Primer Receivebinders

ringmetal

Heavyduty slant D visual NA 5 lot NA clerk checklist

Notify Billcontactsupplier

binderprint

coolgray4

20% ofblack 10% 5 lot 1.5 clerk checklist


binderprint

PMS 492(Red)

Pantonecolor 10% 5 lot 1.5 clerk checklist


binderwidth

3.13" +/- 0.03"

steelruler 6% 5 lot 1.7 clerk checklist


binderheight

11.63" +/- 0.03"

steelruler 6% 5 lot 1.7 clerk checklist


Control Plan for Receiving Primer Binders

In the example above, only the key input column iscontrolled.



V-11 (524)

Illustrative Control Plan (Continued)

Control plan construction is often led by the leader incharge of the improvement project. The team is usuallycross-functional with individuals from different areas,including the process owner.

The control plan must show compliance and controlbefore project closure. A successful control plan willremain a living document to ensure that the benefits ofthe project will be fully realized.


V. PRODUCT AND PROCESS CONTROLMATERIAL CONTROL / MATERIAL IDENTIFICATION

V-12 (525)

Material Control

Material Control is presented in the following topicareas:

C Material identification, status, and traceabilityC Material segregationC Classification of defectsC Material review board (MRB)

Material Identification and Traceability

ISO 9001:2000 and ISO/TS 16949:2002 both requirematerial identification by a suitable means from receiptthrough all stages of production, delivery, andinstallation. In order for the next operation to besuccessful, there must be assurances that the rightinputs are used. This is accomplished by matching thematerial identification with the requirements on theprocess control documents.



V-12 (526)

Material Identification

As material (or product) moves through themanufacturing processes, its current status must beknown. In many instances, control marking, inspectionstamps, and symbols, tags, cards, or labels arenecessary. Material status documents includeinformation about:

C Material identificationC Which process(es) the material has completedC Which inspection(s) the material has completedC Where the material is going nextC Additionally, determine if it is in the right place



V-12 (527)

Material Traceability

Traceability is an ability to trace the history, andapplication, or location of an item using records.Traceability records would show:

C The inputs into the productC The test or production activities performedC The lot, batch, or unit identificationC Where the item is or where it was used

The purpose of traceability records is to demonstrateproduct conformance. If sometime after the productships its conformance is questioned, the records,traceable to the product, would be the evidence ofconformance. Traceability records also show where theproduct went in case the product must be recalled.



V-13 (528)

Part Identification

Part identification normally refers to the following threemajor areas:

C Control marking by the supplier, manufacturingdepartment, or quality assurance as required bydrawing or inspection routing specifications. Thesestamps and symbols may be used to verify theperformance and/or acceptance of specialinspections, fabrication operations, or tests. Thesestamps may or may not be given a serial number.



V-13 (529)

Part Identification (Continued)

C The use of inspection stamps and symbols toindicate inspection status and acceptability.Examples include:

C Incoming acceptance stamp: An inspector’sacceptance stamp is applied to each partaccepted as conforming to drawing orspecification requirements.

C In-process acceptance stamp: Same as above,except the inspection is in-process and eachmanufactured part has been actually inspectedand found to conform to requirements.

C Sample piece identification stamp: A symbol isapplied to each sample piece selected todetermine final acceptance based on samplingtechniques.

C Nonconforming material stamp: Anynonconforming parts shall be identified with theinspector’s personal discrepant part stamp.



V-13 (530)

Part Identification (Continued)

C Items not requiring individual identification:Stamping may be impractical due to physicallimitations or detrimental impact on qualityrequirements. In these cases, an inspection tag,card or label may be attached to a container toindicate the status.

The quality department is traditionally responsible forcentralized stamp control and administration. Thisactivity includes the responsibility to obtain, stock,issue, and maintain records of all inspection stamps andtheir identifying serial numbers.


V. PRODUCT AND PROCESS CONTROLMATERIAL CONTROL / MATERIAL SEGREGATION

V-14 (531)

Material Segregation

When nonconforming items or lots exist, these productsshould immediately be identified and segregated fromgood material. Often the nonconforming material isidentified with a “hold” status. All nonconforming itemsshould be subjected for review by the designated parties(MRB) to determine if the product can be used “as is”,repaired, reworked, or scrapped. Disposition ofnonconforming material should be made as soon aspracticable.

Decisions to “pass” a segregated product should beaccompanied by the appropriate concession, waiver,explanation, etc., and signed by the appropriateauthority. All steps of dealing with a nonconformingproduct should be documented.

Depending upon the severity of the nonconformity, avariety of company functions may be assigned to assistwith the evaluation, investigation, analysis, andresolution of the problem.



V-14 (532)

Control of Nonconforming Material

ISO 9001:2000 states that an organization shall ensurethat product which does not conform to productrequirements be identified and controlled to prevent itsunintended use or delivery. Controls, responsibilities,and authorities for dealing with nonconforming productshall be defined in a documented procedure.

An organization shall deal with nonconforming productin one or more of the following ways:

C Taking action to eliminate the nonconformity

C Authorizing its use, release, or acceptance underconcession by a relevant authority (or customer)

C Taking action to preclude its intended use

Records of the nature of the nonconformity, and anysubsequent action shall be maintained.



V-15 (533)

Control of NC Material (Continued)

Additionally, ISO/TS 16949 (2002) requires that:

C Product with unidentified or suspect status beclassified as nonconforming

C Instructions for rework and reinspection beaccessible and utilized

C Customers be informed promptly if nonconformingproduct has been shipped

C A customer waiver, concession, or deviation permitbe obtained

C Any product shipped on a deviation authorizationbe properly identified

C Records for any authorized deviations bemaintained

C Upon authorization expiration, the originalrequirements must be met



V-15 (534)

Control of NC Material (Continued)

ISO 9001:2000 states that internal procedures shallcontrol nonconforming product so that it is preventedfrom inadvertent use or installation.

A flow chart could be developed to reveal the followingkey process steps to control nonconforming material:

C The nonconformance is discoveredC The nonconforming material is segregatedC The nonconformance is documentedC A MRB determines dispositionC Possible dispositions include:C Scrap the partC Accept the part for use as isC Rework the part

C The actual disposition is madeC The product is returned to normal flowC The paperwork is cleared



V-16 (535)

Production orinspection

discovers ncproduct

Product is heldin special

holding area

Inspection creates adeviation report (DR)to document condition

Qualitysupervisor

reviews product

Deviationreport notedwith action

Reworkproduct

Reworksuccessful

MRBproduct

MRB makesdisposition

Use “as is” Repairproduct

Return toproduction for

repair

Repairsuccessful

Scrapproduct

Follow scrapinstructions

Scrapproduct

Identify asscrap

Send to scrapdisposal area

Clear DR and fileReturn product

to flow

Close DR

No

Yes

No Yes

File in DR quality records

Nonconforming Material Flow Chart



V-17 (536)

Nonconforming Material Procedure

Nonconforming material procedures could varysubstantially, dependent upon the product supplied bya company. The key elements for a hypotheticalnonconforming material procedure are detailed below:

C Nonconforming purchased materials are addressed:

C Receiving inspection identifies any incomingnonconforming material and moves it to areviewing area.

C In the review area, inspection personnel may callupon a quality assurance supervisor and apurchasing representative to make a preliminaryreview. Several decisions are possible:

C Referral to the MRBC Returned to the supplier for rework or scrapC Scrapped internally (after supplier notification)C Salvage repair, requiring MRB authorizationC Accepted for further processing. This generally

involves very minor nonconformancies.



V-17 (537)

NC Material Procedure (Continued)

C Suppliers are often required to take actions similarto those mentioned above.

C Nonconforming fabricated materials are addressed:

C Any nonconforming product found during internalin-process inspection is identified and removedfrom the normal process flow in such a way as toavoid inadvertent return to production.

C In the review area inspectors may call uponquality assurance supervisors to make apreliminary review. Actions may include:

C Referral to the MRBC Scrapping the materialC Reworking the material, requiring reinspection



V-18 (538)

Nonconforming Material Definitions

Critical defect: A defect that could cause hazardous orunsafe conditions for individuals using or maintainingthe product. A defect that could prevent the productfrom performing its intended function.

Defect: Any material, part, or component that fails tomeet specified requirements.

Deviation: The planned departure from requirementsprior to the initial manufacture of an item. A particulardesign requirement, a specific number of units orspecific period or time and will be identified uponshipment.

Deviation permit: Written authorization given inadvance of manufacture to deviate from specifiedrequirements for a given number of units or for aspecific period of time.

Equivalent item: An item that is interchangeable andequal to or better than the item called for in aspecification.



V-18 (539)

Nonconforming Material Definitions

Major defect: A serious defect, but less severe than acritical defect, that is likely to result in failure orsubstantially reduce the usability of an item for itsintended purpose.

Material review board (MRB): A formal multidisciplinarypanel established to perform material review. This panelreviews, evaluates, and either fixes, or disposes of,specific nonconforming materials or services. Importantsupportive responsibilities include the initiation andachievement of corrective action.

Minor defect: A defect not likely to reduce the usabilityof the item for its intended purpose.

Nonconformance: A departure from the requirementsspecified in the contract, specification, drawing, or otherproduct description.



V-19 (540)

NC Material Definitions (Continued)

Preliminary review: The review and disposition ofnonconforming material, by quality assurancesupervisors, as it is initially discovered at the applicableinspection area prior to referral to the material reviewboard.

Recertification: A process for retesting or reevaluatingmaterial with an expired shelf life to determine if theshelf life can be extended.

Reject: A defective or nonconforming item which isunsuitable for use as offered. A product or servicewhich is not accepted because it fails to meet therequirement criteria.

Repair: The subjection of nonconforming material to anapproved process designed to reduce but notcompletely eliminate the nonconformance. The purposeof repair is to bring nonconforming material into anacceptable condition.

Rework: The reprocessing of nonconforming material tomake it conform to the contract requirements.



V-19 (541)

NC Material Definitions (Continued)

Salvage repair process: A technique, of possiblerecurrent use, for repairing a nonconformance when ithas been demonstrated that the technique, whenproperly applied, will result in an adequate and costeffect ive method for disposit ioning thenonconformance.

Scrap: Nonconforming material that is not usable for itsintended purpose or cannot be economically reworkedor repaired.

Suspended: Material not acceptable due to lack ofcorrective action.

Use “as is” material: Material that is found to benonconforming in a minor way but suitable for itsintended purpose and acceptable to the customer.

Waiver: Written permission to accept for use acompleted, but nonconforming, item either “as is,” orupon completion of rework for a specified number ofunits or period of time.


V. PRODUCT AND PROCESS CONTROLMATERIAL CONTROL / CLASSIFICATION OF DEFECTS

V-20 (542)

Classification of Defects

Quality defects are not equal in their effect on theuseability of the final product or service. Some defectsare of critical importance; while others are of minorimportance. The more important the characteristic, thegreater the effort should be to detect and correct it.Many companies utilize a formal system of seriousnessclassification which:

C Establishes the classification levels (3 or 4)C Defines each defect level for inspection purposes



V-20 (543)

Classification of Defects (Continued)

The inspection department then classifies each defectinto its proper level. Often the classifications are givena numeric weight. Listed below is an example fromBenbow (2003):

Category DescriptionCritical May lead directly to severe injury or

catastrophic economic lossSerious May lead to injury or significant economic

lossMajor May cause major problems during normal

use and reduce the usability of the productMinor May cause minor problems during normal

use



V-20 (544)

An illustration of automotive defect seriousnessclassifications follows:

Class Nature ExamplesCritical Defects which are

critical to personalsafety or are essentialto proper vehicleoperation

Poor heat treatment ofmotor mounts orsteering parts,inoperative brakes,etc.

Major Defects which mightaffect the generalfunction of essentialvehicle parts orappearance

Glove box will notopen, body rust,cruise controlinoperative, etc.

Minor Defects which affectthe functions of minorparts or not essentialappearance

Minor paint runs,misaligned decals, aloose door panel, etc.

The major category may be subdivided into types A andB, with type A being more severe.


V. PRODUCT AND PROCESS CONTROLMATERIAL CONTROL / MATERIAL REVIEW BOARD

V-21 (545)

Material Review Board (MRB)

The membership, responsibilities, and supportingactivities of a material review board are presented belowin outline format.

C Membership:

C Includes representatives from the qualityassurance and engineering departments.

C In many instances, customer representatives,planning, and manufacturing departments areincluded.

C Membership may be on a rotating basis.

C The experience and qualifications of MRBmembers are kept on file in the material reviewoffice and should be sufficient to pass an externalcustomer audit or inquiry.



V-21 (546)

MRB (Continued)

C Responsibilities:

C The principal responsibility of the material reviewboard is to determine the disposition ofnonconforming materials.

C The material review board, in many cases, isresponsible for the initiation and follow-up ofcorrective action requests. In some cases, thisresponsibility may be referred to a correctiveaction board (CAB).

C The MRB is further responsible for providingmeaningful and timely feedback to all keymanagement and manufacturing functions.

C The material review board often has the authorityto take the following actions:

C Rework or repair of the productC Use the product “as is”C Reject or scrap the productC Require additional inspection testsC Initiate a corrective action request



V-22 (547)

MRB (Continued)C Supportive Activities:

C A material review area must be set aside for usein holding and accounting for materials awaitingMRB action.

C For a contracted item, the MRB must often receiveconcurrence from the customer. This includes asignature and date.

C A quality assurance representative is usuallyresponsible for providing a full description ofmaterials awaiting MRB action.

C The MRB’s quality assurance representative isusually responsible for the initiation of a materialreview report (MRR) form which can include:

C MRR numberC Discrepant part name and numberC The contract, or work order identificationC The department where detectedC The PO number (customer supplied product)C The quantity of units rejectedC The location of the held itemsC Any pertinent part drawing informationC A description of the nonconformanceC An explanation of the probable cause



V-22 (548)

MRB (Continued)

C The MRB’s quality department representative isgenerally responsible for the generation of a MRRlog sheet (or report) which captures the precedingitems and further details:

C More information on the nature of thediscrepancy

C The final disposition of the nonconformity

C An identification of those responsible forcorrective action

C A due date for those actions



V-23 (549)

MRB (Continued)

C The MRB’s quality department representative mayalso be responsible for:

C Attaching appropriate drawings to thediscrepant material documents

C Transmitting a request for any necessarytesting, inspection, or analysis

C When applicable, the MRB requests andprocesses requests for deviations, and waivers.

C In the case of age-sensitive materials that haveexceeded expiration dates, a recertification maybe requested by the MRB.



V-23 (550)

MRB (Continued)

C The MRB, or quality representative, can beresponsible for the transport of anynonconforming materials and documentation toan appropriate location for disposition.

C After an appropriate time interval, verification ofthe authorized disposition should be made, withthe verifier recording appropriate findings.

C The follow-up on corrective action is a key systemcomponent and may be handled in a variety ofvenues: the MRB, a management steeringcommittee, or a CAB. In every case, there shouldbe a management review of the process.


V. PRODUCT AND PROCESS CONTROLACCEPTANCE SAMPLING / SAMPLING CONCEPTS

V-24 (551)

Acceptance Sampling

Acceptance Sampling is presented in the followingtopic areas:

C Sampling conceptsC Sampling standards and plansC Sample integrity

Sampling Concepts

Sampling refers to the evaluation of a portion of apopulation (lot, batch, etc.) for the purpose of obtaininguseful information about it. Acceptance sampling dealswith the evaluation of either incoming or outgoingvendor product. Normally an accept/reject decision foran entire lot is made based upon the results of a sample.The advantage of sampling is economics. However, noform of inspection or sampling should be used as asubstitute for process control.



V-24 (552)

Sampling Advantages

C Checks on the adequacy of process controlC The inspection labor force can be smallerC There is less handling damage to the productC The product is disposed of in shorter timeC An inspector will be less boredC Generates fewer errors than 100% inspectionC Lot rejection dramatizes the need for correction

Sampling is most useful when:

C Inspection damages the productC The per unit inspection costs are highC The results of passing a defective unit are lowC There are large amounts of product to be inspected



V-25 (553)

Sampling Disadvantages

C There is a risk of rejecting good productC Administration costs are often highC Less information is obtained versus inspection

Sampling Precautions

C Sampling provides no estimate of lot quality.C Rejected product may be fit for use.C There is no single “representative sample.”C Without statistics, sampling costs can be highC Without statistics little information is known.C Sample size is more important than lot %.C Only random samples are statistically valid. C Sample plan misuse of can be costly.C Any AQL allows defectives.C No sample plan eliminates defectives.C Sample access does not guarantee randomness.C Stratified samples are sometimes very informative.C Sampling often places focus in the wrong place. C The supplier should provide evidence of quality.C Sampling plans derive from process knowledge.C Process control is better than sampling.



V-26 (554)

Sampling and Inspection Types

Types of sampling and inspection are presented below:

Type Function DescriptionDetail or 100%inspection

Distinguishesgood piecesfrom bad pieces

Sorts good piecesfrom bad pieces

Acceptancesampling

Distinguishesgood lots frombad lots

Classifies lots as toacceptability

Incominginspection


Is performed onincoming material

Processinspection


Is done betweendepartments of thesame company

Finalinspection


Is done by theproducer prior toshipment



V-26 (555)

Sampling and Inspection Types (Cont’d)

Pre-controltechniques

Determines ifthe process isapproachingspec. limits

Determines if achange is significantenough to makeadjustments

Controlsampling

Determines ifthe process ischanging

Control chartsindicate if theprocess is changing

Accuracyinspection

Evaluates theaccuracy ofinspectors

Measures theeffectiveness ofinspectors

Productauditing

Evaluates thequality of theproduct

Assesses theproduct and processthat produced it

Discoverysampling

Evaluates product qualitybased on anassumedfrequency

Provides a specifiedprobability that thesample will containat least one defect



V-27 (556)

Random Sampling

The use of a sampling plan requires randomness insample selection. Obviously, random sampling requiresgiving every item an equal chance of being selected forthe sample. The sample must be representative of thelot, not just the product that is easy to obtain. Thus, theselection of samples requires some up-front thoughtand planning.



V-27 (557)

Common Sampling Tables

ANSI/ASQ Z1.4-2003 provides tables of sampling plansfor attributes. There are three types of sampling used:

1. Single sampling: Where lots are inspected andthe decision to accept or reject is based on onesample

2. Double sampling: Where the decision to acceptor reject a lot is based on a maximum of twosamples

3. Multiple sampling: Where the decision to acceptor reject the lot is based on a maximum of sevensamples

ANSI/ASQ Z1.9-2003 provides tables of sampling plansfor variables.

Dodge-Romig Tables are attribute plans used foreffective inspection if the the process average is known.



V-27 (558)

Variables Versus Attribute Sampling

Variables sampling plans should be used when themeasurement of a few items is less expensive than thecounting of many items, and the populationapproximates a normal distribution. ANSI/ASQ Z1.4-2003 (attributes) and ANSI/ASQ Z1.9 -2003 (variables)provide OC curves which allow switching between thetwo plans where possible. The following two plans havecomparable OC curves:

Attribute plan Variables plan n = 125 n = 19 c = 3 k = 1.908



V-28 (559)

Fixed Sampling

Taking a fixed sample size from a lot or batch onlyworks if the lot or batch size remains relatively constant.This will be illustrated later with a set of OC curves from10% sample size plans. The only advantage is that afixed sample size in inspection is easy to remember.Fixed, small sample sizes are more widely used inauditing.

Stratified Sampling

Stratified samples are sometimes more informative thanhomogeneous samples. When analyzing inventory, onewould not want to put $25,000 motors in the same stratawith 2¢ screws. Additionally, one might be interested indetermining the amount of pallet damage in a storagearea. There might be a need to sample more row ends,row corners or bottom pallets in preference to toppallets in the middle.



V-28 (560)

Zero Defect Sampling

There is a growing interest in zero acceptance numberplans for two reasons: the advent of six sigmamethodology and the litigious society that currentlyexists. Often, companies claim they are producing partswith very low ppm failure rates. This assumption isbased on varieties of Cpk determinations. In fact, acompany should not make such a claim until they haveinspected millions of parts.

Plans with zero acceptance numbers have existed foryears. A number of these are evident in the ANSI/ASQZ1.4-2003 tables that follow. However, many of theseplans have relatively small sample sizes. Obviously,other plans with nonzero acceptance numbers andlarger sample sizes will better discriminate betweenquality levels.



V-29 (561)

Start

Inspect isuccessive units

Replace unitwith good unit

Defective found

Defective found No defective

No defective

Random selectionfraction f unit

Continuous Sampling

The most widely used continuous sampling plan is theoriginal — the Dodge CSP-1 plan. It is carried out on astream of product, with production units inspected inorder of production. A flow chart follows:

Note that the sampling frequency (f), clearance number(i) must be determined in advance.



V-30 (562)

Sequential Sampling

Sequential sampling is the most discriminating of theacceptance sampling plans. It involves making one ofthree decisions as each sample item is obtained: acceptthe lot, reject the lot, or continue sampling. Onecontinues sampling until the cumulative number ofdefectives crosses either the lot reject limit, or the lotaccept limit. When a limit is crossed, the lot size limit isreached and a new lot begins. Sequential samplingrequires the least average sample size.

Sequential plans are often applied where sampleeconomics are critical, and a minimum sample size isrequired. A sequential plan is more complex and moredifficult to administer than other plans. Samples mustbe obtained one item at a time, and operators requiremore training.



V-30 (563)

Other Sampling Considerations

A sampling plan should take advantage of knowninformation (process average, process capability, etc.)to minimize total inspection costs. A good plan shouldbe simple to administer and easy for inspectors tounderstand.

The sampling risks (both " and $ risks) should beknown, and be compatible with the consumer’spriorities. The quality index chosen (AQL, AOQL, LTPD,LQL, etc.) should reflect the respective needs of boththe producer and the customer.



V-31 (564)

Inspection/Sampling Economics

There are many alternatives for evaluating lots:

C No inspectionC Small samplesC Large samplesC 100 percent inspectionC Redundant inspection (> 100 %)

One cost model for attribute plans is considered below:

Where:

TC = Total costA = Overhead costB = Cost/unit of

sampling

nMAX= Max. Sample size C = Cost/unit of

inspecting = Average sample sizen



V-31 (565)

Inspection/Sampling Economics (Cont’d)

If the percent defective is greater than 5 %, then 100 %inspection should generally be used. If the sample sizeis assumed to be small compared to the lot size, thebreak-even point is determined by:

Where: D = cost if a defective passesC = inspection cost/item



V-32 (566)

The Operating Characteristic Curve

Even 100% inspection does not catch all defects. It isestimated that inspectors using conventional equipmentwill find 85%/90% of all defects. Sampling also involvesrisks that the sample will not adequately reflect theconditions in the lot. Sampling risks are of two kinds:

C Good product is rejected (the producer or alpha "risk)

C Bad product is accepted (the consumer or beta $risk)

The operating characteristics (OC) curve for a samplingplan quantifies these risks.

The OC curve is a graph of the percent defective in abatch versus the probability that the sampling plan willaccept that batch.



V-33 (567)

OC Curve (Continued)

Shown below is an “ideal” OC curve. Assume that it isdesirable to accept all lots 1% defective or less andreject all lots having a quality level greater than 1%defective. All batches with less than 1% defective havea probability of acceptance of 100% (1.0). All lotsgreater than 1% defective have a probability ofacceptance of 0.

Pa

Lot Percent Defective

However, no perfect sampling plan exists. There willalways be some risk that a “good” product will berejected or that a “bad” product will be accepted.



V-33 (568)

Sampling Plan Quality Indices

Many sampling plans are based on the quality indicesbelow:

1. Acceptance quality limit (AQL): This is defined as theworst tolerable quality level that is still consideredsatisfactory as a process average. The probability ofaccepting a lot produced at the AQL should be high.ANSI/ASQ Z1.4-2003 prefers that the phrase“acceptable quality limit “ no longer be used.

2. Rejectable quality level (RQL): This definesunsatisfactory quality. In the Dodge-Romig plans, theterm “lot tolerance percent defective (LTPD)” is usedinstead of RQL. The probability of accepting a RQLlot should be low. In some tables, this is known asthe consumer's risk and has been standardized at 0.1.

3. Indifference quality level (IQL): This is a quality levelsomewhere between the AQL and RQL. It is normallydefined as the quality level having probability ofacceptance of 0.50. The IQL is rarely used.



V-33 (569)

Typical OC Curve

Pa




V-34 (570)

( ) ( ) ( )r r-np -e np eP r = =

r! r!

μ μ

Constructing an OC Curve

An OC curve can be developed by determining theprobability of acceptance for each of several values ofincoming quality. Pa is the probability that the numberof defectives in the sample is equal to or less than thesampling plan acceptance number. There are threeattribute distributions that can be used to find theprobability of acceptance: the hypergeometic, binomial,and the Poisson distribution. When the defective rate isless than 10%, and the sample size is relatively large,the Poisson distribution is preferable because of theease of table use. The Poisson formula as applied toacceptance sampling is:

P(r) = the probability of exactly r defectives in a sampleof n. Note that np = :. The above equation can besolved or Appendix Table III can be used. This tablegives the probability of r or fewer defectives in a sampleof n from a lot having a fraction defective of p.



V-35 (571)

Constructing an OC Curve (Cont’d)

Consider the following example:

Assume: n =150, c = 3

P np Pr#31% (150)(0.01) = 1.50 0.932% (150)(0.02) = 3.00 0.653% (150)(0.03) = 4.50 0.344% (150)(0.04) = 6.00 0.155% (150)(0.05) = 7.50 0.066% (150)(0.06) = 9.00 0.02

Pa




V-36 (572)

OC Curve for Changing Sample Size

c is fixed

Pa




V-36 (573)

OC Curve for Changing c

n = 40 (fixed)

Pa




V-37 (574)

OC Curve for Changing Lot Size

n = 20 fixedc = 0 fixed

Pa




V-37 (575)

OC Curve for a Fixed Lot Percentage

n = 10% of N

Pa


Note why fixed % sampling plans do not provide thesame risks.



V-37 (576)

Average Outgoing Quality Limit (AOQL)

The term AOQL is used in the Dodge-Romig tables andin other sampling plans. The AOQL is equal to themaximum AOQ. The following example should help withthe explanation.

Assumptions:

C The lot size (N) is relatively constantC There is 100% inspection of rejected lotsC All defective material is replaced with good

Where: p = % defective Pa = Probability of acceptance

AOQ = p C Pa

Pa is obtained from the Poisson distribution table.



V-37 (577)

Incoming Lot Percent Defective 0 1 2 3 4 5 6

00.10.20.30.40.50.60.70.80.9

11.11.21.31.4

DecimalPercent

Max AOQ = AOQL = 1.294

AOQL (Continued)

For the OC Curve (N = 150, c=3)

p np Pa AOQ %

0.0 0.00 1.000 0.000

0.5 0.75 0.993 0.496

1.0 1.50 0.934 0.934

1.5 2.25 0.809 1.214

2.0 3.00 0.647 1.294

2.5 3.75 0.484 1.209

p np Pa AOQ %

3.0 4.50 0.342 1.027

3.5 5.25 0.232 0.811

4.0 6.00 0.151 0.605

4.5 6.75 0.096 0.431

5.0 7.50 0.059 0.296

5.5 8.25 0.036 0.197

6.0 9.00 0.021 0.127



V-38 (578)

Sampling Definitions

Some basic sampling definitions follow:

Acceptancequality limit(AQL)

The quality level that is the worsttolerable process average when acontinuing series of lots is submittedfor acceptance sampling.

Acceptancenumber

The maximum number of defectiveunits or defects in a (Ac or C ) samplethat will permit acceptance of theinspection lot.

Averageoutgoingquality (AOQ)

The expected quality of outgoingproduct following the use of anacceptance sampling plan for a givenvalue of incoming product.

Averageoutgoingquality limit(AOQL)

For a given acceptance sampling plan,the maximum AOQ for all possiblelevels of incoming quality.

Clearancenumber

As associated with a continuoussampling plan, the number ofinspected units of product that must befound acceptable during 100%inspection before the amount ofinspection can be changed.



V-38 (579)

Sampling Definitions (Continued)Consumer'srisk ($)

The probability of accepting a bad lot.

Defect A departure of a quality characteristicfrom its intended level or state thatoccurs with a severity sufficient tocause an associated product or servicenot to satisfy its intended use.

Defective A unit of product that contains one ormore defects at least one of whichcauses the unit to fail itsspecifications.

Discrepancy A failure to meet the specifiedrequirement, supported by evidence.

Inspection The process of measuring, examining,testing, or otherwise comparing a unitwith requirements.

100%Inspection

Inspection in which specifiedcharacteristics of each unit of productare examined or tested to determineconformance with requirements.

Inspection byattributes

Inspection, whereby either the unit ofproduct is classified simply asconforming or non-conforming, or thenumber of nonconformities.



V-39 (580)

Sampling Definitions (Continued)Inspection byvariables

Inspection, wherein certain qualitycharacteristics are evaluated withrespect to a continuous numericalscale.

Inspectionlevel

A feature of a sampling schemerelating the size of the sample to thatof the lot.

Inspection,normal

Inspection, used when there is noevidence that the quality of the productbeing submitted is better or poorerthan the specified quality level. This isthe usual inspection starting point.

Inspectionrecord

Recorded data concerning inspectionresults.

Inspection,reduced

A feature of a sampling schemepermitting smaller sample sizes thanare used in normal inspection.

Inspection,tightened

A feature of a sampling scheme usingstricter acceptance criteria than thoseused in normal inspection.



V-40 (581)

Sampling Definitions (Continued)Lot percentdefective(LPD)

This percentage is estimated bydividing the number of defectives bythe sample size and then multiplyingby 100.

Example: d / n x 100Lot size (N) A collection of units of similar product

from which a sample is drawn andinspected.

Operatingcharacteristiccurve

A curve showing, for a given samplingplan, the probability of accepting a lotas a function of the lot quality.

Probability ofacceptance(Pa)

The probability that a lot will beaccepted under a given sampling plan.

Processaverage

The average percent of defectives oraverage number of defects perhundred units of submitted product.

Producer'srisk (")

The probability of rejecting a good lot.

Randomsampling

The selection of units such a mannerthat all combinations of units underconsideration have an equal chance ofbeing selected.



V-41 (582)

Sampling Definitions (Continued)

TheDecision Made

Lot Quality

Good Bad

CalledGood

CalledBad

1 - "

Producer’s Confidence

$

Type II Error

"

Type I Error

1- $

Consumer’s Confidence

Reducedinspection

Inspection under a sampling planusing the same quality level as fornormal inspection, but requiring asmaller sample.

Rejectionnumber (Re)

The minimum number of defects ordefective units in the sample that willreject the lot or batch.

Sample size(n)

The number of units in a sample.

Samplingerrors

In sampling one never knows whetherthe lot is good or bad. See thedecision matrix below:

Sampling Error Matrix



V-42 (583)

Sampling Definitions (Continued)Sampling,double

Sampling inspection in which theinspection of the first sample of size n1leads to a decision to accept a lot, notto accept it, or to take a second sampleof size n2.

Sampling,multiple

Sampling inspection in which, aftereach sample is inspected, the decisionis made to accept a lot; not to accept it,or to take another sample to reach thedecision.

Samplingplan

A statement of the sample size or sizesto be used and the associatedacceptance and rejection criteria.

Sampling, sequential

Sampling inspection in which, aftereach unit is inspected, the decision ismade to accept the lot, not to accept it,or to inspect another unit.

Sampling,single

Sampling inspection in which, aftereach unit is inspected, the decision ismade to accept the lot or reject it.


V. PRODUCT AND PROCESS CONTROLACCEPTANCE SAMPLING / SAMPLING STANDARDS

V-43 (584)

Sampling Standards and Plans

Sampling plans are of two major types:

1. Attributes plans

Defectives: A sample is taken from a lot with eachunit classified as acceptable or defective. Thenumber of defectives is then compared to theacceptance number in order to make an accept orreject decision for the lot.

Defects: A sample is taken from a lot and the defectsare counted. The ratio of defects/100 units is derived.This value is compared to the acceptance number, inorder to make an accept or reject decision for the lot.

Examples: ANSI/ASQ Z1.4-2003.Dodge-Romig tables



V-43 (585)

Sampling Standards and Plans (Cont’d)

2. Variables plans

A sample is taken and one or more qualitycharacteristic measurements are made on each unit.These measurements are then summarized intosimple statistics (such as the sample average orstandard deviation) which are compared with acritical value defined in the plan. A decision is thenmade to accept or reject the lot.

Example: ANSI/ASQ Z1.9-2003

It is not the intent of this text to provide copies ofsampling plans. The intent is to illustrate how the majorplans are used. There are provisions for switchingbetween the ANSI/ASQ plans to provide correspondingOC curves.



V-44 (586)

Attribute Sampling Plan Summaries

Plan Type Application Key FeaturesANSI/ASQ Z1.4MIL-STD-105E

Single,double, and

multiple

Bad lots are generallyrejected, but may be 100%inspected.

Based on an AQL. Minimizes therejection of good lots. Easy toexplain and administer.

Dodge-Romig Single anddouble

Rejected lots are 100%inspected and bad product isreplaced.

Plans for LTPD or AOQL. Minimum inspection is required.

Chain sampling Single andtwo-stage

Useful for destructive orcostly testing.

Minimizes sample sizes withoutlarge rejection risk.

Bayesian(discovery)sampling

Generallysingle

Used when the probability ofdefective lots can beestimated.

Relatively small sample sizes arerequired.

Sequentialsampling

Unit sampling,binomial

Used to screen lots; rejectedlots are 100% inspected.

Examines one item at a time. The ATI is minimal.

Skip-lot plans Single Useful for high quality levelsand when inspection iscostly.

Minimizes inspection withprotection against qualitydeterioration.

MIL-STD-1235MIL-HDBK-107

Continuoussingle-level

Used for continuousproduction andnondestructive inspection.

Plans limit the average quality inthe long run.

MIL-STD-1235MIL-HDBK-106

Continuousmulti-level

Same as above. Plans limit the average quality inthe long run.



V-44 (587)

Variable Sampling Plan Summaries

Plan Distri-bution

Criteria Key Features

ANSI/ASQ Z1.9MIL-STD-414

Normal Acceptancequality limit

Provides lot evaluation to a specified AQL.

Single-samplingvariables plan

Normal Percentdefective

Provides sample size and acceptancevalues for defined risks.

MIL-HDBK-108 Exponential Mean life Provides lot evaluation, with and withoutitem replacement.

MIL-STD-690 Exponential Failure rate Provides tables for process evaluation.

MIL-HDBK-781MIL-STD-781

Exponential Mean life Provides process and lot evaluation.



V-45 (588)

ANSI/ASQ Z1.4

ANSI/ASQ Z1.4-20032 consists of a sample size codeletter table and tables describing acceptance andrejection numbers. Operating characteristic (OC) curvesapplicable to single, double, or multiple plans areprovided.

Single Sampling Tables

Three numbers are necessary to describe a singlesampling plan using these standards.

N = lot size n = sample size

Ac = c = the maximum number of defectives to still beacceptable



V-45 (589)

ANSI/ASQ Z1.4 (Continued)

On the next two pages are a ANSI/ASQ Z1.4-20032 codeletter index and a single sampling table for normalinspection. Consider a lot size of 570 pieces, AQL = 4%and general inspection level II.

C In the code letter table, the sample code is J.

C In the single sampling table, the Ac number is 7 andthe Re number is 8 for a sample size n = 80.



V-45 (590)

ANSI/ASQ Z1.4 Practice Exercises

Example 5.1: For N = 75, AQL = 1.5%, single sampling,general inspection level II, determine the following:

The code letter The acceptance numberThe rejection number The sample size

Example 5.2: For N = 75, what are the code letter,acceptance number, rejection number and sample sizefor an AQL = 4.0%? Assume general inspection level IIand single sampling.

Answers: 5.1: D*, 0, 1, 8 5.2: E, 1, 2, 13

* Note the up arrow which changes code letter E to D.



V-46 (591)

ANSI/ASQ Z1.4 Code Letters

Lot SizeSpecial Inspection

LevelsGeneralLevels

S-1 S-2 S-3 S-4 I II III29

16

tototo

81525

AAA

AAA

AAB

AAB

AAB

ABC

BCD

265191

tototo

5090150

ABB

BBB

BCC

CCD

CCD

DEF

EFG

151281501

tototo

280500

1200

BBC

CCC

DDE

EEF

EFG

GHJ

HJK

1201320110001

tototo

32001000035000

CCC

DDD

EFF

GGH

HJK

KLM

LMN



V-47 (592)

Codeletter

Samplesize

Acceptable Quality Limits (normal inspection)

0.25 0.40 0.65 1.0 1.5 2.5 4.0 6.5 10

Ac Re Ac Re Ac Re Ac Re Ac Re Ac Re Ac Re Ac Re Ac Re

A 2 0 1

B 3 0 1

C 5 0 1 1 2

D 8 0 1 1 2 2 3

E 13 0 1 1 2 2 3 3 4

F 20 0 1 1 2 2 3 3 4 5 6

G 32 0 1 1 2 2 3 3 4 5 6 7 8

H 50 0 1 1 2 2 3 3 4 5 6 7 8 10 11

J 80 1 2 2 3 3 4 5 6 7 8 10 11 14 15

K 125 1 2 2 3 3 4 5 6 7 8 10 11 14 15 21 22

L 200 1 2 2 3 3 4 5 6 7 8 10 11 14 15 21 22

M 315 2 3 3 4 5 6 7 8 10 11 14 15 21 22

N 500 3 4 5 6 7 8 10 11 14 15 21 22

P 800 5 6 7 8 10 11 14 15 21 22

Q 1250 7 8 10 11 14 15 21 22

R 2000 10 11 14 15 21 22

= Use first sampling plan below arrow= Use first sampling plan above arrow

Ac =Acceptance numberRe =Rejection number

ANSI/ASQ Z1.4 Single (Normal) Sampling



V-48 (593)

General ANSI/ASQ Z1.4 Inspection Levels

The inspection level to be used for any particularrequirement is prescribed by the responsible authority.

Three inspection levels: I, II, and III are provided forgeneral use. Unless otherwise specified, inspectionlevel II should be used.

Inspection level I may be specified when lessdiscrimination is required. Inspection level III may bespecified for greater discrimination.



V-48 (594)

Normal, Tightened, and Reduced Inspection

Normal inspection: Normal inspection is used at thestart of inspection, unless otherwise directed by theresponsible authority.

Reduced inspection: Under reduced inspection, theplans allow a smaller sample to be taken than undernormal inspection. Reduced inspection may beimplemented when it is evident that quality is runningunusually well.

Tightened inspection: Under tightened inspection, theinspection plan requires more stringent acceptancecriteria. Such a plan is used when it becomes evidentthat quality is deteriorating.



V-48 (595)

Special Inspection Levels

Four special inspection levels S-1, S-2, S-3, and S-4 areprovided. They are used where relatively small samplesizes are necessary and large sampling risks can ormust be tolerated.

In the designation of inspection levels S-1 to S-4, caremust be exercised to avoid AQLs inconsistent withthese inspection levels.



V-49 (596)

ANSI/ASQ Z1.4 Switching Procedures

Normal ! Tightened:

When 2 out of 5 consecutive lots or batches havebeen rejected on original inspection.

Tightened ! Normal:

When 5 consecutive lots or batches have beenconsidered acceptable on original inspection.

Normal ! Reduced:

All of the following must be satisfied:

C The preceding 10 lots or batches have beenacceptable.

C The total number of defectives from the 10 lots orbatches is equal to or less than an applicablenumber.

C Production is at a steady rate.

C Reduced inspection is considered desirable by theresponsible authority.



V-49 (597)

ANSI/ASQ Z1.4 Switching Procedures (Cont’d)

Reduced ! Normal:

When any of the following occur:

C A lot or batch is rejected.

C Under reduced inspection, the sampling proceduremay terminate without acceptance or rejection. Thelot is considered acceptable, but then normalinspection is used.

C Production becomes irregular or delayed.

C Other conditions warrant it.



V-50 (598)

Single, Double, and Multiple Sampling

Sampling plans like ANSI/ASQ Z1.4-2003 give a choiceamong single, double, and multiple sampling. In singlesampling plans, a random sample is drawn from the lot.If the number of defectives is less than or equal to theacceptance number, the lot is accepted.

In double sampling plans, a smaller initial sample isusually drawn. A decision to accept or reject is reachedon the basis of a single sample if the number ofdefectives is either quite large or quite small. A secondsample is then taken if the first one cannot be acceptedor rejected.

In multiple sampling plans, still smaller samples aretaken (seven in ANSI/ASQ Z1.4-2003), continuing asneeded, until a decision to accept or reject is made.Double and multiple sampling plans usually mean lessinspection but are complicated to administer.



V-50 (599)

Single, Double, and Multiple Sampling (Cont’d)

It is possible to select single, double, or multiplesampling schemes with very similar operatingcharacteristic curves as illustrated below usingANSI/ASQ Z1.4-2003 code letter H, with an AQL = 4.0.

PlanType

SampleNumber

SampleSize

Total Sample Ac Re

Single 1 50 50 5 6Double 1 32 32 2 5

2 32 64 6 7Multiple 1 13 13 # 4

2 13 26 1 53 13 39 2 64 13 52 3 75 13 65 5 86 13 78 7 97 13 91 9 10

Ac = Acceptance number Re = Rejection number# = Acceptance not permitted at this sample size



V-51 (600)

Codeletter

Sample Samplesize

Totalsample

size

Acceptable Quality Limits (normal inspection)

0.25 0.40 0.65 1.0 1.5 2.5 4.0 6.5

Ac Re Ac Re Ac Re Ac Re Ac Re Ac Re Ac Re Ac Re

A

B First 2 2 Second 2 4

C First 3 3 Second 3 6

D First 5 5 0 2Second 5 10 1 2

E First 8 8 0 2 0 3Second 8 16 1 2 3 4

F First 13 13 0 2 0 3 1 4Second 13 26 1 2 3 4 4 5

G First 20 20 0 2 0 3 1 4 2 5Second 20 40 1 2 3 4 4 5 6 7

H First 32 32 0 2 0 3 1 4 2 5 3 7Second 32 64 1 2 3 4 4 5 6 7 8 9

J First 50 50 0 2 0 3 1 4 2 5 3 7 5 9Second 50 100 1 2 3 4 4 5 6 7 8 9 12 13

K First 80 80 0 2 0 3 1 4 2 5 3 7 5 9 7 11Second 80 160 1 2 3 4 4 5 6 7 8 9 12 13 18 19

L First 125 125 0 2 0 3 1 4 2 5 3 7 5 9 7 11 11 16Second 125 250 1 2 3 4 4 5 6 7 8 9 12 13 18 19 26 27

M First 200 200 0 3 1 4 2 5 3 7 5 9 7 11 11 16Second 200 400 3 4 4 5 6 7 8 9 12 13 18 19 26 27

N First 315 315 1 4 2 5 3 7 5 9 7 11 11 16Second 315 630 4 5 6 7 8 9 12 13 18 19 26 27

P First 500 500 2 5 3 7 5 9 7 11 11 16Second 500 1000 6 7 8 9 12 13 18 19 26 27

Q First 800 800 3 7 5 9 5 9 11 16Second 800 1600 8 9 12 13 18 19 26 27

R First 1250 1250 5 9 7 11 11 16Second 1250 2500 1 13 18 19 26 27

= Use first sampling plan below arrow.= Use first sampling plan above arrow

= Use corresponding single sampling plan

ANSI/ASQ Z1.4 Double Sampling



V-52 (601)

Multiple Sampling Plan

An example of a multiple sampling plan is shown onV - 52.



V-53 (602)

Dodge-Romig Sampling Tables

Dodge-Romig sampling inspection tables (Dodge, 1959)provide four sets of attributes sampling planscorresponding to the desired lot tolerance percentdefective (LTPD) or average outgoing quality limit(AOQL).

C Lot tolerance percent defective (LTPD) both singleand double sampling

C Average outgoing quality limit (AOQL): both singleand double

Dodge-Romig plans differ from those in ANSI/ASQ Z1.4-2003 because they assume that all rejected lots are100% inspected and the defectives are replaced withgood product. The tables provide protection againstpoor quality based on the average long-run quality.



V-53 (603)

Dodge-Romig Tables (Continued)

LTPD plans ensure that a lot having poor quality willhave a relatively low probability of acceptance. TheLTPD values range from 0.5% to 10.0% defective. TheAOQL plans ensure that, after all sampling and 100%inspection, the average quality (for many lots) will notexceed the AOQL. The AOQL values range from 0.1% to10.0%. Each AOQL plan lists the corresponding LTPD(LQL) and vice-versa.

The selection of a Dodge-Romig plan requires two itemsof information: the size of lot to be sampled and theexpected process average based on past inspectionrecords and any additional information which may beused to predict the expected quality level.



V-54 (604)

LTPD Sampling Plan

There is an LTPD sampling plan shown on V - 54. Actualuse of Dodge-Romig is not anticipated on the CQEexam.



V-55 (605)

Dodge-Romig Tables (Continued)

Primer page V - 56 shows a typical table of AOQL plansusing double sampling. In contrast to the lot tolerancetable, this table gives plans which differ considerably asto lot tolerance, but which have the same AOQL, 1%.The corresponding lot tolerances are given.

AOQL plans are the Dodge-Romig Tables mostfrequently used. They are appropriate only when allrejected lots are 100% inspected. The average of theperfect quality of the inspected lots with the poor qualityof some accepted lots determines the average outgoingquality limit.

Sampling is uneconomical if the average qualitysubmitted is not considerably better than the specifiedAOQL because of administration expenses.



V-55 (606)

Minimum Inspection per Lot

The Dodge-Romig tables are constructed to minimizethe average total inspection (ATI) per lot for a givenprocess average. This is perhaps the most importantfeature of the Dodge-Romig tables. The total number ofitems inspected is made up of two components: (1) Thesample which is inspected for each lot, and (2) Theremaining items which must be inspected if the lot fails.



V-57 (607)

Variables Sampling

All attribute sampling plans are based on data that canbe counted. Each inspected item is classified as eithergood or bad and an accept/reject decision is madebased on a previously selected sampling risk.

Variables sampling plans require unit measurements.The sample data is recorded and processed to yield astatistic such as a sample average, range, or standarddeviation. These calculated values are then comparedto a critical or table value to arrive at a decision on thelot in question. The sample size and critical value arebased on the desired sampling risk.



V-57 (608)

ANSI/ASQ Z1.9 Sampling Plans

ANSI/ASQ Z1.9-2003 has four sections:

Section A: General description of sampling plans

Section B: Consists of sampling plans that are usedwhen the variability is unknown, and thestandard deviation method is used.

Section C: Consists of sampling plans that are usedwhen the variability is unknown, and therange method is used.

Section D: Consists of sampling plans that are usedwhen the variability is known.

ANSI/ASQ Z1.9-2003 has five inspection levels: S3, S4,I, II, III (When no level is specified, use level II.)



V-57 (609)

ANSI/ASQ Z1.9 Sampling Plans

To use ANSI/ASQ Z1.9-2003, follow the sequence below:

C Choose the levelC Choose the method (standard deviation or range)C Know the AQLC Know the lot size



V-58 (610)

Z1.9 AQL Conversion Table

An AQL conversion table is required to align withstandard AQLs used in ANSI/ASQ Z1.9 tables.

ANSI/ASQ Z1.9AQL Conversion Table

For specifiedAQL values

Use thisAQL value

0.109 0.10 0.110 to 0.164 0.150.165 to 0.279 0.250.280 to 0.439 0.40 0.440 to 0.699 0.65 0.700 to 1.09 1.0 1.10 to 1.64 1.5 1.65 to 2.79 2.5 2.80 to 4.39 4.0 4.40 to 6.99 6.5 7.00 to 10.9 10.0



V-58 (611)

Z1.9 Code Letters

The lot size is used to determine an inspection levelcode.

ANSI/ASQ Z1.9Code Letters

Lot Size

Inspection LevelsSpecial General

S3 S4 I II III2 to 8 B B B B C

9 to 15 B B B B D16 to 25 B B B C E26 to 50 B B C D F51 to 90 B B D E G

91 to 150 B C E F H151 to 280 B D F G I281 to 400 C E G H J401 to 500 C E G I J

501 to 1,200 D F H J K1,201 to 3,200 E G I K L

3,201 to 10,000 F H J L M10,001 to 35,000 G I K M N

35,001 to 150,000 H J L N P150,001 to 500,000 H K M P P500,001 and over H K N P P



V-59 (612)

U L

U - X X - LQ = Q = s s

Standard Deviation Method-Section B

An upper value, QU, or lower value, QL, is calculated fora single specification limit. For double specificationlimits, both the QU and QL are calculated. The techniqueused is similar to that of determining a Z value inSection X of this Primer.

Where: s = Sample standard deviationU = Upper specification limit

= Sample meanXL = Lower specification limit

The acceptability criteria is based on a comparison of QUand QL with the acceptability constant k, which is givenin a master table. If QU > k or QL > k, the lot meets theacceptability criterion. If QU < k or QL < k, the lot doesnot meet the acceptability criterion.

A plan from ANSI/ASQ Z1.9-2003 Section B, standarddeviation method, single specification limit, Form 1,isshown as a Primer example.



V-60 (613)

ANSI/ASQ Z1.9-2003 General Information

Detailed use of the Z1.9-2003 standard is not anticipatedon the CQE exam. The student should be familiar withthe general concepts.

Note that the whole process is very similar to capabilitydeterminations and Z table usage presented in PrimerSection X.



V-61 (614)

U L

U - X X - LQ = Q = R R

Z1.9 Range Method-Section C

When using the range method, it is necessary to find R6,which is the average range of the subgroups. Allsubgroups consist of five measurements, n = 5. (If thereis only one subgroup, R is used.) There are threedifferent severities for inspection: normal, tightened,and reduced. Each of these severities has rules. Theseverity must be known for the sampling plan to befound. The student is referred to the standard itself forall procedures and calculations.

An upper value, QU, or lower value, QL, is calculated fora single specification limit. For double specificationlimits, both the QU and QL are calculated. The techniqueused is similar to that of the standard deviation methodshown previously, except that the average sample rangeis used:

The acceptability criteria is based on a comparison of QUand QL with the acceptability constant k. If QU > k or QL> k, the lot meets the acceptability criterion.



V-61 (615)

Sample Integrity

A sample is a subset from the population used to gatherdata about the population. This sample is used togather acceptance data about each lot. The samplesshould be a random (unbiased) representation of the lot.

Since the sample is used to determine the acceptance ofa lot, care is taken to ensure that the sample is notcontaminated. In some products, such as foods, anyunsanitary factor introduced by the sampling processcould influence the outcome. Some commoninfluencing factors are:

C Personnel C Storage areasC Instruments C Environment conditionsC Containers C Laboratory conditions

Acceptability results may also become questionable byinappropriate labeling which would void the linkbetween the sample and the lot. Cross contaminationbetween samples must be avoided.



V-62 (616)

Sample Integrity (Continued)

The recruitment and selection of sampling andinspection personnel should follow the same soundjudgment as with other company positions. The majorjob functions that impact sample integrity typicallyinclude the following:

C The ability to interpret blueprints, specifications C The ability to operate test equipment proficientlyC The appropriate physical capacityC The ability to properly record and analyze dataC Knowledge of materials and processesC Adherence to company policies and proceduresC The ability to prepare reports and communicate

Some pre-testing may prove beneficial in identifying thepresence or absence of necessary skills. Many of theabove items can be taught.



V-62 (617)


Many experiments indicate that a typical individualunder normal (often interrupted) conditions, will onlycatch 80%-90% of the defects present in a high volumeoperation. The attainment of inspection accuracydepends in large measure on advanced planning, theidentification of key characteristics, the proper tools,specifications, facilities, etc. However, other sources ofhuman error exist. Examples include:

Rounding: The discard of some test accuracy

Pencil whipping: This indicates the faking of data

Pressure: An individual yielding to delivery needs

Flinching: Moving readings inside the specification



V-62 (618)


Unknown errors are unintentional and may beconsistent or intermittent:

Inadvertent errors: These errors are sporadic in natureand difficult to avoid. Rigidly enforced procedures,automated inspection, or error-proofing may help.

Technique errors: These errors are consistently madeby some individuals and may indicate lack of training,lack of skill, or lack of capacity. Remedies include:additional training, product magnification, and/orindividual replacement.


V. PRODUCT AND PROCESS CONTROLQUESTIONS

V-65 (619)

5.1. The primary reason that nonconforming material should be identifiedand segregated is:

a. So that the cause of nonconformity can be determinedb.So it cannot be used in production without proper authorizationc. To obtain samples of poor workmanship for use in the company's

training programd.So that responsibility can be determined and disciplinary action

taken

5.2. Using ANSI/ASQC Z1.4 for a lot of 1,000 parts, a general inspectionlevel II, the code letter J, an AQL of 1.0%, and a sample size of 80,what is the accept number?

a. 0b.1c. 2d.3

5.8. Which of the following is the principal purpose of the MRB?

a. Identifying potential suppliersb.Disposing of nonconforming materialc. Appraising suppliersd.Detecting nonconforming material

Answers: 5.1. b, 5.2. c, 5.8. b



V-66 (620)

5.12. Two quantities which uniquely determine a single sampling attributesplan are:

a. AQL and LTPDb.Sample size and rejection numberc. AQL and producer's riskd.LTPD and consumer's risk

5.15. Using visual inspection standards and traditional methods, some 100defects are located in a large batch of product. What is the bestestimate of the total number of defects in the product beforeinspection?

a. 95 - 98b.108 - 111c. 117 - 120d.125 - 128

5.21. What is the importance of the reaction plan in a control plan?

a. It describes what will happen if a key variable goes out of controlb. It indicates that a new team must be formed to react to a problemc. It lists how often the process should be monitoredd. It defines the special characteristics to be monitored

Answers: 5.12. b, 5.15. c, 5.21. a



V-67 (621)

5.22. ANSI/ASQ Z1.4 sampling plans allow reduced inspection when fourrequirements are met. One of these is:

a. Inspection level I is specifiedb.10 lots have been on normal inspection and none have been rejectedc. The process average is less than the AOQLd.The maximum percent defective is less than the AQL

5.27. The most important activity of a material review board (MRB) wouldnormally be:

a. Making sure that corrective action is taken to prevent recurrence ofthe problem

b.To provide a segregated area for holding discrepant material pendingdisposition

c. To prepare discrepant material reports for management reviewd.To accept discrepant material when "commercial" decisions dictate

5.29. In a visual inspection situation, one of the best ways to minimizedeterioration of the quality level is to:

a. Retrain the inspector frequentlyb.Have a program of frequent eye examsc. Add variety to the taskd.Have a standard to compare against as an element of the operation

Answers: 5.22. b, 5.27. a, 5.29. d



V-68 (622)

5.32. The purpose of a written inspection procedure is to:

a. Provide answers to inspection questionsb.Let the operator know what the inspector is doingc. Fool-proof the inspection functiond.Standardize methods and procedures of inspectors

5.35. A sampling plan that may use up to 4 samples to make a decision toaccept or reject is:

a. Single samplingb.Double samplingc. Multiple samplingd.Quadruple sampling

5.40. Which of the following elements would NOT be expected on a controlplan form?

a. Specificationsb.Potential causes of failurec. Key input variablesd.Key output variables

Answers: 5.32. d, 5.35. c, 5.40. b


VI. TESTING & MEASUREMENT

VI-1 (623)

THERE IS MEASURE IN ALLTHINGS.

HORACESATIRES, BOOK I, 35 B.C.


VI. TESTING & MEASUREMENTMEASUREMENT TOOLS

VI-2 (624)

Testing and Measurement

Testing and Measurement are presented in the followingtopic areas:

C Measurement toolsC Testing and measurement definitionC Destructive testsC Nondestructive testsC MetrologyC Measurement system analysis

Measurement Tools

At least 30 types of measurement tools are described inthe Primer. Destructive and nondestructive tests aredescribed later in this Section.



VI-3 (625)

Instrument Selection

Listed below are some gage accuracies andapplications.

Type of Gage Accuracy Application

Adjustablesnap gages

Usually accurate within 10%of the tolerance.

Measures diameters on aproduction basis where an exactmeasurement is needed.

Air gages Accuracy depends upon thegage design. Measurementsof less than 0.000050" arepossible.

Used to measure the diameter ofa bore or hole. However, otherapplications are possible.

Automaticsorting gages

Accurate within 0.0001". Used to sort parts by dimension.

Combinationsquare

Accurate within one degree. Used to make angular checks.

Coordinatemeasuringmachines

Accuracy depends upon thepart. Axis accuracies arewithin 35 millionths andT.I.R. within 0.000005".

Can be used to measure avariety of characteristics, suchas contour, taper, radii,roundness, squareness, etc.

Dial bore gages Accurate within 0.0001"using great care.

Used to measure borediameters, tapers, or out-of-roundness.

Dial indicator Accuracy depends uponthe type of indicator. Somemeasure within 0.0001".

Measures a variety of featuressuch as: flatness, diameter,concentricity, taper, height, etc.

Electroniccomparator

Accurate from 0.00001" to0.000001".

Used where the allowabletolerance is 0.0001" or less.



VI-4 (626)

Instrument Selection (Continued)Type of Gage Accuracy Application

Fixed snapgages

No set accuracy. Normally used to determine ifd i a m e t e r s a r e w i t h i nspecification.

Flush pin gages Accuracy of about 0.002". Used for high volume singlepurpose applications.

Gage blocks Accuracy of the gage blockdepends upon the grade.Normally the accuracy is0.000008" or better.

Gage blocks are best adaptedfor precision machining and as acomparison master.

Height verniers Mechanical models measureto 0.0001". Some digitalmodels attain 0.00005".

Used to check dimensionaltolerances on a surface plate.

Internal andexternal threadgages

No exact reading. Willdiscriminate to a givenspecification limit.

Used for measuring inside andoutside pitch thread diameters.

Micrometer(inside)

Mechanical accuracy isabout 0.001". Some digitalmodels are accurate to0.00005".

Used for checking large holediameters.

Micrometer(outside)

Mechanical accuracy isabout 0.001". Some digitalmodels are accurate to0.00005".

Normally used to check diameteror thickness. Special modelscan check thread diameters.

Opticalcomparator

The accuracy can be within0.0002".

Measures difficult contours andpart configurations.

Optical flat Depending on operator skill,accurate to a few millionthsof an inch.

Used only for very precise toolroom work. Best used forchecking flatness.

Plug gages Accuracy very good forchecking the largest orsmallest hole diameter.

Checking the diameter of drilledor reamed holes. Will not checkfor out of roundness.



VI-5 (627)

Instrument Selection (Continued)Type of Gage Accuracy Application

Precisionstraight edge

Visual 0.10". With a feelergage 0.003".

Used to check flatness,waviness or squareness of aface to a reference plane.

Radius &template gages

Accuracy is no better than0.015".

Used to check small radii, andcontours.

Ring gages Wil l only discriminateagainst diameters larger orsmaller than the printspecification.

Best appl icat ion is toapproximate a mating part inassembly. Will not check for outof roundness.

Split sphere &telescope

No better than 0.0005" usinga micrometer graduated in0.0001".

Used for measuring small holediameters.

Steel ruler orscale

No better than 0.015". Used to measure he ights ,depths, diameters, etc.

Surface plates Flatness expected to be nobetter than 0.0005" betweenany 2 points.

Used to measure the overallflatness of an object.

Taperedparallels

U s i n g a n a c c u r a t emicrometer, the accuracy isabout 0.0005".

Used to measure bore sizes inlow volume applications.

Tool maker'sflat

Accuracy is no better than0.0005" depending upon theinstrument used to measurethe height.

Used with a surface plate andgage blocks to measure height.

Vernier calipers About 0.001". Some digitalmodels are accurate to0.00005".

Used to check diameters andthickness.

Vernier depthgage

About 0.001". Some digitalmodels are accurate to0.00005".

Used to check depths.



VI-6 (628)

Surface Plates

To make a precise dimensional measurement, theremust be a reference plane or starting point. The idealplane for dimensional measurement should be perfectlyflat. Surface plates are customarily used withaccessories like: a toolmaker's flat, angles, parallels, Vblocks and cylindrical gage block stacks. Dimensionalmeasurements are taken from the plate up since theplate is the reference surface. Surface plates mustpossess the following important characteristics:

C Sufficient strength and rigidityC Sufficient and known accuracy

Surface plates require appropriate care andmaintenance:

C The surface should be cleaned before useC The surface should be covered between usesC Work should be distributed to avoid wearC Move the test pieces and equipment carefullyC A surface plate should not become a storage area



VI-6 (629)

Surface Plates (Continued)

Surface plates are made of cast iron or granite. Bothhave merits:

Cast iron plates:

C Usually weigh less per square foot of plate areaC Are not likely to chip or fractureC Are acceptable for magnetic fixturesC Can provide a degree of wringability

Granite plates:

C Are noncorrosiveC Require less maintenanceC Do not burr or retain soft metalsC Are cheaper per relative sizeC Have greater thermal stabilityC Have closer flatness tolerancesC Are nonmagnetic



VI-7 (630)

Angle Measurement Tools

Angle measurement tools include protractors, sine barsand angle blocks. Note that angles may also bemeasured using tools described elsewhere in thisSection (such as optical comparators, profile projectorsand coordinate measuring machines).



VI-7 (631)

Universal Bevel Protractor

One of the most widely used pieces of equipment tomeasure angles is the universal bevel protractor. It is ahand held tool used to obtain an angular reading indegrees and minutes of the workpiece. The scale isoften magnified for easier reading. The most commonerrors that occur in the use of the bevel protractor are:

C Misreading of the scale

C Improper seating of the protractor base



VI-7 (632)

Sine Bar

Angle measurements in dimensional standardization areoften made using a device known as a sine plate or sinebar. The sine bar is a machined steel bar that has twocylinders spaced at known dimensions on the bar.

An angle is generated indirectly by using precisiongeometry based on gage block stacks to define theheight of one leg of a right triangle. The hypotenuse ofthe triangle is a known, fixed dimension. From thesetwo measurements, the angle of the plate may becalculated. Normally, the desired part angle is knownand a calculation is made for the gage block stack.

The sine bar is different than the bevel protractorbecause:

C No direct reading may be obtainedC It is used in conjunction with gage blocks



VI-8 (633)

Sine Bar (Continued)

The sine bar, cylinder and gage block combinationcreates an angular plane to seat the workpiece. To usea sine bar, one must first know the length of the sinebar. Standard sine bar lengths are 5", 10", and 15". Theangle, ", to be checked is determined from the partdrawing or other source. The required height of gageblocks is then determined from a sine bar table orcalculated using a trigonometric function relationship.In the figure below the sine (sin) of angle " equals thegage stack height divided by the effective sine barlength.

Illustration of a Sine Bar in use



VI-9 (634)

Block 1Block 1

Block 2

Angle Blocks

Angle blocks are used for the alignment andmeasurement of precise angles. They are typically soldin sets, containing several different angles.

Stacking of angle blocks is used to create angles otherthan those of the individual blocks. Note that the anglesmay be added together to form a new angle, or byinverting one of the blocks, the angles may besubtracted.

Angles are Added Angles are Subtracted

Stacking of Angle Blocks



VI-10 (635)

Variable Gages

Variable measuring instruments provide a physicalmeasured dimension. Examples of variable instrumentsare line rules, vernier calipers, micrometers, depthindicators, runout indicators, etc. Variable informationprovides a measure of the extent that a product is goodor bad, relative to specifications. Variable data is oftenuseful for process capability determination and may bemonitored via control charts.



VI-10 (636)

The Steel Rule

The steel rule is a linear scale which is widely usedfactory measuring tool for direct length measurement.Steel rules and tapes are available in different degreesof accuracy and are typically graduated on both edges.

A Typical Steel Rule

The fine divisions on a steel rule (thirty-seconds on theone above) establish its discrimination. The steel ruletypically has discriminations of 1/32, 1/64, or 1/100 of aninch. Obviously, measurements requiring accuracies of0.01" or finer should be performed with other tools (suchas a digital caliper).



VI-11 (637)

The Steel Rule (Continued)

Shown below are the correct and incorrect methods ofmeasurement.

Incorrect Correct



VI-11 (638)

Hook Rules

Steel rules may be purchased with a moveable bar orhook on the zero end which serves in the place of a buttplate. These rulers may be used to measure aroundrounded, chamfered or beveled part corners. The hookattachment becomes relied upon as a fixed reference.However, by its inherent design, it may loosen orbecome worn. The hook should be checked often foraccuracy.

Steel Rule with Hook Attachment



VI-12 (639)

Micrometers

Micrometers, or “mics,” are commonly used hand-heldmeasuring devices. Micrometers may be purchasedwith frame sizes from 0.5 inches to 48 inches. Normally,the spindle gap and design permits a 1" reading span.Thus, a 2" micrometer would allow readings from 1" to2". Most common “mics” have an accuracy of 0.001".With the addition of a vernier scale, an accuracy of0.0001" can be obtained. Fairly recent digitalmicrometers can be read to 50 millionths of an inch.

The two primary scales for reading a micrometer are thesleeve scale and the thimble scale. Most micrometershave a 1" “throat.” All conventional micrometers have40 markings on the barrel consisting of 0.025" each.The 0.100", 0.200", 0.300", etc. markings are highlighted.The thimble is graduated into 25 markings of 0.001"each. Thus, one full revolution of the thimble represents0.025".



VI-12 (640)

Micrometers (Continued)

Shown below, are simplified examples of typicalmicrometer readings.

Micrometer set at 0.245" Micrometer set at 0.167"

0.200" 0.100"+0.025" +0.050"+0.020" +0.017"

0.245" +0.167"

Two Micrometer Reading Examples



VI-13 (641)

Measuring Pitch Diameter

In order to determine the pitch diameter of screwthreads by measuring the corresponding over-wire size,the most practical procedure is the use of three wires,actually small hardened steel cylinders, placed in thethread groove, two on one side and one on the oppositeside of the screw. The arrangement of the wires, asindicated in the diagram (below), permits the oppositesensing elements of a length-measuring instrument tobe brought into simultaneous contact with all threewires.

An Illustration of Three Wire Measurement



VI-13 (642)

Measuring Pitch Diameter (Continued)

The best wire size may be calculated by:

w = 0.5p sec "

Where: w = wire diameter" = 1/2 the included thread anglep = thread pitch



VI-14 (643)

Measuring Pitch Diameter (Continued)

The formula to calculate the pitch diameter aftermeasurement is:

E = M + (0.86603p) - 3W

Where: E = pitch diameterM = over the wire measurementp = thread pitchW= wire size used

Example: Assume that M is 0.360", p is 0.050" and W is0.030". Calculate the pitch diameter.

E = M + (0.86603p) - 3WE = 0.360 + (0.86603 x 0.050) - 3(0.030)E = 0.360 + 0.0433 - 0.090E = 0.3133 inch

E is the pitch diameter which must be checked with thetolerance limits on the drawing to determine if the partis acceptable.



VI-14 (644)

Gage Blocks

Near the beginning of the 20th century, Carl Johanssonof Sweden, developed steel blocks to an accuracybelieved impossible by many others at that time. Hisobjective was to establish a measurement standard thatnot only would duplicate national standards, but alsocould be used in any shop.

Today gage blocks are used in almost every shopmanufacturing a product requiring mechanicalinspection. They are used to set a length dimension fora transfer measurement, and for calibration of a numberof other tools.

ANSI/ASME B89.1.9 (2002), distinguishes three basicgage block forms - rectangular, square and round. Therectangular and square varieties are in much widerusage. Generally, gage blocks are made from highcarbon or chromium alloyed steel.



VI-15 (645)

Gage Blocks (Continued)All gage blocks are manufactured with tight toleranceson flatness, parallelism and surface smoothness. Gageblocks may be purchased in 4 standard grades:

Federal Accuracy Grades AccuracyIn Length *New

DesignationOld Designation

0.5 AAA ± 0.0000011 AA ± 0.0000022 A+ + 0.000004

- 0.0000023 A & B + 0.000008

- 0.000004* Applies to gage blocks up to 1". The accuracy

tolerance then increases as the gage block sizeincreases.

Master blocks are grade 0.5 or 1Inspection blocks are grade 1 or 2

Working blocks are grade 3



VI-16 (646)

Gage Blocks (Continued)Gage blocks should always be handled on the non-polished sides. Blocks should be cleaned prior tostacking with filtered kerosene, benzene or carbontetrachloride. A soft clean cloth or chamois should beused. A light residual oil film must remain on blocks forwringing purposes.

Block stacks are assembled by a wringing processwhich attaches the blocks by a combination ofmolecular attraction and the adhesive effect of a verythin oil film. Air between the block boundaries issqueezed out. The sequential steps for the wringing ofrectangular blocks is shown below.

Hold Crosswise Swivel the Pieces Slip into Position Finished Stack

Illustration of the Wringing of Gage Blocks



VI-16 (647)

Wear Blocks

For the purpose of stack protection, some gagemanufactures provide wear blocks. Typically, theseblocks are 0.050 inch or 0.100 inch thick. They arewrung onto each end of the gage stack and must becalculated as part of the stack height. Since wearblocks “wear” they should always be used with thesame side out.



VI-16 (648)

Gage Block Sets

Individual gage blocks may be purchased up to 20" insize. Naturally, the length tolerance of the gage blocksincreases as the size increases. Typical gage block setsvary from 8 to 81 pieces based upon the neededapplication.

Listed below are the contents of a typical 81 piece set:

Ten-thousands blocks (9) 0.1001, 0.1002 ... 0.1009

One-thousands blocks (49) 0.101, 0.102 ... 0.149

Fifty-thousands blocks (19) 0.050, 0.100 ... 0.950

One inch blocks (4) 1.000, 2.000, 3.000, 4.000

Also included in the set, are two wear blocks that areeither 0.050" or 0.100" in thickness.



VI-16 (649)

Minimum Stacking

A minimum number of blocks in a stack lessens thechance of unevenness at the block surfaces. Stack up2.5834" using a minimum number of blocks:

2.5834- 0.1004 (use 0.1004" block)

2.483- 0.133 (use 0.133" block)

2.350- 0.350 (use 0.350" block)

2.000 (use 2.000" block)

This example requires a minimum of four blocks anddoes not consider the use of wear blocks.



VI-17 (650)

Attribute Gages

Attribute gages are fixed gages which typically are usedto make a go, no-go decision. Examples of attributeinstruments are master gages, plug gages, contourgages, thread gages, limit length gages, assemblygages, etc.

Attribute data indicates only whether a product is goodor bad (in most cases, it is known in what direction theproduct is good or bad). Attribute gages are quick andeasy to use but provide minimal information forproduction control.

Snap Gages

Snap gages are used to check outside dimensions inhigh volume operations. Snap gages are constructedwith a rigid frame and normally contain hardened anvilinserts. These gages may have provisions for a smallrange of adjustments and can be used to make rapid“go, no-go” decisions.



VI-17 (651)

Ring Gages

Ring gages are used to check external cylindricaldimensions, and may also be used to check tapered,straight, or threaded dimensions. A pair of rings withhardened bushings are generally used. One bushinghas a hole of the minimum tolerance and the other hasa hole of the maximum tolerance.

Ring gages have the disadvantage of accepting out ofround work and taper if the largest diameter is withintolerance.



VI-18 (652)

Ring Gages (Continued)

A thread ring gage is used to check male threads. Thego ring must enter onto the full length of the threads andthe no-go must not exceed three full turns onto thethread to be acceptable. The no-go thread ring isidentified by a groove cut into the outside diameter.

A No-go Thread Ring Gage



VI-18 (653)

Plug Gages

Plug gages are generally “go, no-go” gages, and areused to check internal dimensions. The average pluggage is a hardened and precision ground cylinder aboutan inch long. A set is usually held in a hexagonal holderwith the “go” plug on one end and the “no-go” plug onthe other end. To make it more readily distinguishable,the “no-go” plug is generally made shorter.

The thread plug gage is designed exactly as the pluggage but instead of a smooth cylinder at each end, theends are threaded. One end is the go member and theother end is the no go member. A threaded plug gagehas a feature used to clear chips out of the femalethreads. This feature is called the chip groove or notch.

A Thread Plug Gage



VI-19 (654)

Spring Calipers

Spring calipers are transfer tools that perform a roughmeasurement of wide, awkward or difficult to reach partlocations. These tools usually provide a measurementaccuracy of approximately 1/16 inch. A spring calipermeasurement is typically transferred to a steel rule byholding the rule vertically on a flat surface. The caliperends are placed against the rule for the final readings.See the diagram below.

Inside Calipers Outside Calipers



VI-20 (655)

Telescoping Gages

Telescoping gages (telescope gages) are a type oftransfer gage. They consist of a handle and a T-shapedportion that has a spring loaded cylinder and a fixedcylinder at right angles to the handle. The springcylinder is compressed and the gage is placed inside abore or interior surface of a part.

Small Hole Gages

Small hole gages or split sphere gages are similar totelescoping gages, but are used for the size range fromabout 1/8 inch to 1/2 inch. The gage consists of twohemispherical contact surfaces that are spread apart byan adjustable wedge.



VI-20 (656)

Radius Gages

Radius gages come in sets for checking inside andoutside radii over the range of about 1/16 inch to 1 inch,or larger. They are made from thin pieces of metal sheetand have the dimension stamped or printed on the side.These gages provide only an attribute measurementsince the gage only provides an approximate range forthe radius of interest, e.g. between 13/16 and 7/8 inch.Template gages may be custom made for checking morecomplex surfaces.

Radius Gage with Fixed Radii



VI-21 (657)

Dial Indicators

Dial indicators are mechanical instruments formeasuring distance variations. Most dial indicatorsamplify a contact point reading by use of an internalgear train mechanism. The standard nomenclature fordial indicator components is shown in the diagrambelow:

Commonly available indicators have discriminations(smallest graduations) from 0.00002" to 0.001" with awide assortment of measuring ranges.



VI-22 (658)

Dial Indicators (Continued)

Dial indicators are available in a variety of measurementranges and graduations. Thus, the proper dial must beselected for the length measurement and requireddiscrimination. Dial indicators also come with balancedor continuous dials. Shown below are examples of both.

Continuous Dial Balanced Dial With Revolution Counter

Contact Tips

Contact points are available in a variety of shapes(standard, tapered, button, flat, wide-face, etc.). The tipsare made from a number of wear resistant materials(carbide, chrome plated steel, sapphire or diamond).



VI-23 (659)

Indicator Errors

Although dial indicators offer advantages in operationalflexibility, there are numerous potential opportunities formistakes. Some of the more common errors include:

C Loose clamping of the gage.

C Reading errors - These errors occur when theindicator face is not viewed at a 90° angle or whenthe shadow of the needle is mistaken for the needleitself.

C Not adjusting for indicator over-travel.

C Rounding errors - Generally due to improper dialdiscrimination or inadequate training.

C Over-looking the number of tip revolutions.

C Cosine error - Created by misalignment between thework piece and indicator tip. This error could allowboth the rejection of an acceptable dimension andthe acceptance of a rejectable dimension.



VI-23 (660)

Digital Indicators

Digital indicators use the same principle of operation asis found in dial indicators, however the display is adigital readout. Key advantages of digital indicatorsover dial indicators are the elimination of the readingerrors, indicator over-travel errors, rounding errors,over-looking the number of revolutions and the cosineerrors.

Many digital tools have an optional interface forconnection to a computer or other electronic datacollection devices. A yellow faceplate on a dial indicatormeans that the readings are in metric (SI).



VI-24 (661)

The Vernier Scale

Vernier scales are used on a variety of measuringinstruments such as height gages, depth gages, verniercalipers and gear tooth verniers. Except for the digitalvarieties, readings are made between a vernier plate andbeam scales.

A vernier scale may have line divisions of 0.025 inch or0.050 inch. One must identify the “plate” and “bar”components on the instrument. The proper figure isindicated where a line of the plate aligns with a line ofthe bar. The two numbers are added together to makea composite reading. Shown below is an illustrativeexample.

Record 1.050"Add 0.019"

Final reading 1.069"



VI-25 (662)

Analog and Digital Displays

The measurement scales can be analog or digital. Theanalog display is defined as one having a continuousrange of values. For example, one would visuallyinterpret the time of day (10:20 am) by looking at atraditional watch face with hour and minute hands. Thedigital watch would not have a clock face, but insteadprovide a numerical display (10:20 am).

Some instruments can incorporate both analog anddigital displays.



VI-25 (663)

Nongraduated and Graduated Scales

Various general purpose measuring tools or instrumentscan be divided into two classes: nongraduated toolsand graduated tools.

Nongraduated tools or instruments do not have linear orangular graduations on the tool. Examples of thesetypes of tools would be: calipers, dividers, telescopegages, straightedges, squares, surface plates, and sinebars.

Graduated tools or instruments have linear or angulargraduations. The user can make a direct measurementon the part. Examples of graduated tools would be:rules, slide calipers, vernier calipers, vernier depthcalipers, micrometers, protractors, and mechanicalindicating gages.



VI-26 (664)

Electronic Measuring Equipment

There are hundreds of types of instruments that can beclassified as electronic measuring equipment. Most ofthese instruments are produced in both analog anddigital display formats, although the digital formats arerapidly replacing the analog units, in most cases.Examples of electronic measuring equipment include:

C VoltmetersC OhmetersC AmmetersC WattmetersC Capacity metersC Inductance metersC pH metersC Load sensorsC Torque sensors

Obviously this list is not exhaustive. The digitalequipment normally has an optional interface forcommunication with external computers or other datastorage and processing equipment.



VI-26 (665)

Electronic Gaging

There are hundreds of types of electronic gagingdevices. A summary of three basic electronic tools, theoscilloscope, multimeter, and pyrometer, are describedin the Primer.

Oscilloscopes

An oscilloscope displays voltage on the vertical axisand time on the horizontal axis. Grid lines in the displayshow relative values for both the x and y directions. Bychanging ranges for either voltage or time, signals canbe displayed as waveforms over frequencies from directcurrent (DC) up to MHz range and above, and from mVto 100 V or more.



VI-27 (666)

Electronic Gaging (Continued)

Multimeters

A multimeter is an electrical meter that measuresseveral electrical properties including voltage, current,and resistance. Multimeters use multiple scale ranges,within a measurement property, to improve resolution ofthe readings. The two general types of multimeters areanalog and digital.

Pyrometers

A pyrometer is an instrument used for measuring hightemperatures. The two main types of pyrometers are athermocouple with a temperature display and an opticalpyrometer.



VI-28 (667)

Laser Designed Gaging

The use of lasers are prevalent when the intent ofinspection is a very accurate non-contact measurement.The laser beam is transmitted from one side of the gageto a receiver on the opposite side of the gage.Measurement takes place when the beam is broken byan object and the receiver denotes the dimension of theinterference to the laser beam. The laser has many usesin gaging. Automated inspection, fixed gaging, andlaser micrometers are just a few examples of the manyuses of the laser.

Machine Vision Gaging

Machine vision gaging is accomplished using some typeof light source and an image capture device, such as avideo camera. The image is digitized and thenprocessed using a computer. Computer analysis of theimage can determine dimensions, angles, areas andperimeters.



VI-28 (668)

Pneumatic Gages

There are two general types of pneumatic amplificationgages in use. One type is actuated by varying airpressure and the other by varying air velocity atconstant pressure. There are numerous advantages ofpneumatic gages. Some of the more important ones arelisted below:

C A high level of skill is not requiredC Air gages tend to be self-cleaningC The equipment is safe, fast, reliable and accurateC The equipment is very versatileC Attribute or variable measurements can be madeC Measurements can be read to millionths of an inch



VI-29 (669)

Balances and Scales

Balances and scales cover the weight range from 1 mgand smaller for laboratory balances to over 100,000 lbcapacity truck and crane scales. There are two primarytypes of balances and scales: those that balance aknown mass, sometimes through a lever arm system,against the unknown weight; and those that use a loadcell to measure the applied force. Most electronicbalances and scales have the optional output capabilityto interface with a computer.

Whenever balances or scales are moved, they should berecalibrated. When weights, balances and scales arecalibrated, it is recommended that they be sent to anaccredited calibration laboratory



VI-29 (670)

Surface Analyzers

Surface analyzers include instruments such asinterferometry and surface roughness testers.

Interferometry

The greatest possible accuracy and precision areachieved by using light waves as a basis formeasurement. A measurement is accomplished by theinteraction of light waves that are 180° out of phase.This phenomenon is known as interference.



VI-30 (671)

Surface Roughness Testers

A surface profiler or profilometer is the most commonmethod of measuring surface roughness, although othertechniques are available. The profilometer (or profiletracer) uses a stylus or probe to traverse the surface ofinterest. The average roughness is the total area of thepeaks and valleys divided by the evaluation length, it isexpressed in :m.

Surface finish describes the deviation from the ideal flatsurface. This deviation is normally expressed in termsof roughness, lay, and waviness, defined as:

C Roughness represents the size of the finelydistributed surface pattern deviations from thesmooth surface.

C Lay represents the dominant direction of thesurface pattern, such as grinding scores.

C Waviness represents deviations which are relativelyfar apart.



VI-30 (672)

Surface Roughness Testers (Continued)

The figure below depicts roughness, lay and wavinesson a magnified surface.

Y = Roughness, S = Lay, V = Waviness



VI-31 (673)

Fingernail Comparator

When an approximate indication of the surfaceroughness is sufficient, a fingernail comparator may beused. A small sheet of metal with a variety of machinedareas and finishes is used as the surface roughnessstandard. A person’s fingernail is run across thestandard at the specified roughness, perpendicular tothe lay, and then across the part surface for comparison.If the standard “feels” rougher than the part, then thepart is considered acceptable.



VI-31 (674)

Shape and Profile Measurement

Shape and profile measurement is done usingcomparators and roundness testers.

Comparators

Mechanical or bench comparators have a dial or digitalindicator on a stand with a reference base. Theindicator may be adjusted vertically with respect to thebase to accommodate various part sizes. Using astandard, such as a gage block, the indicator is zeroedto a known dimension. The part to be inspected is thenplaced on the base, and the difference from the knowndimension is read on the indicator gage. Cylindricalparts can be checked for runout or T.I.R. (total indicatorreading) by placing the part on a v-block and rotatingthe part manually.

Pneumatic comparators (commonly called air gages) areoften used for tight tolerance measurements.



VI-32 (675)

Roundness Testers

Roundness testers are used for measuring roundness,cylindricity, coaxiality, concentricity, straightness,parallelism, flatness and a number of other features onround and cylindrical parts. These testers utilize arotating base and a vertical column with a probeextending from the column. The probe may be movedvertically and is held in contact with the part surfacewhile the part is rotated on the support base orturntable. Data from the probe is processed usingcomputer software to create the desired measurementsand/or graphic outputs.

Schematic of a Roundness Tester



VI-33 (676)

Optical Tools

Optical tools include such items as comparators, profileprojectors, optical flats and microscopes.

Optical Comparators

Optical comparators or profile projectors are devices forcomparing a part to a form that represents the desiredpart contour or dimension. The relationship of the formwith the part indicates acceptability. A beam of light isdirected upon the part to be inspected, and the resultingshadow is magnified by a lens system, and projectedupon a viewing screen by a mirror.

The figure below shows a schematic of a simple opticalcomparator.



VI-33 (677)

Microscopes

The term microscope refers to several types ofinstruments including the following:

C Compound light microscopeC Dissection microscope or stereoscopeC MetallographC Confocal microscopeC Scanning electron microscope (SEM)C Transmission electron microscope (TEM)C Scanning probe microscope

Microscopes are used to analyze structures ofspecimens, determine chemical composition, andmeasure feature dimensions. Each type of microscopehas specific advantages, as well as limitations.



VI-34 (678)

PART

OPTICAL FLAT

MONOCHROMATIC LIGHT

ABCDEF

LIGHT

LIGHT

LIGHT

PART

11.623.2

34.8

HALF - WAVELENGTHS

AIRWEDGE

MICRO-INCHES

1 2 3

DARKDARK

DARK

Optical FlatsAn optical flat is a highly polished transparent material -such as glass - ground into approximately two to fourinch diameter cylinders. These cylinders are 3/8 inch to3/4 inch thick. They are used to measure the flatness ofa surface using the principles associated withinterferometry. See the diagram below:

When the optical flat is placed over the workpiece, a thinsloping air space is created. Monochromatic light raysenter the optical flat and are reflected from the surfaceof the workpiece. The light rays are reflected from thesurface of the workpiece. When the light rays arereflected, interference bands are visible.



VI-34 (679)

Optical Flats (Continued)The illustration below shows the bands as they mightappear through an optical flat.

Flat Surface Convex Surface Concave Surface Warped Surface

The above images may vary considerably based on theamount and type of out of flat condition.



VI-35 (680)

Digital Vision Systems

Advances in computer hardware and digital imagecapture devices have resulted in tremendous growth inthe use of digital vision systems for quality inspectionapplications. A basic digital vision system has thefollowing components:

C Test specimens (S)C Reference standardsC Lighting system (L)C Digital image capture devices (D)C Computer hardware (C)C User interface, controls, monitor (M)C Networking, data storage, remote data transfer (N)

C Analysis softwareC Sample control system, servo-control (V)



VI-35 (681)

Digital Vision Systems (Continued)

The arrangement of digital vision components isillustrated in the figure below.



VI-36 (682)

Coordinate Measuring Machines (CMMs)

A coordinate measuring machine (CMM) is used fordimensional measurements in three dimensions. TheCMM has three basic directions of movement, the X, Yand Z axes. The Z axis is vertical, the X axis ishorizontal left to right, and the Y axis is horizontal frontto back. In some cases, the X and Y axes are reversed.Some machines also have a W axis, which is rotational.

The base of the CMM is a surface plate. Workpieces areplaced on the surface plate and a stylus is maneuveredto various contact points to send an electronic signal toa computer that is recording the measurements. Aschematic of a CMM is shown below.



VI-37 (683)

Gage Maintenance and Storage

The control of measuring and monitoring devices fromISO 9001 (2000), Section 7.6, is paraphrased below.

The organization must identify the measurements to bemade, and the measuring and monitoring devicesrequired for product conformity to specifiedrequirements. Measuring and monitoring devices mustbe used and controlled to ensure that measurementcapability is consistent with measurement requirements.

Where applicable, measuring and monitoring devicesmust be calibrated and adjusted prior to use; besafeguarded from adjustments that would invalidate thecalibration; be protected from damage and deteriorationduring handling, maintenance and storage; havecalibration results recorded; and have the validity ofprevious results reassessed if subsequently found to beout of calibration, with corrective action taken. Softwareused for measuring and monitoring specifiedrequirements must be validated prior to use.



VI-37 (684)

Gage Maintenance and Storage (Cont’d)

The appropriate organizational authority should ask thefollowing questions:

C Are the appropriate measurements determined? C Will the measurements provide adequate evidence?C Are processes determined?C Are devices calibrated at specified intervals?C Are calibration actions recorded and maintained?C Are measuring devices adjusted as necessary?C Is the calibration status identified? C Are devices safeguarded from invalid adjustments?C Are measuring devices protected from damage?C Are devices protected during handling?C Are nonconforming measurements assessed? C Are nonconforming measurements recorded?C Is measurement software confirmed?C Is the measurement software reconfirmed?



VI-37 (685)

Gage Maintenance and Storage (Cont’d)

Some instruments require storage in a customized caseor controlled environment when not in use. Even sturdyhand tools are susceptible to wear and damage.

Hardened steel tools require a light film of oil to preventrusting. Care must be taken in the application of oilsince dust particles will cause buildup on the gage'sfunctional surfaces. Tools should be examinedfrequently for wear on the measuring surfaces.


VI. TESTING & MEASUREMENTDEFINITIONS

VI-38 (686)

Testing and Measurement Definitions

The following definitions are pertinent to understandingand communicating testing and measurement.

Accuracy (ofmeasurement)

An unbiased true value which is normallythe difference between the average ofseveral measurements and the true value.

Attribute gage A gage that measures on a good/bad orgo/no-go basis.

Bias inmeasurement

Bias occurs when the actual reading isadversely affected by misalignment,overpressure, the use of an improperstarting point, etc.

Brittleness The property of a metal that allows it todeform very little prior to fracture.

Charpy test An impact test which measures thetoughness of a material by measuring theresistance to fracture in the presence of anotch.

Compressivestrength

The maximum amount of resistance topressing or squeezing type stress beforefailure.

Creep The resistance of a material to plasticdeformation under a static load.



VI-38 (687)

Testing & Measurement Definitions (Cont’d)

Critical stress The stress below which the number offatigue failures is dramatically reduced.

Deformation The amount a material is stretched orcompressed when force is applied.

Differentialmeasurement

The use of a measuring device thattransforms actual movement into a knownvalue (a dial indicating gage).

Directmeasurement

A standard or tool is applied to the partsuch that a direct reading can be made.

Discrimination The ability to distinguish between thedivisions on a scale.

Discriminationrule

According to AIAG (1995)3, measurementincrements should be no greater than one-tenth of the smaller of either the processvariability or the specification tolerance.

Ductility The property of a material that allows it tostretch prior to fracture.

Elastic region The area of the stress-strain curve in whichstress is proportional to strain according toHooke's law.

Elastic limit The point in the stress-strain curve in whichthe strain becomes plastic.



VI-39 (688)


Elongation The extension of material caused by theuniform strain of an external load prior tonecking.

Fatigue Material failure due to repeated strains.Fatiguestrength

The ability of a material to withstanddynamic stress.

Impactstrength

A material’s resistance to shock due totoughness which is dependent on strengthand ductility.

Malleability The property that allows a material to bebent and shaped by rolling or hammering.

Measuredsurface

That surface of a measuring tool that ismovable and with which the actualmeasurement is made.

Measurementdeviation

The difference between a measurement andits stated value or intended level.

Measurementerror

The difference between a measured valueand a true value.

Measurementpressure

A positive, nonexcessive measurement toolforce. The most important factor is that thepressure used on the work piece be thesame as that used during calibration.

Measurementstandard

A standard of measurement that is arecognized and accepted true value.



VI-39 (689)


Measuring andtestequipment

All devices used to measure, gage, testinspect, diagnose, or otherwise examinematerials, supplies and equipment todetermine compliance with technicalrequirements.

Mechanicalproperties

Properties such as tensile, impact, andcompression that indicate how a materialwill behave when force is applied.

Metrology The science and practice of measurement.Parallax error The error in measurement caused by a

reading misalignment. An example is theact of viewing an indicator dial from animproper angle.

Percentelongation

A measure of ductility during a tensile test.The percent a material increases in gagelength (after fracture).

Plasticdeformation

Deformation of a permanent nature whichoccurs when a material has been stretchedbeyond the elastic limit.

Plasticity The ability of a material to stretch or deformprior to failure.

Pressure The action of a force per unit area applied toa substance.



VI-40 (690)


Primaryreferencestandard

An extremely accurate reference standardthat is traceable to a NIST standard.

Quenching Rapid cooling by water, air, oil, or brine inorder to control microstructural changes inthe material.

Referencesurface

That surface of a measurement tool that isfixed.

Secondaryreferencestandard

A standard that may be used to perform testequipment or working level calibration.They are of a lower level than a primarystandard.

Shear strength The ability of atoms to resist sliding in thecrystal lattice.

Shear failure Occurs when atoms slide past one anotherin the crystal lattice and cause failure.

Slip A failure of a material when stress is appliedas atoms slide past one another in thecrystal lattice.

Slip plane Weakly bonded planes in the crystal latticethat allow atoms to slide over one another.

Specificationlimits

Limits that define the conformanceboundaries for a product or service.



VI-41 (691)


Strain Deformation of a material due to appliedforces. It is the ratio of elongation to theoriginal sample length in tensile testing.

Stress The ability to withstand an amount ofapplied force. The amount of load per unitcross-section of force applied.

Stress-straincurve

A method of determining mechanicalproperties by plotting stress against strain.Values for the elastic limit, proportionallimit, yield strength and failure point can bedetermined.

Tensilestrength

Ability of a material to withstand beingpulled apart.

Testing A means of determining the capability of anitem to meet specified requirements bysubjecting the item to a set of physical,chemical, or environmental conditions.

Transfer tool A tool or measuring instrument that has noreading scale. This device will make a partmeasurement and then transfer it to anotherscale for direct reading.

Variable gage A gage that is capable of measuring theactual size of a part.

Viscosity The property of a liquid to offer continuousresistance to flow.



VI-41 (692)


Wear The ability of a material to withstand contactstress and deterioration (scratching,abrasion, corrosion, pitting).

Workingstandards

Standards that are used to performequipment calibration. These standards areof a lower (third) level and are usuallycalibrated to secondary standards.

Yield point The limiting stress for elastic behaviorfound on the stress-strain curve.

Yield strength A calculated point on the stress-strain curvewhen the yield point is not clearly defined.A 0.2% offset method is used to construct aline parallel to the elastic modulus line.


VI. TESTING & MEASUREMENTDESTRUCTIVE TESTS

VI-42 (693)

Destructive Testing

Destructive testing includes tensile tests, impact tests,shear tests, compression tests, fatigue testing andflammability tests. Leak testing is also reviewed in thiselement although it can also be considered a non-destructive or functional test, as well.



VI-42 (694)

STRAIN (IN/IN)

R

T

Y

P

E

0.0002

0.002

Tensile Test

Tensile strength is the ability of a metal to withstand apulling apart tension stress. The tensile test isperformed by applying a uniaxial load to a test bar andgradually increasing the load until it breaks. The load isthen measured against the elongation using anextensometer. The data may be analyzed using a stress-strain curve.

In the diagram above, the elastic limit (E), theproportional limit (P), the highest stress value (T), andthe rupture strength (R) are identified.



VI-43 (695)

Impact Test

Impact strength is a material's ability to withstandshock. Tests such as Charpy and Izod use notchedsamples which are struck with a blow from a calibratedpendulum. The major difference between the two arethe way the bar is anchored and the speed in which thependulum strikes the bar. The Charpy holds the barhorizontally and strikes with a velocity of 17.5 ft/sec.The Izod holds the test bar vertically and has a velocityof 11.5 ft/sec.



VI-43 (696)

Shear Test

Shear strength is the ability to resist a “sliding past”type of action when parallel but slightly off-axis forcesare applied. Shear can be applied in either tension orcompression.

An Illustration of a Shear Test



VI-43 (697)

Compression Test

Compression is the result of forces pushing towardeach other. The compression test is run much like thetensile test. The specimen is placed in a testingmachine, a load is applied and the deformation isrecorded. A compressive stress-strain curve can bedrawn from the data.

A Typical Compression Test Curve



VI-44 (698)

Fatigue Test

Fatigue strength is the ability of material to takerepeated loading. There are several types of fatiguetesting machines. In all of them, the number of cyclesare counted until a failure occurs and the stress used tocause the failure is determined.

A Typical Fatigue Curve



VI-44 (699)

Flammability Tests

The purpose of flammability testing is to determine therates that items burn when exposed to a specifiedignition source, under specified conditions. Theresulting flammability ratings are used to accept orreject materials for given applications. Commonapplications of flammability tests include toys, buildingmaterials, textiles used for furniture, clothing, carpetsand drapes, and fire safety systems. These tests arealso used to determine burn rates where it is desirableto have a flame, such as candles, matches, and heatingfuels such as natural gas and kerosene.

Flammability tests are conducted at varioustemperatures, which include the intended usetemperature such as ambient conditions. The relativehumidity (R.H.) during the test must also be controlledand measured, since the R.H. affects the flamepropagation rate. The air velocity must also bemeasured during testing and some methods require thetest to be performed in still-air or draft-free conditions.



VI-45 (700)

Leak Testing

Leak testing is concerned with the escape of liquids,vacuum, or gases from sealed components or systems.Leak testing may be destructive or nondestructivedepending upon the purpose of the test. Leak testingsaves costs by reducing the number of reworkedproducts, warranty repairs and liability claims. Thethree most common reasons for performing a leak testare:

C To avoid material loss in chemical or energy areasC To avoid contamination or personnel hazardsC To provide component reliability for critical parts



VI-46 (701)

Non-Destructive Testing (NDT)

NDT is a technique of testing material properties withoutimpairing their future usefulness. Tests like the tensiletest, bend test, creep test, voltage breakdown, acid etch,spectroscopic test and gas and liquid chromatographyare categorized as destructive tests, since a portion ofthe material is destroyed during the test.

In recent years, engineers and scientists have beensuccessful in applying natural phenomena to non-destructive testing. The use of X-rays, light waves,magnetism and sound waves, are all important NDTtechniques. Common among these methods areultrasonics, radiography, fluoroscopy, microwave,magnetic particle, liquid penetrant, and eddy current.More recently, the development of the laser has led to anew method of NDT (holography).



VI-46 (702)

Choosing the Most Suitable NDT Method

There are numerous material types, defects,applications, and needed product quality levels.Therefore, many factors must be evaluated beforedeciding upon a particular test method. Some of theimportant considerations are listed below:

Part size Part geometryMaterial composition Material conditionInspection rate Defect locationSurface condition Defect orientationReference standards Defect sizeAccessibility Acceptance criteriaInspector training Cost of equipmentPart usage SafetyTest recording Test specifications



VI-47 (703)

Basic NDT Techniques

Listed in the table below are some of the most widelyused NDT techniques.

Technique Description

Electromagnetic The test object is magnetized. Magneticparticles are applied to the object surface. Surface or subsurface defects will disrupt themagnetic field and be indicated by theparticles.

Image generation X-rays are passed through a test object whichcause some materials to fluoresce. Animmediate image of defects is displayed on ascreen.

Optical A clean test surface is covered with a dyepenetrant that permeates into surface cracks. A developer is then applied which displays anydefects visually.

Radiation X-rays are imposed on a test object to detectdefect size and location.

Thermal The measurement of temperature and heat-flowvariations through a test object will indicate thepresence of defects.

Ultrasonic A sound frequency is introduced to match thepart resonant frequency. Part thickness anddefect location are determined.



VI-48 (704)

Nondestructive Testing ComparisonTest Type Application Advantages Limitations

Eddy Current Can check material thickness,conductivity, coating thicknessand physical properties.Adaptable to 100 % high speedapplications where no probecontact is desired. The costs canbe relatively low.

Only useful for conductive materials.Reliable standards and frequentcalibration are required. Partthickness and penetration depth canpose problems. Results arenormally comparative.

LiquidPenetrant

A simple accurate, inexpensivetechnique to locate surfacedefects. The penetrant/developercontrast makes visual inspectioneasy. Works on nonmetallic andnonmagnetic materials.

Does not work for porous materials.The process requires cleaningoperations. Works on surfacedefects only. Not as fast as eddycurrent methods.

MagneticParticle

Can detect surface ands u b s u r f a c e d e f e c t s i nferromagnetic parts. Portableequipment may be used. Thistechnique is economical.

Used for ferromagnetic parts only.Surfaces must be clean and dry.Magnetism may have to be twodirectional to find all discontinuities.Parts may require demagnetizing.

Microwave Used for thickness measurement.Can also monitor moisture andchemical composition of bothliquids and solids.

Cannot detect subsurface defects inmetals.

Ultrasonic

TransmissionPulse echo

orResonance

Can locate and determine therelative size and orientation ofinternal defects. Can measurethicknesses difficult to reach withmechanical methods. Inspectionunits can be portable.

Complex part geometries presentdifficulties. Requires skilledoperators and good test standards.Coupling materials such as water,glycerine or petroleum jelly must beused.

X-Ray

FluoroscopyGamma Ray

TVX

Useful in detecting internaldefects in metals. Sometechniques provide a permanentrecord of defects. Providescontinual product movement andrapid decisions.

Relatively high initial costs. Trainedtechnicians are required. Notapplicable to extremely thinproducts. The results may not beimmediately known. Inherent safetyrisks.



VI-49 (705)

Visual InspectionOne of the most frequent inspection operations is thevisual examination of products, parts and materials.The color, texture, and appearance of a product givesvaluable information if inspected by an alert observer.Lighting and inspector comfort are important factors invisual inspection. In this examination, the human eye isfrequently aided by magnifying lenses or otherinstrumentation. This technique is sometimes calledscanning inspection.



VI-49 (706)

Ultrasonic TestingThe application of high frequency vibration to thetesting of materials is a widely used and importantnondestructive testing method. Ultrasonic waves aregenerated in a transducer and transmitted through amaterial which may contain a defect. A portion of thewaves will strike any defect present and be reflected or“echoed” back to a receiving unit, which converts theminto a “spike” or “blip” on a screen. Refer to the figurebelow.



VI-50 (707)

Ultrasonic Testing (Continued)The three basic elements of an ultrasonic test systemare:

C A transducer which transmits pulsed waves andthen receives their echoes

C A test object through which the high frequencywaves are transmitted

C An electronic system which converts the soundwaves into a visual pattern

Ultrasonic inspection has been widely usedmeasurement of dimensional thickness. The ultrasonictesting technique is similar to sonar. Sonic energy istransmitted by waves containing alternate, regularlyspaced compressions and refractions. Audible humansound is in the 20 to 20,000 Hertz range. Fornondestructive testing purposes, the vibration range isfrom 200,000 to 25,000,000 Hertz. The three fundamentaltechniques of ultrasonic inspection are called pulseecho, through transmission and resonance.



VI-50 (708)

Pulse EchoThe pulse echo technique utilizes a transducer to bothgenerate and receive high frequency sound waves. Thereturning echo must travel the same path as the originalpulse. The amount of returned energy depends uponthe size and orientation of any defect obstruction.

Through TransmissionThis variation is similar to the pulse echo techniqueexcept that matched transducers are utilized. The signalis transmitted from a sending transducer through thepart to a receiving transducer.

ResonanceAny material has a natural resonant frequency which isproportional to its thickness. In resonance testing, atransducer produces a continuous signal. Thefrequency of the signal is varied until it exactly matchesthe resonant frequency of the test material. Resonancetesting is frequently used for measuring thickness anddetecting large laminar defects.



VI-51 (709)

Holographic InspectionHolography is a method of photography that involvesthree-dimensional instead of conventional two-dimensional images. A laser beam of coherent light issplit to create a hologram. One part of the beamilluminates the object being photographed, while theother is used as a reference beam. Instead of taking aphotograph, only interference patterns are recorded.Convergence of the two beams creates a pattern ofinterference fringes which produces a hologram on film.

Acoustical holography is a further adaptation ofinterference holography. This technique utilizes highfrequency sound waves to create a three-dimensionalreal time image of the internal structure of a test piece.



VI-51 (710)

Magnetic Particle TestingMagnetic particle inspection is a nondestructive methodof detecting the presence of many types of defects orvoids in ferromagnetic metals or alloys. This techniquecan be used to detect both surface and subsurfacedefects in any material capable of being magnetized.

The first step in magnetic particle testing is to magnetizea part with a high amperage, low voltage electriccurrent. Then fine steel particles are applied to thesurface of the test part. These particles will alignthemselves with the magnetic field and concentrate atplaces where magnetic flux lines enter or leave the part.The test part is examined for concentrations of magneticparticles which indicate that discontinuities are present.See the figure below:

Flux Lines in a Defective Test Piece



VI-52 (711)

Magnetic Particle Testing (Continued)There are three common methods in which magneticlines of force can be introduced into a part. Theselected method will depend upon the configuration ofthe part and the orientation of the defects of interest.The three methods are:

1) Longitudinal Inside a Coil

2) Circular Magnetization

3) Circular Magnetization (Internal Conductor)



VI-53 (712)

Types of CurrentAlternating current (AC) magnetizes the surface layer ofthe material more strongly than the interior region of thepart and is used to discover surface discontinuities.Direct current (DC) gives a more uniform field intensityover the entire section. DC provides greater sensitivityfor the location of subsurface defects. The rapidshifting of both currents, using some specializedequipment, can permit the detection of most internal andexternal defects in one operation.



VI-53 (713)

Types of ParticlesThere are two general categories of magnetic particles(wet or dry), which depend upon the carrying agentused. Either water or oil may be used as a vehicle in thewet method. In the dry method, the particles aretypically sprinkled or dusted on. In either case, theparticles are made of carefully selected magneticmaterials of proper size, shape, and retentivity. They areoften dyed to give good contrast with the inspectedsurface and may be fluorescent for viewing under blacklight.

Wet particles are best suited for the detection of finesurface cracks. When using wet particles the surface ofthe test piece should be free from oil, grease, sand,loose rust, or loose scale. Degreasing is preferred.

Dry particles are more sensitive in detecting subsurfacedefects and are usually used with portable types ofequipment. Reclaiming and reusing dry particles is notrecommended.

Magnetic particle testing is limited to products made ofiron, steel, nickel and cobalt. In some cases, the partsrequire demagnetization before subsequent operationsare performed.



VI-54 (714)

Liquid Penetrant Testing

Liquid penetrant inspection is a rapid method fordetecting open surface defects in both ferrous andnonferrous materials. It may be effectively used onnonporous metallic and nonmetallic materials.

Tests have shown that penetrants can enter materialcracks as small as 3,000 angstroms. The size of dyemolecules used in fluorescent penetrant inspection areso small that there may be no surface cracks too smallfor modern penetrants to detect.

The factors that contribute to the success of liquidpenetrant inspection are the ability of a penetrant tocarry a dye into a surface defect and the ability of adeveloper to contrast that defect by capillary attraction.

False positive results may sometimes confuse aninspector. Irregular surfaces or insufficient penetrantremoval may indicate nonexistent flaws.



VI-55 (715)

Penetrant Advantages and Limitations

Penetrants are much faster and more economical thanultrasonic methods for finding surface discontinuities.Penetrants are not limited by part geometry and arecheaper for mass production applications. Penetrantsare more flexible than eddy current techniques and willwork on nonmagnetic materials.

Penetrants are not successful in locating internaldefects. Magnetic particle inspection is superior topenetrants for ferromagnetic materials with opensurface defects. Penetrants are not as fast on bars andtubing as eddy current testing.



VI-55 (716)

Eddy Current Testing

Eddy currents involve the directional flow of electronsunder the influence of an electromagnetic field.Nondestructive testing applications require theinteraction of eddy currents with a test object. This isachieved by:

C Measuring the flow of eddy currents in a materialhaving virtually identical conductivitycharacteristics as the test piece

C Comparing the eddy current flow in the test piece(which may have defects) with that of the standard

Eddy currents are permitted to flow in a test object bypassing an alternating current through a coil placednear the surface of the test object. Eddy currents will beinduced to flow in any part that is an electricalconductor.



VI-56 (717)

Eddy Current Testing (Continued)

The induced flow of electrons produces a secondaryelectromagnetic field which opposes the primary fieldproduced by the probe coil. This resultant field can beinterpreted by electronic instrumentation. See thefollowing diagram:

Defect size, and location cannot be read directly duringeddy current testing. This test requires a comparativeanalysis. Therefore, test conditions must be tightlycontrolled and reject standards must be developed.



VI-56 (718)

Eddy Current Advantages/Limitations

Advantages include 100 % high speed inspection, noprobe contact, portability of equipment and the use ofautomatic part rejection. Thin film coating and thin walltubing products are excellent applications. The costsare comparatively low and relatively unskilled operatorscan be used.

Limitations include a maximum depth of penetration(approximately 1/2 inch), the need for reliable standardsand the need for frequent calibration. Part cleanlinessand test equipment sensitivity are importantconsiderations. The service technicians should beskilled and qualified. Test parts must be able to conductelectricity.



VI-57 (719)

Radiography

Many internal characteristics of materials can bephotographed and inspected by the radiographicprocess. Radiography is based on the fact that gammaand X-rays will pass through materials at different levelsand rates. Therefore, either X-rays or gamma rays canbe directed through a test object onto a photographicfilm and the internal characteristics of the part can bereproduced and analyzed.

Because of their ability to penetrate materials anddisclose subsurface discontinuities, X-rays and gammarays have been applied to the internal inspection offorgings, castings, welds, etc. for both metallic andnonmetallic products.



VI-57 (720)

Radiography (Continued)

The major steps associated with radiography inspectionare:

C Making the test piece setupC Exposing the test piece to X-raysC Processing the film containing the part imageC Analyzing the radiographic filmC Making a decision based upon the results

For proper X-ray examination, adequate standards mustbe established for evaluating the results. A radiographcan show voids, porosity, inclusions, and cracks if theylie in the proper plane and are sufficiently large.However, radiographic defect images are meaningless,unless good comparison standards are used. Astandard, acceptable for one application, may beinadequate for another.



VI-57 (721)

How X-Rays are Produced

Typically, X-rays are produced when high speedelectrons strike a tungsten target in a vacuum tube.These electrons can then be propelled against a testtarget producing X-rays.



VI-58 (722)

Related X-Ray Techniques

There have been new developments in the radiographicfield of nondestructive testing. Several common recentapplications include:

C Fluoroscopy

C Gamma Radiography

C Televised X-Ray (TVX)

All radiographic techniques require trained technicians.In some cases, the results are not immediately known.There are inherent human risks involved in the use of allradiographic techniques.



VI-59 (723)

Hardness Testing

A large number of field and laboratory tests have provento be useful for material hardness evaluation. Listedbelow are the most commonly used techniques.

Type Technique Penetrator Loading Scale

Brinell Area ofPenetration

10 mmBall

500-3000kg.

HBW,HBS, BHN

File Appearanceof Scratch File Manual None

Knoop Area ofPenetration

PyramidalDiamond 25-3600 g HK

Mohs Presenceof Scratch

10Stones Manual Units

Mohs

Rockwell Depth ofPenetration

DiamondPoint or

1/16-1/8 Ball

60-100-150 kg. Rc

RockwellSuperficial

Depth ofPenetration

DiamondPoint or

1/16-1/8 Ball

15-30-45 kg.

15N, 30T,45X, etc.

Shore Height ofBounce

40 GrainWeight Gravity Units

Shore

Sonodur VibrationFrequency

VibratingRod N.A. BHN

Vickers Area ofPenetration

PyramidalDiamond

25 g to120 kg HV, DPH



VI-59 (724)

Brinell Hardness Testing

The Brinell hardness testing method is primarily usedfor bulk hardness of heavy sections of softer steels andmetals. Compared to other hardness tests the imprintleft by the Brinell test is relatively large. This type ofdeformation is more conducive to testing porousmaterials such as castings and forgings. Extremely thinsamples cannot be tested using this method. Since alarge force would be required to make a measurabledent on a very hard surface, the Brinell methodgenerally is restricted to softer metals.



VI-60 (725)

Rockwell Hardness Testing

The most popular and widely used of all the hardnesstesters is the Rockwell tester. This type of tester usestwo loads to perform the actual hardness test. Surfaceimperfections in samples are eliminated by the use of apreliminary load. This “minor load” is applied before theactual hardness is taken. This makes the readings veryaccurate when the second load is applied. Rockwellmachines may be manual or automatic.

The Rockwell hardness value is based on the depth ofpenetration with the value automatically calculated anddirectly read off the machine scale. At least threereadings should be taken and averaged. The Rockwellmethod has two key advantages:

C Because of the minor load, surface imperfectionshave little effect

C Because the hardness value can be read directly,error is minimized



VI-60 (726)

Shore Scleroscope Hardness Testing

The Shore Scleroscope is a dynamic hardness test thatuses a material’s absorption factor and measures theelastic resistance to penetration. It is unlike the othertest methods in that there is no penetration. In the test,a hammer is dropped and the bounce is determined tobe directly proportional to the hardness of the material.Some machines are available with a scale follower whichrecords the first bounce on a dial. The advantages ofthe Shore method are:

C There is negligible indention on the sample surfaceC A variety of materials and shapes can be testedC The equipment is very portable

The major disadvantage to Shore testing is that thesample must be smooth, flat, clean, and horizontal.



VI-61 (727)

Vickers Hardness TestingThe Vickers hardness testing differs from Brinell in thefollowing ways:

C A square-based pyramid is used (not a round ball)C The load or force is less (1 to 120 kg)C The units are HV (previously called DPH)

The surface should be as smooth, flat and clean aspossible with the test piece placed horizontally on theanvil before testing. The angle of the diamondpenetrator should be approximately 136 degrees. TheVickers test does not damage the sample as severely asthe Brinell test because of the lighter load. The Vickerstest is very sensitive and is considered a surface test.Small areas, very thin samples and hard materials maybe tested using this method.



VI-61 (728)

Knoop Hardness TestingThe Knoop is a microhardness testing method used fortesting surface hardness of very small or thin samples.A sharp elongated diamond is used as the penetratorwith a 7-1 ratio of major to minor diagonals. Surfacesmust be very fine ground, flat, and square to the axis ofthe load. The sample must be very clean as even smalldust particles can interfere. Loads may go as low as 25grams. The Knoop hardness testing method is used forextremely thin materials like coatings, films, and foils.It is basically used for research testing in the researchlab.

Sonodur Hardness Testing MethodThe Sonodur is one of the newer test methods and usesthe natural resonant frequency of metal as a basis ofmeasurement. Hardness of a material affects thisfrequency and therefore can be measured. This methodis considered to be very accurate.



VI-61 (729)

Mohs Hardness TestingThe scratch test was probably the first hardness testingmethod developed. It is very crude and fast and isbased on the hardness of ten minerals. In 1824, anAustrian mineralogist by the name of F. Mohs chose tenminerals of varying hardness and developed acomparison scale. The softest mineral on the MOHSscale is talc and the hardest is diamond.

File Hardness TestingFile hardness is a version of the scratch testing methodwhere a metal sample is scraped with the edge of a file.If a scratch results, the material is “not file hard” but ifthere is no mark the material is “file hard.” This is avery easy way for inspectors to determine if the materialhas been hardness treated.



VI-62 (730)

Functionality Testing

Functionality testing involves a large number ofcommon physical and mechanical applications. Torqueand surface tension measurement are discussed in thePrimer.

Various tension and compression tests are alsoconsidered to be functional tests except that loading isnot applied until part failure. These tests are usuallyconducted to confirm that a customer specification orrequirement is met. In fact, torque may also bemeasured to a predetermined value, or to failure of acomponent.



VI-62 (731)

Torque Measurement

Torque is measured using a torque wrench. There aremany types of torque wrenches. Two types mostcommonly used are the flexible beam type, and the rigidframe type. Torque wrenches may be preset to thedesired torque. The wrench will either make a distinct“clicking” sound or “slip” when the desired torque isachieved.

Torque measurement is required when the product isheld together by nuts and bolts. The torque applied toa fastener is an indication of the tensile preload in thebolt. The wrong torque can result in the assemblyfailing due to a number of problems. Parts may not beassembled securely enough for the unit to functionproperly or threads maybe stripped because torque istoo high, causing the unit to fail. Torque is described asa force producing rotation about an axis.



VI-62 (732)

Torque Measurement (Continued)

The formula for torque is:

Torque = Force x Distance

Example: A force of 2 pounds applied at a distance of 3feet equals:

Torque = Force x DistanceTorque = 2 lbf x 3 ftTorque = 6 ft-lbf

Torque may be applied in either the clockwise (CW)direction or counterclockwise direction (CCW).Tightening right-hand threaded fasteners is done byapplying a clockwise torque. Loosening of the samefastener is done by applying a counterclockwise torque.When tightening, always follow the manufacturer’sspecifications for recommended torque values.



VI-63 (733)

Torque Wrench Precautions

C Handle torque wrenches carefully

C Hold the center of the handle

C Apply the force slowly and smoothly

C Hold the wrench steady for a short time afterreaching the desired torque

C Use torque wrenches within 80 percent of theirstated range

C Beware of false applications of torque, such as along bolt bottoming out

C Keep torque wrenches calibrated against a knownstandard

C If it is necessary to extend a torque wrench, ensurethat compensation is made for the change indistance

C Ensure that the extension is in line to avoid cosineerror


VI. TESTING & MEASUREMENTNONDESTRUCTIVE TESTS

VI-63 (734)

Tensiometers

Tensiometers measure the surface tension of liquids.The surface tension is measured either as a forcedivided by a length, expressed as mN/m, or a forcedivided by an area (which is equivalent to a pressure),expressed in bar, millibar (mbar), centibar (cbar), or cmof water pressure.

Tensiometers are also used to measure the pressure ormatric potential of the soil. This is the force with whichwater is held in the soil. If the tension of a soil is high orthe pressure potential low, plants use more energy toremove water from the soil. Under these conditions,plants may grow at a slower rate. Soil moisture controlis very important in many areas of the world.


VI. TESTING & MEASUREMENTMETROLOGY

VI-64 (735)

Metrology

Metrology is the science of measurement. The wordmetrology derives from two Greek words: matron(meaning measure) and logos (meaning logic).Metrology encompasses the following key elements:

C The establishment of measurement standards thatare both internationally accepted and definable

C The use of measuring equipment to correlate theextent that product and process data conforms tospecification.

C The regular calibration of measuring equipment,traceable to established international standards



VI-64 (736)

Units of Measurement

There are three major international systems ofmeasurement: the English, the Metric, and the SystemInternational D`unites (or SI). The U.S. has effectivelyretained the English System as a remnant of Britishcolonial influence.

The metric and SI systems are decimal-based, the unitsand their multiples are related to each other by factorsof 10. The SI system was established in 1968 and theU.S. officially adopted it in 1975. The transition isoccurring very slowly.

The final authority for standards rests with theinternationally based system of units. Fundamental,supplementary, and derived SI units.



VI-65 (737)

SI System Units

Listed below is a summary table of the fundamental andsupplement SI units:

Quantity Measured Unit Symbol

Fundamental Unitsamount of substancelengthmasstimeelectric currenttemperatureluminous intensity

molemeterkilogramsecondamperekelvincandela

molmkgsAKcd

Supplementary Unitsplane anglesolid angle

radiansteradian

radsr

The Primer lists a large number of derived SI units.



VI-66 (738)

Types of Measurements

There are three common types of measurements: direct,indirect, and comparative.

Direct Measurement

The direct type of measurement is also termed anabsolute measurement. A direct measurement is madevia using an instrument (a steel ruler) to determine thelength of a steel rod. A measuring instrument is appliedto an unknown and a measurement value is read from ascale.

Indirect Measurements

Some measurements are made indirectly. That is, thevariable of interest is not the one that is actuallymeasured. Angle measurements are often madeindirectly by using a sine plate or sine bar.



VI-66 (739)

Types of Measurements (Continued)

Comparative (Transfer) Measurements

A comparative measurement is made when a gage blockof a specified height is compared to a part. Comparativemeasurements can often obtain great accuracy. Thethree most commonly used comparative gages aremechanical, pneumatic, and electronic.

Comparative (Differential) Measurement

Differential gaging occurs where two sensing devices,in simultaneous contact with the part surface, mutuallyreference their positions. The measured dimension isthe change in position of the sensing devices.

Other Measurements

In laboratory situations, zero difference, substitution,ratio, and ratio transfer measurements are used. Thesetechniques are outside the scope of the CQE Exam.



VI-67 (740)

instrument environment calibration sample analysisfixture

2 2 2 2 2 2 2M E E E E E E = + + + + + + σ σ σ σ σ σ σ ξ

10:1 RuleAIAG (1995) states that measurement increments shouldbe no greater than one-tenth of the smaller of either theprocess variability or the specification. An instrumentmust be capable of dividing the process variability ortolerance into ten parts.

UncertaintyThe calculation of uncertainty requires a detailed budgetwhich breaks down the variance of measurement errorinto consistent components, each of which can beseparately estimated. The detailed model becomessomething like:

Historically, a measurement term called test accuracyratio (TAR) has been used. TAR is calculated as theratio of the tolerance of the unit under test divided bythe tolerance of the reference standard. In the past, aTAR of 10:1 was considered acceptable. Today, a TARof 4:1 or 3:1 is much more common.



VI-67 (741)

Unnecessary Accuracy

In the real world, unnecessary accuracy is expensive.The two most common examples of loss result fromunnecessary tight design tolerances and the use ofmeasuring instruments that are too discriminating.Obviously, a gage with 0.0001" graduations should notbe used for a +_ 0.250" tolerance.

With the advent of modern electronics and computertechnology is not uncommon to obtain a resistor with aCpk of 40. To be able to measure the variation in theperformance of the resistor to one-tenth the processvariation could cost a supplier 100,000 times the originalcost of the resistor. The current philosophy is to selectthe most economic means of measurement.



VI-68 (742)

The 10:1 Calibration Rule

In some cases, it is possible to calibrate an instrumentwith a standard that has 10 times more accuracy. Thesecases are few and far between. ANSI/NCSL Z540-1-1994states that the accuracy, stability, range and resolutionof measurement standards should not exceed 25 % ofacceptable tolerance. The advent of true measurementuncertainty and more accurate measuring instrumentsmakes even this ratio hard to maintain.



VI-68 (743)

The 10:1 Measurement Rule

For heavens sake on an ASQ exam, use the 10: rule.However, the origin of this 10 % “rule of thumb” appearsto date back to MIL-STD-120 (1950), which was canceledin 1996. This standard stated that the accuracy of themeasuring instrument should be less than 20 % of thetolerance and that instruments with an accuracy of 10 %of the tolerance should be used if available.

The only current basis for the 10:1 measurement rulelies with the AIAG MSA (1995). This manual states thata measuring system with less than a 10 % error in thespecification spread is acceptable. However, thestandard goes on to state that 10 % to 30 % R&R errormay be acceptable based upon the importance of theapplication, cost of the gage, and cost of repairs, etc.



VI-69 (744)

CalibrationCalibration is the comparison of a measurementstandard or instrument of known accuracy with anotherstandard or instrument to detect, correlate, report oreliminate by adjustment, any variation in the accuracy ofthe item being compared. The elimination ofmeasurement error is the primary goal of calibrationsystems.

Calibration Definitions

CalibrationControl

A documented system for assuring thatmeasuring and test equipment devicesand measurement standards arecalibrated at appropriate intervals.

Calibrationinterval

The period of time between calibrations.Intervals can vary depending upon theirstability, purpose and degree of usage.

Calibrationrecall

A system for indicating in advance whenmeasuring and test equipment is nextdue to be calibrated.



VI-69 (745)

Calibration Definitions (Continued)

Certification Approval given for the use of newlyacquired or modified measuring and testequipment devices following averification and calibration examination.

StandardInterim

A standard used until a permanentstandard is established.

StandardReference

An instrument or device of the high orderof accuracy used in a calibration systemas a primary reference standardtraceable to NIST.

StandardTransfer

An instrument or device in a calibrationsystem used to transfer measurementsfrom the reference standard to a workingstandard.



VI-70 (746)

Calibration Interval

It is generally accepted that the interval of calibration ofmeasuring equipment be based on stability, purposeand degree of usage.

Intervals should be shortened if previous calibrationrecords and equipment usage indicate this need. Theinterval can be lengthened if the results of priorcalibrations show that accuracy will not be sacrificed.

Measuring and test equipment should be traceable torecords that indicate the date of the last calibration, bywhom it was calibrated, and when the next calibration isdue. Coding is frequently used.



VI-71 (747)

Calibration Standards

Any system of measurement must be based onfundamental units that are virtually unchangeable.

In all industrialized countries, there exists an equivalentto the United States National Institute of Standards andTechnology whose functions include the constructionand maintenance of “primary reference standards.”These standards consist of copies of the internationalkilogram plus measuring systems which are responsiveto the definitions of the fundamental units and to thederived units of the SI table.



VI-72 (748)

Calibration Standards (Continued)

Linear standards are easy to define and describe if theyare divided into functional levels. There are five levelsin which linear standards are usually described.

WorkingLevel

This level includes gages used at thework center.

CalibrationStandards

These are standards to which workinglevel standards are calibrated.

FunctionalStandards

This level of standards is used only in themetrology laboratory of the company formeasuring precision work and calibratingother standards.

ReferenceStandards

These standards are certified directly tothe NIST and are used in lieu of nationalstandards.

National &InternationalStandards

This is the final authority of measurementto which all standards are traceable.



VI-72 (749)

Calibration Standards (Continued)

Since the continuous use of national standards isneither feasible nor possible, other standards aredeveloped for various levels of functional utilization.National standards are taken as the central authority formeasurement accuracy, and all levels of workingstandards are traceable to this “grand” standard. Thedownward direction of this traceability is shown asfollows:

1. National Institute of Standards and Technology2. Standards Laboratory3. Metrology Laboratory4. Quality Control System (Inspection Department)5. Work Center



VI-73 (750)

Calibration Functional Responsibilities

Listed below are some of the responsibilities normallyassigned to calibration personnel:

1. Maintain a record system to assure the initial andperiodic calibration of all measuring and testequipment serviced both internally and externally.

2. Assure that the calibration program complies withthe established practices and standards.

3. Ensure the traceability of all performed calibrationsto known standards.

4. Perform measurements or calibrations, as specifiedby the company, utilizing known standards.

5. Determine at the time of calibration that theequipment is free of foreign matter that couldcompromise the calibration.

6. Perform necessary calibrations or functional testson newly acquired or relocated measurementequipment.



VI-73 (751)

Calibration Functional Responsibilities (Continued)

7. Identify equipment with a proper calibration status.

8. Suspend measuring and test equipment from usewhen conditions warrant.

9. Obtain corrective action from the responsibleorganization for any conditions found to bedetrimental to the calibration program and system.

10. When requested or when conditions warrantprovide personnel for operation of gages,measuring, and test devices for verification of theiraccuracy.

11. Perform gage studies to determine the suitability ofmeasuring instrumentation for the measurementsystem.

The calibration of measuring instruments is necessaryto maintain accuracy, but does not necessarily increaseprecision. Precision most generally stays constant overthe working range of the instrument.


VI. TESTING & MEASUREMENTMEASUREMENT SYSTEM ANALYSIS

VI-74 (752)

Measurement System AnalysisThe following are summaries of what must beaccomplished to meet measurement systemrequirements.

C Measuring equipment (devices) - All measuringequipment (company or employee owned) must beidentified, controlled, and calibrated. Records ofthis action must be kept.

C Confirmation system - The system by which themeasuring equipment is evaluated to meet therequired sensitivity, accuracy, and reliability mustbe defined in written procedures.

C Periodic audit and review - The calibration systemmust be evaluated on a periodic basis by internalaudits and by management reviews.

C Planning - The actions involved with the entirecalibration system must be planned. This planningmust consider management system analysis.

C Uncertainty of measurement - Generally thedetermination of the uncertainty of measurementinvolves gage repeatability and reproducibility aswell as other statistical methods.



VI-74 (753)

Measurement System Analysis (Cont’d)C Environmental conditions - Gages, measuring

equipment, and test equipment will be used,calibrated, and stored (when not in use) inconditions that ensure the stability of theequipment. Laboratories must also control dust,temperature, noise, lighting, and humidity.

C Records - Records must be kept on the operationsthat are used to calibrate measuring and testequipment. The retention time for these recordsmust be specified. A gage status record is required.

C Nonconforming measuring equipment - Suitableprocedures must be in place to assure thatnonconforming measuring equipment is not used.

C Confirmation labeling - A labeling system must bein place that shows the unique identification of eachmeasuring device and its status.

C Intervals of confirmation - The frequency that eachmeasuring device is recalibrated must beestablished and documented.



VI-75 (754)

Measurement System Analysis (Cont’d)C Sealing for integrity - Where adjustments may be

made that may logically go undetected, sealing ofthe adjusting devices is required.

C Use of outside products and services - Proceduresmust define controls that will be followed when anyoutside calibration source or service is used.

C Traceability - Calibrations must be traceable tonational standards. If no national standard isavailable, the method of establishing andmaintaining the standard must be documented.

C Storage and handling - Measuring equipment, whenin use, will be handled according to establishedprocedures and in accordance with operatortraining. When the measuring equipment is not inuse, it will be in storage as prescribed byprocedures to ensure unwanted use.

C Personnel - Documented procedures are requiredfor the qualifications and training of personnel thatmake measurement or test determinations.



VI-75 (755)

Measurement ErrorThe error of a measuring instrument is the indication ofa measuring instrument minus the true value.

F2 ERROR = F2 MEASUREMENT - F2 TRUE

or F2 MEASUREMENT = F2 TRUE + F2 ERROR

The precision of measurement can best be improvedthrough the correction of the causes of variation in themeasurement process. However, it is frequentlydesirable to estimate the confidence interval for themean of measurements which includes themeasurement error variation. The confidence intervalfor the mean of these measurements is reduced byobtaining multiple readings according to the central limittheorem using the following relationship.

READINGSMEASUREMENT

σσ =n

The formula states that halving the error ofmeasurement requires quadrupling the number ofmeasurements.



VI-76 (756)

Measurement Error (Continued)There are many reasons that a measuring instrumentmay yield erroneous variation, including the followingcategories:

C Operator Variation

C Operator to Operator Variation

C Equipment Variation

C Material Variation

C Procedural Variation

C Software Variation

C Laboratory to Laboratory Variation



VI-77 (757)

R&R TermsAIAG MSA (1995) defines five sources of measurementvariation that can be determined by gage R&R studies.

Reproducibility - The “reliability” of the gage system orsimilar gage systems to reproduce measurements.

Repeatability - The variation in measurements obtainedwith one instrument, by the same operator, measuringthe same characteristic on the same part at or near thesame time (virtually the same as precision).

Bias - The difference between the observed average ofmeasurements and a reference value.

Linearity - The difference in bias (offset) valuesthroughout the expected operating ranges of a gage.

Stability - Is the drift or change in bias obtained with ameasurement system on the same measurementcharacteristic over an extended time period.

The calibration of measuring instruments is necessaryto maintain accuracy (lack of bias), but does notnecessarily increase precision (repeatability).



VI-78 (758)

Parameters that Change Slowly

Bias or Offset

The systematic difference between the measurementresults from two different processes attempting toperform the same measurement.

Accuracy

Accuracy is the lack of bias between the user’s currentmeasurement process and the same process using anaccepted standard as a reference.

Drift or Stability

Drift is a change in bias, which means the bias isn’treally constant, just changing on a slower time scalethan the measurement.



VI-78 (759)

Parameters that Change Quickly

Precision or Noise

Precision describes how close in value successivemeasurement results fall when attempting to repeat thesame measurement. Precision is usually visualized asvarying rapidly so that successive measurements willcapture all aspects of the distribution.



VI-79 (760)

Other Measurement Parameters

Repeatability

Repeatability is a measure of the ability of ameasurement process to get the same answer when hasan attempt is made to keep all factors constant, or atleast as stable as possible.

Reproducibility

Reproducibility is the measure of the ability of ameasurement process to get the same answer underconditions of all relevant factors varying normally.

Linearity

Linearity is a description of measurement biasindicating how the value of the bias varies over theentire capability range of a measurement system.



VI-79 (761)

Other Measurement Parameters (Cont’d)

Sensitivity

Sensitivity is a measure of the smallest value of themeasured parameter that can be sensed by ameasurement system.

Selectivity

Selectivity is a measure of the ability of a measurementsystem to distinguish between and display thedifference in two measured results when theirmeasurands actually have two different values.

Resolution

Resolution is a measure of the smallest change in themeasurand that can be represented by the displaymechanism of the measurement system.



VI-80 (762)

Repeatability and Reproducibility

There are three widely used methods to quantifymeasurement error: the range method, the average andrange method and the ANOVA method. A briefdescription of each follows:

Range Method

The range method is a simple way to quantify thecombined repeatability and reproducibility of ameasurement system.

Average and Range Method

The average and range method computes the totalmeasurement system variability, and allows the totalmeasurement system variability to be separated intorepeatability, reproducibility, and part variation.

Analysis of Variance Method

ANOVA is the most accurate method for quantifyingrepeatability and reproducibility and allows thevariability of the interaction between the appraisers andthe parts to be determined.



VI-81 (763)

Average and Range Method

The average range method partitions variation intorepeatability, reproducibility, and process variation. Theresult of this analysis will:

C Determine repeatability by examining the variationbetween the individual technicians and within theirmeasurement readings

C Determine reproducibility by examining thevariation between the average of the individualtechnicians for all parts measured

C Establish process variation by checking thevariation between part averages that are averagedamong the technicians



VI-81 (764)

Average and Range Method (Continued)

Note that the R&R determination described in thisfollowing example is referred to as the “short method.”

Technician Part Readings Within Part WithinTech

BetweenTech

1st 2ndSet Set R1 R2 R31X 2X

A

12345

2.0 1.0 2.0 3.0 1.5 1.0 3.0 3.0 2.0 1.5

1.01.00.50.00.5

1.52.51.253.01.75

1.75 2.0

=AR 0.6

B

12345

1.5 1.5 2.5 2.5 2.0 1.5 2.0 2.5 1.5 0.5

0.00.00.50.51.0

1.52.51.752.251.0

1.50 1.8

=BR 0.4

C

12345

1.0 1.0 1.5 2.5 2.0 1.0 2.5 3.0 1.5 0.5

0.01.01.00.51.0

1.02.01.52.751.0

1.75 1.65

=CR 0.7

Grand Ranges and Averages 0.567 1.817 1.67 1.817 0.35

1R 1X 2R 2X 3R

R&R Data for Average and Range Method



VI-82 (765)

2

Rˆ = d

σ

( )32

1 Repro = R = (0.524)(0.35) = 0.183d

⎛ ⎞σ ⎜ ⎟

⎝ ⎠

( )12

1 Repeat = R (0.885)(0.567) 0.502d

⎛ ⎞σ = =⎜ ⎟

⎝ ⎠


To proceed further, one must determine severalstandard deviations using the range formula:

Using 1/d2 table values the calculation for repeatabilityis:

Where 1/d2 is based on K = 15 samples and n = 2. FromTable 6.40, the ∞ column is used for K and 1/d2 equals0.885. is the grand average range within parts.1R

The calculation for reproducibility is:

Where 1/d2 is based on one sample, K = 1, and n = 3.From Table 6.40, 1/d2 equals 0.524. R3 is the rangebetween the average of all measurements taken by eachtechnician.



VI-83 (766)

( ) ( )

( ) ( )

2 2

2 2

Meas = Repeat + Repro

Meas = 0.502 + 0.183 = 0.534

σ σ σ

σ

( )22

1 Process = R = (0.420)(1.67) = 0.701d

⎛ ⎞σ ⎜ ⎟

⎝ ⎠


The total measurement standard deviation is determinedby the additive law of variances according to thefollowing formula:

The production process standard deviation isdetermined by:

Where 1/d2 is based on three samples, K = 3, and asample size n = 5. From Table 6.40, 1/d2 equals 0.420.

equals the average range between technicians.2R



VI-83 (767)

( ) ( )

( ) ( )

2 2

2 2

Observed = Proc + Meas

Observed = 0.701 + 0.534 = 0.881

σ σ σ

σ


The total observed standard deviation in the examplecan also be determined by the additive law of variancesaccording to the following formula:

In this example, the measurement error constitutes asubstantial portion of total observed variation (about37%).

The AIAG (2002) method of calculating the percentage oftolerance consumed by the measuring system yields avalue of 49% as shown in the Primer.



VI-84 (768)

Analysis of Variance Method

The example in the Primer is for five parts, threetechnicians and two replications.

ANOVA TABLE " = 0.05

Source SS DF MS Fcal F(") Var Adj Var %

Technician 0.6167 2 0.3083 1.28 3.68 0.0111 0.0111 2.34

Part No. 9.867 4 2.467 10.21 3.06 0.2225 0.2225 46.81

Interaction 1.633 8 0.2041 0.84 2.64 -0.019 0 0

Error 3.625 15 0.2417 0.2417 50.85

Total DF 29 SIGe = 0.4916 Totals 0.4753 100

SIGtot = 0.7368

For this example, repeatability is the error variance andcontributes 50.85% of the total variation in the data.

Reproducibility is the variation among technicianswhich contributes 2.34% of the variation in the data.

Process variation accounts for 46.81% of the totalvariation in the data.

Hypothesis tests based on the F distribution are used todetermine if there are differences between techniciansor between processes.



VI-87 (769)

0

0.5

1

1.5

2

2.5

3 UCL = 2.883

LCL = 0.751

1.817

TECH A TECH B TECH C PARTS

UNSTACKED STACKED

Control Chart Methods

In addition to the R&R methods that have beenpreviously discussed, a number of graphical tools (suchas control charts) have been useful in screeningmeasurement data for special causes of variation. Someauthorities maintain that these graphical presentationsshould precede any other form of statistical analysis.

The average and range data, presented earlier, will beplotted on both unstacked and stacked control charts.the resulting average chart provides an indication of the“usability” of the measurement system.



VI-87 (770)

Control Chart Methods (Continued)

By traditional control chart analysis, the average chartlooks pretty good. There’s only one “special” event fortechnician A. However, the area within the control limitsrepresents the measurement sensitivity. Since thegroup of parts being measured represents the partvariation, approximately one half (or more) of theaverages should fall outside the control limits.

In this case, the data does not show this pattern. Thisindicates that either the measurement system lackseffective resolution or the samples do not represent theexpected process variation. If the samples do representthe anticipated process variation, corrective action mustbe taken on the measurement system.



VI-88 (771)

0

0.5

1

1.5

2 UCL = 1.85

LCL = 0

R = 0.567

TECH A TECH B TECH C PARTS

UNSTACKED STACKED


The range chart is used to determine if the measurementprocess is in control. Even if the measurement error islarge, the calculated control limits will adjust for thaterror. Any special causes should be identified andremoved before a measurement study is initiated.

Shown below are unstacked and stacked versions of therange chart for the data collected earlier. It should benoted that the data used for this example is limited.



VI-88 (772)


The range chart can be analyzed as follows:

C If all ranges are in control, all technicians are doingthe same job. That is, there is statistical controlwith respect to repeatability.

C If one technician is out of control, that individual’smethod differs from the others.

C If multiple technicians have out of control points,the measurement system is overly sensitive totechnique errors and needs improvement.

Neither the average or range chart should show patternsin the data relative to the technician or part. Trendanalysis must not be used.


VI. TESTING & MEASUREMENTQUESTIONS

VI-91 (773)

6.1. Precision can best be defined as:

a. The ability to target a process to a specified normal valueb. The average reading determined after repeated measurements by

different operatorsc. The difference between the repeated measurements on the same itemd. The agreement or closeness of measurements on the same item

6.3. A subsurface discontinuity in some purchased steel bar stock is asuspected to be the cause of high failure rates. All of the followingnondestructive test (NDT) methods could be used to screen the barstock, EXCEPT:

a. Magnetic particle testingb. Liquid penetrant testingc. Eddy current testingd. Radiographic testing

6.8. Products should be subjected to tests which are designed to:

a. Demonstrate the basic function at a minimum testing costb. Approximate the conditions to be experienced in the customer's

applicationc. Ensure that specifications are met under laboratory conditionsd. Ensure performance under severe environmental conditions

Answers: 6.1. d, 6.3. b, 6.8. b



VI-92 (774)

6.11. When specifying the "10:1 calibration principle", one is referring to:

a. The ratio of the frequency of calibration of a secondary standard toa primary standard

b. The ratio of the frequency of calibration of the instrument to that ofthe primary standard

c. The ratio of the main scale to vernier scale calibrationd. The ratio of calibration standard accuracy to calibrated instrument

accuracy

6.16. What type of measurement error is caused by drift?

a. Equipment variationb. Material variationc. Operator-to-operator variationd. Laboratory-to-laboratory variation

6.20. Because it takes the least amount of surface preparation, thehardness test most generally used for bulk hardness in foundry workwould be the:

a. Vickersb. Rockwellc. Knoopd. Brinell

Answers: 6.11. d, 6.16. a, 6.20. d



VI-93 (775)

6.23. Reproducibility in an R & R study would be considered the variabilityintroduced into the measurement system by:

a. The change in instrument differences over the operating rangeb. The total measurement system variationc. The bias differences of different operatorsd. The part variation

6.26. The error term in an ANOVA based R & R study is a reflection of:

a. Reproducibilityb. Part variationc. Mathematical errorsd. Repeatability

6.28. Why would control chart methods be used in screening measurementdata before other measurement analysis?

a. They might replace the need for an ANOVAb. They are more effective than the average and range methodc. They can indicate if the measurement system is adequated. They require the collection of less data

Answers: 6.23. c, 6.26. d, 6.28. c



VI-94 (776)

6.33. The interaction term in an ANOVA R & R study indicates aninteraction between:

a. The technician and measurement errorb. The technician and the partc. The part and the total variationd. The repeatability and the reproducibility

6.34. On which of the following would a liquid penetrant be the LEASTsuccessful?

a. Polyurethane foamb. Plasticc. Glassd. Steel

6.39. Identify the factual comment regarding torque wrench usage:

a. Most torque wrenches will operate to 120% of stated rangeb. Holding a torque wrench handle below midpoint may produce a low

torque readingc. Torque wrenches cannot be calibrated in a conventional sensed. Applying an extension, without compensation, may result in a low

torque reading

Answers: 6.33. b, 6.34. a, 6.39. b


VII. QUALITY & MANAGEMENT TOOLSQUALITY CONTROL TOOLS

VII-1 (777)

QUALITY IS NEVER ANACCIDENT, IT IS ALWAYS THERESULT OF INTELLIGENTEFFORT.

JOHN RUSKIN



VII-2 (778)

Control and Management Tools

Control and Management Tools are presented in thefollowing topic areas:

C Quality control toolsC Management and planning tools

Quality Control Tools

Quality Control Tools are presented in the followingtopic areas:

C Cause-and-effect diagramsC Flow chartsC Check sheetsC HistogramsC Control chartsC Pareto diagramsC Scatter diagrams



VII-2 (779)

Basic Problem Solving Steps

The six basic problem solving steps are:

C Identify the problem (Select a problem to work on)

C Define the problem (If a problem is large, break itinto smaller pieces)

C Investigate the problem (Collect data and facts)

C Analyze the problem (Find all possible causes andpotential solutions)

C Solve the problem (Select from the availablesolutions and implement)

C Confirm the results (Was the problem fixed? Wasthe solution permanent?)

Other problem solving techniques like PDCA and DMAICcan be used.



VII-3 (780)

Problem Solving Using Control Tools



VII-4 (781)

Cause-and-Effect Diagrams

The relationships between potential causes andresulting problems are often depicted using a cause-and-effect diagram which:

C Breaks problems down into bite-size piecesC Displays many possible causes in a graphic mannerC Is also called a fishbone, 4-M, or Ishikawa diagramC Shows how various causes interactC Follows brainstorming rules when generating ideas

A fishbone session is divided into three parts:brainstorming, prioritizing, and development of anaction plan. The problem statement is identified andpotential causes are brainstormed into a fishbonediagram. Polling is often used to prioritize problemcauses. The two or three most probable causes may beused to develop an action plan.



VII-4 (782)

Method

ProblemStatement

Manpower Environment

Machine Material Measurement

Cause-and-Effect Diagrams (Continued)

Basic Fishbone 5 - M and E Example



VII-5 (783)

M ateria l M achine M an

M easurement Environm ent M ethod

S US P EC T PA NTARE W EIGH TS

TARE W EIGH TSN OT O N PAN S

S CALE C ALIB RA TION

THR EE D IFFE RE NTS CALE S

S CALE # 2 MOR EAC CU RATE THANS CALE # 1

AIRFLOW

D EB RIS

V EN DO R CO UN TS ACC E PTED

N ON -S TAN DAR D S AMP LIN GP RO CE DU RE (IN AD EQ UA TES AMP LE QU ANTITY)

W R ON G PA RT N UMB E RSFRO M DE PA RTMEN TS

INTER RU PTIO NS

R ED UC E IN CO MING R EC E IP TE RR OR S FRO M

4% TO 1% OFTRAN SA CTIO NS

INS UFFIC IE N T TR AIN IN G

K EY PU NC H E RR OR S

O VE R IS S UE U PD ATE S N OT MAD E

P ULLE D W RO NG P AR TSFRO M LO CA TION

W E AR AN D TE AR

1. W O RN N UMB E RSO N SC ALE KE Y S

2. C ON TAINE RSB RO KE N

V ARIATIO N INTOLE RAN CE

1. P LATING

2. MATE RIALTHICK NE SS

3. S CR AP AN DFOR E IG N ELE ME NTS

4. LE NG TH S

Cause-and-Effect Diagrams (Continued)

An Actual Fishbone Example



VII-6 (784)

Flow Charts

A flow chart, or process map, is useful both to peoplefamiliar with a process and to those that have a need tounderstand a process, such as an auditor. A flow chartcan depict the sequence of product, containers,paperwork, operator actions or administrativeprocedures. A flow chart is often the starting point forprocess improvement. Flow charts are used to identifyimprovement opportunities as illustrated in the followingsequence:



VII-6 (785)

Process Flow Applications

Purchasing: Processing purchase orders, placingactual purchases, vendor contract negotiations

Manufacturing: Processing returned goods, handlinginternal rejections, production processes, training newoperators

Sales: Making a sales call, taking order information,advertising sequences

Administration: Correspondence flow, processingtimes, correcting mistakes, handling mail, typing letters,hiring employees

Maintenance: Work order processing, p.m. scheduling

Laboratory: Delivery of samples, testing steps, selectionof new equipment, personnel qualification sequence,management of workflow



VII-6 (786)

Process Mapping

There are advantages to depicting a process in aschematic format. The major advantage is the ability tovisualize the process being described.

Process mapping or flow charting has the benefit ofdescribing a process with symbols, arrows and wordswithout the clutter of sentences. Many companies useprocess maps to outline new procedures and review oldprocedures for viability and thoroughness.



VII-7 (787)

Process Mapping (Continued)

Most flow charting uses certain standardized symbols.Computer flow charting software may contain 15 to 185shapes with customized variations extending to the 500range. Many software programs have the ability tocreate flow charts or process maps, although theinformation must come from someone knowledgeableabout the process. Some common flow chart or processmapping symbols are shown below:



VII-8 (788)

Material received

Visualinspection

Visualdefects?

Inform purchasingof rejection.

Generatecorrective

action report

Return tosupplier

Dimensionalinspectionrequired?

Dimensionalinspection

Acceptable?

Place in inventory

Start

No Yes

Yes

No

End

Yes

No

End

Flow Chart Example

There are a number of flow chart styles includingconceptual, person-to-person and action-to-action.



VII-9 (789)

Check Sheets

Check sheets are tools for organizing and collectingfacts and data. By collecting data, individuals or teamscan make better decisions, solve problems faster andearn management support.



VII-10 (790)

Recording Check SheetsA recording check sheet is used to collect measured orcounted data. The simplest form of the recording checksheet is for counted data. Data is collected by makingtick marks in this particular check sheet.

DAYS OF WEEK

ERRORS 1 2 3 4 5 6 TOTAL

DefectivePilot Light 40

LooseFasteners 16

Scratches 21

MissingParts 3

DirtyContacts 32

Other 9

TOTAL 19 19 16 19 23 25 121



VII-10 (791)

Checklists

The second major type of check sheet is called thechecklist. A grocery list is a common example of achecklist. On the job, checklists may often be used forinspecting machinery or product. Checklists are alsovery helpful when learning how to operate complex ordelicate equipment.

Measles Charts

Not illustrated is a locational variety of check sheetcalled a measles chart. This check sheet could be usedto show defect or injury locations using a schematic ofthe product or a human.



VII-11 (792)

Histograms

Histograms are frequency column graphs that display astatic picture of process behavior. Histograms usuallyrequire a minimum of 50-100 data points in order toadequately capture the measurement or process inquestion.

A histogram is characterized by the number of datapoints that fall within a given bar or interval. This iscommonly referred to as “frequency.” A stable processis most commonly characterized by a histogramexhibiting unimodal or bell-shaped curves. A stableprocess is predictable.

Column Graph Bar Graph Normal Histogram



VII-11 (793)

MEASUREMENT (INCHES)

282624222018161412108642

.50

.51

.52

.53

.54

.55

.56

.57

.58

.59

.60

.61

.62

.63

.64

.65

Histogram Example

Tally Histogram



VII-12 (794)

Histograms Examples

Histogram with special causes Bimodal histogram(May also be polymodal)

LSL USL

Negatively skewed distribution Truncated histogram(After 100% inspection)



VII-12 (795)

Histogram Comments

C As a rule of thumb the number of cells shouldapproximate the square root of the number ofobservations.

As an alternative, use the table below:

N K31 - 50 5 - 751 - 100 6 - 10

101 - 250 7 - 12Over 250 10 - 20

C An unstable normal distribution process is oftencharacterized by a histogram that does not exhibita bell-shaped curve.

C For a normal distribution, variation inside the bell-shaped curve is chance or natural variation. Othervariations are due to special or assignable causes.

C There are many distributions that do not follow thenormal curve. Examples include the Poisson,binomial, exponential, lognormal, rectangular, U-shaped and triangular distributions.



VII-13 (796)

Histogram - Classroom Exercise

Foil Pouch Powder Weights (In Grams)

19.5 21.3 21.3 21.3 21.3 21.2 21.4 21.4 21.419.6 21.3 21.4 21.3 21.3 20.9 19.5 21.3 21.519.6 21.4 21.5 19.8 21.0 20.6 21.5 19.7 21.321.3 21.3 19.7 21.4 21.4 19.9 21.3 19.8 19.821.6 20.4 21.4 21.4 21.4 21.4 19.6 21.5 21.221.4 21.5 21.4 21.5 21.4 19.8 19.8 21.2 21.319.4 21.4 21.4 21.3 21.3 19.7 20.1 19.9 21.319.5 21.3 21.2 21.5 19.9 21.5 19.6 21.2 21.419.8 21.3 21.2 21.4 21.6 21.4 19.8 21.3 19.421.3 21.2 21.3 21.6 21.4 21.5 20.2 19.4 21.121.3 20.2 21.4 19.7 21.4 20.1 21.3 21.4 21.521.3 19.5 21.3 21.5 19.7 21.3 19.5 21.5 21.521.4 21.4 21.2 21.5 21.4 21.3 21.5 21.3 19.821.4 19.5 21.4 21.4 21.2 21.4 21.4 21.3 21.321.5 21.3 19.9 19.8 19.6 21.3 19.7 20.2 21.419.7 21.4 21.6 19.4 21.4 21.4 19.6 21.2 19.221.5 21.4 19.8 21.3 21.4 21.5 21.4 19.5 21.421.0 20.3 19.7 21.4 21.3 21.3 19.6 21.2 19.821.1 19.3 21.1 21.3 21.5 19.6 21.3 21.4 19.721.4 19.6 21.0 20.0 21.4 19.7 19.8 21.3 21.6



VII-14 (797)

Column Intervals Tally Sheet1 19.2 - 19.392 19.4 - 19.59 3 19.6 - 19.79 4 19.8 - 19.99 5 20.0 - 20.196 20.2 - 20.39 7 20.4 - 20.59 8 20.6 - 20.799 20.8 - 20.99

10 21.0 - 21.19 11 21.2 - 21.39 12 21.4 - 21.60

Histogram - Classroom Exercise (Cont.)

Does the above tally sheet indicate two distinctpopulations? The data represents product returnedbecause of weight variation. The material had beenproduced on two different filling lines.



VII-15 (798)

Characteristics of a Normal Distribution

C Most of the points (data) are near the centerlineC The centerline divides the curve into two halvesC Some points approach the min and max valuesC The normal histogram is bell-shaped C Very few points are outside the bell-shaped curve



VII-15 (799)

68.26%

95.44%

99.73%: – 3F : – 2F : – F : : + F : + 2F : + 3F

The Normal Distribution

When all special causes of variation are eliminated, theprocess will produce a product that, when sampled andplotted, has a bell-shaped distribution. If the base of thehistogram is divided into six (6) equal lengths (three oneach side of the average), the amount of data in eachinterval exhibits the following percentages:



VII-16 (800)

Control Charts

Control charts are effective statistical tools to analyzevariation in many processes. They are line graphs thatdisplay a dynamic picture of process behavior. Aprocess which is under statistical control ischaracterized by points that do not exceed calculatedupper or lower control limits.

Charts for variables are generally most costly sinceeach separate variable (thought to be important) musthave data gathered and analyzed. Variables charts arealso the most valuable and useful. Control charts arecovered in substantial detail in Section X of this Primer.



VII-16 (801)

Control Chart Advantages

C They provide a display of process performanceC They are statistically soundC They can plot both attributes and variablesC They can detect special and assignable causes C They indicate the time that things changeC Variables charts can measure process capabilityC They can determine if improvements are effective



VII-16 (802)

Control Chart Disadvantages

C They require mathematical calculationsC They can provide misleading informationC The sample frequency can be inappropriateC There may be an inappropriate chart selectionC The control limits can be miscalculatedC They can have differing interpretationsC The assumed population distribution can be wrongC Very small but sustained shifts can be missedC Statistical support may be necessary



VII-17 (803)

Pareto Diagrams

Pareto diagrams are very specialized forms of columngraphs. They are used to prioritize problems so that themajor problems can be identified. Pareto diagrams canhelp teams get a clear picture of where the greatestcontribution can be made.

Briefly stated, the principle suggests that a few problemcategories (approximately 20 %) will present the mostopportunity for improvement (approximately 80 %).



VII-17 (804)

Pareto Diagrams (Continued)

Dr. Joseph M. Juran, world renowned leader in thequality field, needed a short name to apply to thephenomenon of the “vital few” and the “trivial many.”He depicted some cumulative curves in The QualityControl Handbook and put a caption under them,“Pareto's principle of unequal distribution...” The textmakes it clear that Pareto only applied this principle inhis studies of income and wealth; Dr. Juran applied thisprinciple as “universal.”

Pareto diagrams are used to:

C Analyze a problem from a new perspectiveC Focus attention on problems in priority orderC Compare data changes during different time periodsC Permit the construction of a cumulative line

“First things first” is the thought behind the Paretodiagram. Our attention is focused on problems inpriority order.



VII-18 (805)

Cumulative Line

Problem Categories

300

200

100

A B C D E F G H I J K L M N

100

75

50

25

0

Typical Pareto Diagram

The defects for a book product are shown in Pareto formbelow:

The “all others” category is placed last. Cumulativelines are convenient for answering such questions as,“What defect classes constitute 70 % of all defects?”

The Pareto method assumes that there will besegregation of the significant few from the trivial many.

Pareto diagrams can also be arranged based on costs orcriticality (not just the number of occurrences).



VII-21 (806)

Scatter DiagramA scatter diagram (correlation chart) is a graphic displayof many data points which represent the relationshipbetween two different variables.

Low-positive High-positive

No-correlation High-negative

In most cases, there is an independent variable and adependent variable. By tradition, the dependent variableis represented by the vertical axis and the independentvariable is represented by the horizontal axis.



VII-22 (807)

Scatter Diagrams (Continued)

The ability to meet specifications in many processes aredependent upon controlling two interacting variablesand, therefore, it is important to be able to control theeffect one variable has on another.

The dependent variable can be controlled if therelationship is understood. Correlation originates fromthe following:

C A cause-effect relationship

C A relationship between one cause and anothercause

C A relationship between one cause and two othercauses



VII-22 (808)

Scatter Diagrams (Continued)

Not all scatter diagrams display linear relationships.


VII. QUALITY & MANAGEMENT TOOLSMANAGEMENT & PLANNING TOOLS

VII-23 (809)

Quality Management and Planning Tools

Formal research on the seven new quality tools beganin 1972, as part of the Japanese Society of QCTechnique Development meetings. It took several yearsof research before the new 7 tools were formalized. The7 new tools as written by Japanese authors are:

1. Relations diagram2. Affinity diagram (KJ method)3. Systematic diagram4. Matrix diagram5. Matrix data analysis6. Process decision program chart (PDPC)7. Arrow diagram

The American adaptations are:

2. Affinity diagram (KJ method)3. Tree diagram*6. Process decision program chart (PDPC)5. Matrix diagram1. Interrelationship digraph (I.D.)*4. Prioritization matrices*7. Activity network diagram*

* Renamed or modified tool



VII-24 (810)

Affinity Diagrams

The affinity diagram uses an organized technique togather facts and ideas to form developed patterns ofthought. It can be widely used in the planning stages ofa problem to organize the ideas and information.

The steps can be organized as follows:

C Define the problem under consideration

C Have 3" x 5" cards for use

C Enter ideas, facts, opinions, etc. on the cards

C Place the cards or notes on a table or wall

C Arrange the groups into similar categories

C Develop a main category for each group

C Outline the affinity groups



VII-25 (811)

HAVE A Q & A SOURCE

TAKE UNIVERSITY LEVEL COURSES IN QUALITY

HAVE A TUTORSTUDY IN GROUPS

ATTEND CQE REFRESHER

TAKE QUALITY ENGINEERINGSEMINARS

WATCH VIDEO PRESENTATION

HAVE PRACTICALEXPERIENCE

MAKE YOUR OWN CQE EXAMS

STUDY OLD CQE TESTS

STUDY 1 SUBJECTAT A TIME FOR 3 - 4 WEEKS

START EARLY 1-2 YEARS

STUDY INTENSIVELY

PUMP YOURSELF UP

BE AROUND OTHERSWHO ARE POSITIVEPRIDE

MOTIVATE SELF GET BONUS

LISTEN TO SUCCESSFUL PASSEDCQE’S

TEACH CQE SUBJECTS

GET CQE PRIMER

GET OTHER PRIMERS

GET MANY OTHERQUALITY TEXTBOOKS

CALL ASQ TO OBTAINBODY OF KNOWLEDGE

Example Affinity Diagram



VII-26 (812)

Tree Diagram

The tree diagram is a systematic method to outline allthe details needed to complete a given objective. Thetree diagram can also be referred to as a systematicdiagram. It is an orderly structure similar to a family treechart or an organization chart. The method of logic issimilar to that of value analysis. The organization is bylevels of importance (i.e., why - how, goals - means).

The tree diagram can be used to:

C Develop the elements for a new productC Show the relationships of a production processC Create new ideas in problem solvingC Outline project implement steps

The supplies needed for tree diagram developmentshould include 3" x 5" cards, Post-it® notes, flip charts,or a large board.



VII-27 (813)

ASK FOR BONUS

LISTEN TO SUCCESSFUL

CQES

MOTIVATE YOURSELF

TEACH CQE SUBJECTS

MAKE UP YOUR OWN CQE EXAMS

HAVE A CONTACT SOURCE FOR Q/A

START EARLY

1 - 2 YEARS

NEED RESOURCES

GET CQE PRIMER

CALL ASQ FOR BOK

GET OTHER TEXTBOOKS

OBTAIN VIDEOS

CRITIQUE VIDEOS

STUDY VIDEOS

TAKE CQE SEMINARS

RESTUDY SEMINAR MATERIALS

OBTAIN KNOWLEDGE ATTEND CQE

REFRESHERSTUDY IN A GROUP

STUDY AT HOME

HAVE A TUTOR

STUDY VIA TUTOR

TAKE UNIVERSITY LEVEL COURSES

IN QUALITY

STUDY BOK

USE PRACTICAL EXPERIENCE

NEED TO PREPARE

STUDY OLD CQE TESTS

BE AROUND OTHERS WHO ARE POSITIVE

ASK FOR HELPFUL TIPS

REWARD YOURSELF FOR

EACH STEPPRIDE

EXAMINE MOTIVATION

PASS THE CQE EXAM

Example Tree Diagram



VII-28 (814)

Process Decision Program Charts (PDPC)

The process decision program chart (PDPC) method isused to chart the course of events that will take us froma start point to a final complex goal. This method issimilar to contingency planning.

Some uses for PDPC charts include:

C The problem is new, unique, or complex in nature.It may involve a sequence that can have verydifficult and challenging steps.

C The opportunity to create contingencies and tocounter problems are available to the team.Sidesteps in the problem solving sequence areunknown, but anticipated. The PDPC method isdynamic.



VII-29 (815)

NEEDFOR THE

CQE

ENROLL IN CQE

REFRESHER

OBTAINRESOURCES

STUDYWITH

CLASS

GETTUTOR

NO CQE CLASSES

LOSS OFMOTIVATION

STUDYVIA

TUTOR

FIND OTHERS

STUDYALONE

HAVEFRIENDSSUPPORT

GETPUMPED

UP

STUDY IN A

GROUP

FIND ACQE

CALLEXPERT

PASSTHETEST

A2 A4 RESULTRA4

RA5A5A3

B2 B4 RB4

CONTINGENCY

CONTINGENCY

B3 B5 RB5

CONTINGENCY

CONTINGENCY

A1

B1

STARTGOAL

MajorCategories

2ndLevel

LastLevel

Last Level"What- ifs"

Solutions to"What- ifs"

PDPC Examples



VII-30 (816)

Matrix Diagram

The matrix diagram method is used to show therelationship between objectives and methods, resultsand causes, tasks and people, etc. The objective is todetermine the strength of relationships between a gridof rows and columns. The intersection of the grid willclarify the problem strength.

There are several basic types of matrices:

C L-type...elements on the Y-axis and elements on theX-axis

C T-type...2 sets of elements on the Y-axis, split by aset of elements on the X-axis

C X-type...2 sets of elements on both the Y-axis and X-axis

C Y-type...2 L-type matrices joined at the Y-axis toproduce a matrix design in 3 planes



VII-31 (817)

L-Type Matrix ExampleKnowledge

Factors

QualityMgmt

Concepts

QualityCosts

Metrology&

InspectionSampling Auditing Basic

StatisticsAdvancedStatistics

ControlCharts

ProbabilityDistributions Reliability

WorkExperience ± ± ±

HaveTutor ± Î ± Æ ± Æ ±

Study InGroup Î ± ± ± Æ Æ ±

Attend CQERefresher ± Æ ± ± ±

Study OldTests Î ±

HighMotivation Æ ÆCan CallExpert Î Î Î

Æ Strong Relationship (3) Relationship (2) Î Possible (1)



VII-32 (818)

Interrelationship Digraph (I.D.)

This technique is created for the more complexproblems or issues that management may face. If theissue is very complex, exact relationships may bedifficult to determine. There may be intertwined causalrelationships involved. The idea is to have a process ofcreative problem solving that will eventually indicatesome key causes.

Several other tools can be used as material for thistechnique: affinity diagrams, tree diagrams, or cause-and-effect diagrams.

The fun begins when relationship arrows are drawn in.The relationship arrow goes from the cause item to theeffect item (cause ----> effect). This is done for everycard until completed.



VII-33 (819)

BONUSFORCQE

PEERSHAVECQE

JOB EVALUATIONNEEDS CQE

ATTENDCQE

REFRESHER

MOTIVATIONOF SELF

GETCQE

PRIMER

NEXTPROMOTIONNEEDS CQE

CALL ASQ

TAKE ASQCQE

WORKSHOP

HOW TO PASS THE CQE EXAM

STUDYOLD CQE TESTS

HAVE ACALL-INSOURCE

STUDYINTENSIVELY

HAVE A

TUTOR

STUDY INGROUPS

TAKE UNIVERSITY

COURSES

Interrelationship Digraph Example

A high number of outgoing arrows indicates a rootcause or driver. A high number of incoming arrowsindicates an outcome.



VII-34 (820)

Prioritization Matrix

The original Japanese matrix data-analysis tool is not aseasy to use, due to its heavy emphasis on statisticalanalysis.

To use the prioritization matrices, the key issues andconcerns must be identified and with alternativesgenerated. There are several approaches:

1. The full analytical criteria method

2. The consensus criteria method

3. The combination I.D./matrix method

Examples of the prioritization matrices follow.



VII-35 (821)

Prioritization Matrix ExampleThe Criteria Composite Ranking (4 People)

TotalA. Work Experience 0.05 + 0.10 + 0.10 + 0.20 = 0.45

B. Have Tutor 0.10 + 0.20 + 0.30 + 0.10 = 0.70

C. Study In Group 0.15 + 0.10 + 0.05 + 0.20 = 0.50

D. Attend CQE Refresher 0.25 + 0.20 + 0.20 + 0.30 = 0.95

E. Study Old Tests 0.15 + 0.15 + 0.25 + 0.10 = 0.65

F. High Motivation 0.30 + 0.25 + 0.10 + 0.10 = 0.751.00 1.00 1.00 1.00 = 4.00

Completed Rank Order Scores

Criteria

Factors

0.45Work

Experience

0.70HaveTutor

0.50StudyGroup

0.95Attend

Refresher

0.65Study

Old Tests

0.75High

Motivation

Total

Quality Management 1(0.45) 1(0.70) 1(0.50) 1(0.95) 1(0.65) 1(0.75) 4.00

Quality Costs 5(0.45) 2(0.70) 2(0.50) 3(0.95) 2(0.65) 2(0.75) 10.30

Inspection Methods 4(0.45) 4(0.70) 5(0.50) 4(0.95) 3(0.65) 3(0.75) 15.10

Metrology 3(0.45) 5(0.70) 6(0.50) 5(0.95) 5(0.65) 4(0.75) 18.85

Sampling 2(0.45) 3(0.70) 4(0.50) 2(0.95) 4(0.65) 5(0.75) 13.25

Auditing 12(0.45) 6(0.70) 3(0.50) 6(0.95) 6(0.65) 7(0.75) 25.95

*Basic Statistics 9(0.45) 7(0.70) 11(0.50) 7(0.95) 12(0.65) 6(0.75) 33.40

*Advanced Statistics 11(0.45) 12(0.70) 12(0.50) 12(0.95) 8(0.65) 12(0.75) 44.95

*Control Charts 10(0.45) 11(0.70) 7(0.50) 8(0.95) 9(0.65) 8(0.75) 35.15

*Probability 8(0.45) 10(0.70) 9(0.50) 10(0.95) 11(0.65) 10(0.75) 39.25

*Probability Distributions 7(0.45) 9(0.70) 10(0.50) 11(0.95) 10(0.65) 11(0.75) 39.65

*Reliability 6(0.45) 8(0.70) 8(0.50) 9(0.95) 7(0.65) 9(0.75) 32.15

*Important Areas



VII-36 (822)

Activity Network Diagram

The arrow diagram is the original Japanese name forthis tool. The activity network diagram describes amethodology that includes program evaluation andreview techniques (PERT), critical path method (CPM),node/activity on node diagrams (AON), precedencediagrams (PDM), and other network diagrams.

As with other methods, the use of Post-it® notes or 3" x5" cards will help in the preparation stage of theplanning of the chart. After the identification ofactivities, the following would occur:

C Arrange the cards in sequenceC Identify links to other activitiesC Record times for each activityC Verify the critical pathC Calculate the earliest start and finish times C Calculate the latest start and finish times C Calculate the slack timesC Review the activity network diagramC Find ways to reduce the time neededC Put diagram on paper and distribute



VII-37 (823)

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Example Activity Network Diagram


VII. QUALITY & MANAGEMENT TOOLSQUESTIONS

VII-39 (824)

7.2. What other problem solving tool is customarily used to complementthe fishbone diagram?

a. Scatter diagramsb. Pareto diagramsc. Brainstormingd. Force field analysis

7.4. The seven basic tools of quality focus on:

a. Quantitative and qualitative datab. Management directed analysisc. Customer requirementsd. External and internal customer satisfaction

7.8. An advantage of process mapping is the ability to:

a. Accumulate data for Pareto analysisb. Detect assignable causes of behaviorc. Discover the underlying distribution of a processd. Check current processes for duplication or redundancy

Answers: 7.2. c, 7.4. a, 7.8. d



VII-40 (825)

7.12. For organizing information, facts or data into a systematic, logicalmanner, which of the following new quality tools would be used?

a. An interrelationship digraphb. A tree diagramc. An activity network diagramd. Prioritization matrix

7.14. Which of the following would be the best application of a Paretochart?

a. To determine when to make proactive adjustments to a processb. To detect special behavior causes in the processc. To gather data and to design experimental controlled changesd. To evaluate the results of other problem solving techniques

7.20. As a problem solving technique, which of the following would be thebest application for an Ishikawa diagram?

a. Problem identification and corrective actionb. To support the PDCA cyclec. The determination of potential root problem causesd. The determination of short-term corrective action

Answers: 7.12. b, 7.14. d, 7.20. c



VII-41 (826)

7.21. What is the major advantage in flow charting or process mappingprocedures and work instructions?

a. So that computer programs with standardized symbols can be usedb. So that concurrent engineering activities may be plannedc. So that improvements in product or process flow are apparentd. So that the process of concern can be easily visualized

7.24. Which of the following statements can be safely made about Paretodiagrams?

a. They have little application outside of the quality areab. They reflect an observation of factc. They are bound by a universal set of lawsd. They have no validity for discrete data

7.27. Which of the following statements is the major technical criticism ofthe use of the cause-and-effect diagram?

a. It is too time consuming when the major contributing factors to aproblem are known

b. It tends to oversimplify the problem by ignoring contributing factorinteractions

c. It tends to ignore contributing factors that do not start with the letterM

d. It treats contributing factors equally, but some may be moresignificant

Answers: 7.21. d, 7.24. b, 7.27. b



VII-42 (827)

7.30. The new problem solving tool which incorporates PERT and CPMtechniques into a project flow chart is called a/an:

a. Activity network diagramb. Prioritization matrixc. Tree diagramd. Process decision program chart

7.31. Which of the following process mapping symbols would NOT beassociated with a decision point?

a.

b.

c.

d.

7.33. Which of the following quality tools would be LEAST important in theproblem definition phase?

a. Fishbone diagramsb. Control chartsc. Process flow diagramsd. Pareto diagrams

Answers: 7.30. a, 7.31. b, 7.33. b


VIII. IMPROVEMENT TECHNIQUES

VIII-1 (828)

YOU CAN HELP AN ELEPHANTUP, IF IT’S TRYING TO GET UP.

BUT, YOU CANNOT HELP ANELEPHANT IF IT’S TRYING TOLIE DOWN

OLD THAI SAYING


VIII. IMPROVEMENT TECHNIQUESIMPROVEMENT MODELS

VIII-2 (829)

Improvement Techniques are presented in the followingtopic areas:

C Improvement modelsC Corrective and preventive actions

Improvement Models

Using any improvement approach, the problem oropportunity statement must be clearly defined. Oftenproblem statements are unclear.

C The true problem must be clearly identified. Thereis often a tendency to work on a downstreamsymptom of an upstream problem.

C A problem is the gap between:

C What is and what should be

C Current results and desired results

C A clearly defined problem statement should bemeasurable and include a target timetable.



VIII-3 (830)

Plan/Do/Check/Act

The historical evolution of the PDCA problem solvingcycle is interesting. Kolsar (1994) states that Demingpresented the following product design cycle (which heattributed to Shewhart) to the Japanese in 1951:

1. Design the product2. Make the product3. Put the product on the market4. Test the product in service5. Redesign the product, using consumer reaction

and continue the cycle



VIII-3 (831)

PDCA (Continued)

Perhaps from this concept, the Japanese evolved ageneral management control process called PDCA.Refer to the illustration below:

Action (A): Implement Plan (P): Establish anecessary reforms when plan for achievingthe results are not a goal.as expected.

Check: Measure Do (D): Enact theand analyze the Plan.results.

The PDCA Cycle

The PDCA cycle is very popular in many problemsolving situations because it is a logical representationof how most individuals already solve problems.



VIII-4 (832)

Plan/Do/Study/Act

Deming (1986) was somewhat disappointed with theJapanese PDCA adaption. He proposed a PDSAcontinuous improvement spiral, which he consideredprincipally a team oriented problem solving technique.

1. Plan - What changes might be desirable? Whatdata is needed?

2. Do - Carry out the change or test decided upon,preferably on a small scale.

3. Study - Observe the effects of the change

4. Act - Study the results. What was learned? Whatcan one predict from what was learned?

5. Repeat step 1 with new knowledge accumulated.

6. Repeat step 2 and onward.

Both PDCA or PDSA are very helpful techniques inproduct and/or process improvement projects.



VIII-5 (833)

Process Improvement

Most companies, that survive, effect processimprovement. However, progress is often at anevolutionary rate. What is needed in many cases(particularly in high-tech fields) is revolutionaryprogress. See the following schematic:

From an internal perspective, Company A is makingprogress. It is proceeding along at a steadyimprovement rate. Without competition, Company A isin good shape. However, Company B is proceeding ata revolutionary improvement rate and will soon have allbut the most loyal of Company A’s customers.



VIII-5 (834)

Break Through Achievement

Some companies fail when making either evolutionaryor revolutionary progress. This could certainly be thecase if a competitor enters the market with an entirelynew concept.

Companies producing tube-style television sets ormainspring watches were shocked when solid state TVsand quartz crystal watches took their markets away.



VIII-6 (835)

Six Sigma Approach

Six Sigma is a highly disciplined process that focuseson developing and delivering near-perfect products andservices consistently. Six sigma is also a managementstrategy to use statistical tools and project work toachieve breakthrough profitability and quantum gains inquality.

Snee (1999) provides some reasons why six sigmaworks:

C Bottom line resultsC Senior management is involvedC A disciplined approach is used (DMAIC)C Short project completion times (3 to 6 months)C Clearly defined measures of successC Trained individuals (black belts, green belts)C Customers and processes are the focusC A sound statistical approach



VIII-7 (836)

Six Sigma Approach (Continued)

Six sigma black belts serve as project managers forbusiness improvement projects to ensure timelycompletion of the improvement objectives.

All projects need charters, plans, and boundaries. Sixsigma projects may be selected from a broad range ofareas including:

C Improved process capabilitiesC Lean manufacturing principlesC Reduction in customer complaintsC Improved work flowsC Reduction of internal defectsC Administrative improvementsC Cost reduction opportunitiesC Cycle time reductionsC Supplier related improvementsC Market share growth

The actual project should be consistent with companystrategies for survival and/or growth.



VIII-8 (837)

DMAIC Process

Many six sigma improvement teams employ a problemsolving methodology called DMAIC.

Define the customer’s critical-to-quality issues and corebusiness process.

C Define customer requirements and expectationsC Define project boundariesC Define the process to be improved by mapping

Measure the performance of the core business processinvolved.

C Develop a data collection planC Collect data from many sourcesC Collect customer survey results

Analyze the data and determine root causes orimprovement opportunities.

C Identify performance gapsC Identify improvement opportunitiesC Identify objective statistical procedures



VIII-8 (838)

DMAIC Process (Continued)

Improve the target process with creative solutions to fixand prevent problems.

C Create innovative solutions using technologyC Develop and deploy improvement

Control the improvements to keep the process on thenew course.

C Develop a monitoring plan to prevent relapseC Institutionalize the improvements

The DMAIC steps as described by Hahn (1999) are:

Define: Select the appropriate area to improveMeasure: Measure the response variableAnalyze: Identify the root causesImprove: Reduce variability or eliminate the causeControl: Sustain the improvements



VIII-9 (839)

Six Sigma Responsibilities

Potential black belts often undertake a 4 month trainingprogram consisting of one week of instruction eachmonth. A set of software packages are used to aid inthe presentation of projects, including Excel or Minitabfor the statistics portion. There are portions of thecourse focusing on team and project management.Dependent on the provider of the course, specificelements will differ, but all stress an understanding ofvariation reduction and a statistical approach.

Breyfogle (2000) defines the roles and responsibilities ofsix sigma black belts to include:

C Lead the (cross-function) teamC Possess interpersonal and facilitation skillsC Develop and manage a detailed project planC Schedule and lead team meetingsC Sustain team motivation and stabilityC Communicate project benefits to key partiesC Track and report milestones and tasksC Interface between key management areas



VIII-9 (840)

Six Sigma Responsibilities (Continued)

Black belts have the following duties in their company:

Mentor: Provide a six sigma assistance networkTeacher: Train local personnelCoach: Provide support to project personnelIdentifier: Discover opportunities for improvementInfluencer: Be an advocate of six sigma strategy

(Harry,1998)

Harry (1998) reports that the average black belt projectwill save about $175,000. There should be about 5 - 6projects per year per black belt. The ratio of one blackbelt per 100 employees, can provide a 6% cost reductionper year. For larger companies there is usually onemaster black belt for every 100 black belts.



VIII-10 (841)

Six Sigma Management Support

Effective six sigma programs do not happenaccidentally. Careful management planning andimplementation are required to ensure that the properresources are available and applied to the rightproblems. Key resources may include people trained inproblem solving tools, measurement equipment,analysis tools, and capital resources. Assigning humanresources may be the most difficult element, sincehighly skilled problem solvers are a valuable resourceand may need to be pulled from other areas where theirskills are also needed.



VIII-10 (842)

Linking Six Sigma Projects to Goals

Pande (2000) suggests that embarking on a six sigmainitiative begins with a management readinessassessment, which includes a review of the followingareas:

C Assess the outlook and future path of the business:

C Is the strategy course clear for the company?C Can we meet our financial and growth goals?C Does our organization respond effectively to new

circumstances?

C Evaluate the current organizational performance:

C What are our current overall business results?C Do we meet customer requirements?C How effectively are we operating?

C Review the capacity for systems change andimprovement:

C How well do we manage system changes?C Do our cross-functional processes work?C Are there conflicts with our current efforts?



VIII-11 (843)

Kaizen

Kaizen is Japanese for continuous improvement (Imai,1997). The word kaizen is taken from the Japanese kai“change” and zen “good.” This is usually referred to asincremental improvement, but on a continuous basisand involving everyone. Kaizen is an umbrella term for:

C ProductivityC Total quality controlC Zero defectsC Just-in-time productionC Suggestion systems

The kaizen strategy involves:

C Management maintains operating standardsC Progress improvement is the key to successC PDCA improvement cycles are usedC Problems are solved with hard dataC The next process is considered the customerC Quality is of the highest priority



VIII-11 (844)

The Kaizen Blitz

While most kaizen activities are considered to be of along-term nature by numerous individuals, a differenttype of kaizen strategy can occur. This has been termeda kaizen event, kaizen workshop, or kaizen blitz, whichinvolves a kaizen activity in a specific area within a shorttime period.

The kaizen blitz, using cross-functional volunteers in a3 to 5 day period, results in a rapid workplace change ona project basis. Various metrics are used to measurethe outcomes of a kaizen blitz:

C Floor space savedC More line flexibilityC Improved work flowC Improvement ideasC Increased quality levelsC Safer working environmentC Reduced non-value added time



VIII-12 (845)

Lean Techniques

There are a large number of lean manufacturingtechniques that are widely used by organizations today.Some of the more common processes include:

C Minimization of non-value added activities (muda)C Decreased cycle timesC Single minute exchange of dies (SMED)C Set-up reduction (SUR)C The use of standard operating proceduresC The use of visual workflow displaysC Total productive maintenanceC Poka-yoke techniques to prevent or detect errorsC Principles of motion study and material handlingC Systems for workplace organization (5S approach)C Just-in-time principles C A large number of kaizen methodsC Continuous flow manufacturing conceptsC Value stream mapping

Many of these approaches support and complementeach other.



VIII-13 (846)

Lean Glossary

Andon board - A visual control device. It is typically a litoverhead display, giving the current status of theproduction system and alerting employees to problems.

Continuous flow manufacturing (CFM) - Material movesone piece at a time, at a rate determined by the needs ofthe customer, in a smooth and uninterrupted sequence.

Cycle time - The time required to complete one cycle ofan operation.

Inventory turns - The number of times inventory isconsumed in a given period.

Just-in-time (JIT) - A system for producing anddelivering the right items at the right time in the rightamounts.

Level loading - The smoothing or balancing of the workload in all steps of a process.

Muda - A Japanese term meaning any activity thatconsumes resources but creates no value.



VIII-13 (847)

Lean Glossary (Continued)

Non-value added - Any activity that does not add valueto the product or service.

Perfection - The complete elimination of muda so that allactivities along a value stream create value.

Poka-yoke - A mistake proofing device or procedure toprevent or detect an error which adversely affects theproduct and results in the waste of correction.

Pull - A system of cascading production and deliveryinstructions from downstream to upstream activities inwhich nothing is produced by the upstream supplieruntil the downstream customer signals a need.

Queue time - The time a product spends awaiting thenext processing step.

Single minute exchange of dies (SMED) - A series oftechniques for rapid changeovers of productionmachinery. Ten minutes is a common initial objective.

Single piece flow - A situation in which one completeproduct proceeds through various operations withoutinterruptions, back flows, or scrap.



VIII-14 (848)


Small lot principles - Effectively reducing lot size untilthe optimum of one piece flow is realized.

Standard work - A precise description of each workactivity, specifying cycle time, takt time, the worksequence of specific tasks, and the minimum inventoryof parts needed to conduct the activity.

Takt time - The available production time divided by therate of customer demand. For example, if a customerwants 480 widgets per day, and the factory operates 960minutes per day, takt time is two minutes. Takt timebecomes the heartbeat of any lean organization.

Value stream - The specific activities required to design,and provide a specific product, from concept to launch,from order to delivery.

Visual control - The placement in plain view of all thetools, parts, production activities, and indicators ofproduction system performance, such that the status ofthe system can be understood easily and quickly.



VIII-14 (849)


Waste - All overproduction ahead of demand, waiting forthe next processing step, unnecessary transport ofmaterials, excessive inventories, unnecessary employeemovements, and production of defective parts.

Work cell - The layout of machines or businessprocesses of different types, performing differentoperations in a tight sequence, typically a U or L shape,to permit single piece flow and flexible deployment ofhuman effort.

Work center - One process station in a work cell.



VIII-15 (850)

Cycle Time Reduction

Cycle time is the amount of time required to completeone transaction of a process. The reduction in cycletime is customarily undertaken for many of the followingreasons:

C To please customersC To reduce wastesC To increase capacityC To simplify the operationC To reduce product damageC To remain competitive



VIII-15 (851)

Value Stream Mapping

A value stream map is created to identify all of theactivities involved in product manufacturing from startto finish. This value stream may include suppliers,production operations and the end customer. Forproduct development, value stream mapping includesthe design flow from product concept to launch. Benefits of a value stream map include:

C Seeing the complete process flowC Identifying sources and locations of wasteC Providing common terminology for discussionsC Helping to make decisions about the flowC Tying multiple lean concepts togetherC Providing a blueprint for lean ideasC Linking information and material flowsC Describing how the process can changeC Determining effects on various metrics

(Rother, 1999)



VIII-16 (852)

Current State Mapping

A current state map of the process is developed tofacilitate process analysis. Basic tips on drawing acurrent state map include:

C Start with a quick orientation of process routesC Personally follow the material and information flowsC Map the process with a backward flowC Collect the data personallyC Map the whole streamC Create a pencil drawing of the value stream

Some of the typical process data includes: cycle time(CT), changeover time (COT), uptime (UT), number ofoperators, pack size, working time (minus breaks, inseconds), WIP, and scrap rate.



VIII-16 (853)

Future State Map

A future stream map is an attempt to make the processlean. This involves creativity and teamwork on part ofthe lean team to identify creative solutions. Everythingthe team knows about lean manufacturing principles isused to create the process of the future. Questions toask when developing a future state map are:

C What is the required takt time?C Do manufactured items move directly to shipping?C Are items available for customer pull?C Is continuous flow processing applicable?C What is the pacemaker process? C What is the increment of work to be released?C What improvements can be used?C Can the process be leveled? (Rother, 1999)



VIII-16 (854)

Implementation Planning

The final step in the value stream mapping process is todevelop an implementation plan for establishing thefuture state. This includes a step-by-step plan,measurable goals, and checkpoints to measureprogress. A Gantt chart may be used to illustrate theimplementation plan. (Rother, 1999)



VIII-17 (855)

Value Stream Mapping Icons

The following icons are used:

Electronic Flow FIFO Finished Goods Go See

Inventory Kaizen Burst Kanban Batches Kanban Post

Kanban Production Kanban Load LevelingKanban Signal Withdrawal

Manual InformationFlow Operator Process Box Pull Arrow

Push Arrow SourcePull Circle Schedule Box

Supermarket Truck Shipment Buffer Stock Data Box



VIII-18 (856)

5S Workplace Organization

The presence of a 5S program is indicative of thecommitment of senior management to workplaceorganization, lean manufacturing and the elimination ofmuda (waste). The 5S program mandates that resourcesbe provided in the required location, and be available asneeded to support work activities. The five Japanese“S” words for workplace organization are:

C Seiko (proper arrangement)C Seiton (orderliness)C Seiketso (personal cleanliness)C Seiso (cleanup)C Shitsuke (personal discipline) Imai (1997)



VIII-18 (857)

5S Workplace Organization (Cont’d)

For American companies, the 5Ss are translated intoapproximate English equivalents:

C Sort: Separate what is unneeded and eliminate it.

C Straighten: Put everything in its place.

C Scrub: Make the workplace spotless.

C Systematize: Make cleaning and checking routine.

C Standardize: Sustain the previous 4 steps.

The 5S approach exemplifies a determination toorganize the workplace, keep it neat and clean, establishstandardized conditions, and maintain the discipline thatis needed to do the job. Numerous modifications havebeen made on the 5S structure.



VIII-19 (858)

Non-Value Added Activities

Non-value added activities are classified as muda. It isanother term for waste that exists in the process. Theuseful activities that the customer will pay for areconsidered value added. The other activities are notvalue added. Imai (1997) provides a list of seven mudacategories that have been widely used in industry:

C Overproduction C ProcessingC Inventory C WaitingC Repair/rejects C TransportC Motion

Overproduction

The muda of overproduction is producing too much ata particular point in time. Overproduction ischaracterized by:

C Producing more than needed by the next process C Producing earlier than needed by the next processC Producing faster than needed by the next process



VIII-19 (859)

Inventory

Parts, raw materials, work-in-process (semi-finishedgoods), inventory, supplies, and finished goods are allforms of inventory. Inventory is considered muda sinceit does not add value to the product. Inventory willrequire extra space, transportation and materials.

Repair/ Rejects

Rejects involving scrapping the part are a definite wasteof resources. Having rejects on a continuous flow linedefeats the purpose of continuous flow. Line operatorsand maintenance will be used to correct problems,putting the takt time off course.

Motion

Extra unneeded operator motions are wasteful. Thelayout of the workplace should be redesigned to takeadvantage of proper ergonomics.



VIII-20 (860)

Processing

Processing muda consists of additional steps oractivities in the manufacturing process.

Waiting

The muda of waiting occurs when an operator is readyfor the next operation, but must remain idle. Theoperator is idle due to machine downtime, lack of parts,unwarranted monitoring activities, or line stoppages.

Transport

All forms of transportation are muda. This describes theuse of forklifts, conveyors, pallet movers, and trucks.



VIII-21 (861)

Continuous Flow Manufacturing (CFM)

In the lean environment, continuous flow manufacturingis a basic principles. Material should always be movingone piece at a time, at a rate determined by the needs ofthe customer. The flow of product must be smooth anduninterrupted by:

C Quality issuesC SetupsC Machine reliabilityC BreakdownsC DistanceC Handling methodsC Transportation arrangementsC Staging areasC Inventory problems

(Productivity, 1999)



VIII-22 (862)

Continuous Flow Manufacturing (Cont’d)

The following techniques are important for continuousflow manufacturing:

C Poka-yoke: To prevent defects from proceeding tothe next step

C Source inspection: To catch errors to correct theprocess

C Self-checks: Operator checks to catch defects andto correct the process

C Successive checks: Checks by the next process tocatch errors

C TPM is used to help achieve high machine capability

(Womack, 1996), (Robinson, 1990)



VIII-22 (863)

Takt Time

Takt time is a term used (first by Toyota) to define a timeelement that equals the demand rate. In a CFM or onepiece flow line, the time allowed for each line operationis limited. The line is ideally balanced so that eachoperator can perform their work in the time allowed. Theword takt is German meaning baton, as used by anorchestra conductor (Imai, 1997). This provides arhythm to the process.

(Conner, 2001), (Sharma, 2001)



VIII-22 (864)

Total Productive Maintenance (TPM)

Total productive maintenance promotes coordinatedgroup activities for greater equipment effectiveness andrequires operators to share responsibility for routinemachine maintenance. The professional maintenancestaff retains responsibility for major maintenanceactivities and act as coaches for the routine and minoritems. There are “six big losses” that contributenegatively to equipment effectiveness:

C Equipment failureC Setup and adjustmentC Idling and minor stoppagesC Reduced speedC Process defectsC Reduced yields



VIII-23 (865)

Visual Factory

Imai (1997) provides three reasons for using visualmanagement tools:

C To make problems visibleC To keep all workers in contact with the workplaceC To clarify targets for improvement

Production boards and schedule boards are examplesof a visual factory. These generally include the postingof daily production, maintenance items, or qualityproblems for everyone to see and understand.

Jidohka is defined as a device that stops a machinewhenever a defective product is produced. The operatoror maintenance personnel must respond to find thesource of the problem and to resolve it.



VIII-23 (866)

Visual Factory (Continued)

The kanban system provides material control for thefactory floor. The cards control the flow of productionand inventory.

The tool board is a display designed for the toolsneeded at a work station. This method is a part of 5Sactivities. The board is constructed to hold or mark theplace for the tools and includes only the tools requiredfor that work station.

The visual factory places an emphasis on setting anddisplaying targets for improvement. The concept is thatvarious operations have a target or goal to achieve. The visual factory enables management and employeesto see the status of the factory floor at a glance. Thecurrent conditions and progress are evident. Anyproblems can be seen by everyone.



VIII-24 (867)

Kanban

Kanban is the Japanese word for “sign.” It is a signal tointernal processes to provide some product. Kanbansare usually cards, but they can be flags, a space on thefloor, etc. Kanban provides some indication of:

C Part numbersC QuantitiesC LocationsC Delivery frequenciesC Times of deliveryC Color of shelves at destinationC Bar codes, etc.

All of the above items can be forms of material control.Kanban is intended to help provide product to thecustomer with the shortest possible lead times.

The order to produce parts at any one station isdependent on receiving an instruction, the kanban card.Only upon receiving a kanban card will an operatorproduce more goods. This system aims at simplifyingpaperwork, minimizing WIP and finished goodsinventories.



VIII-25 (868)

Standard Work

Standard work provides the discipline for attainingperfect flow in a process. Under normal workconditions, with no abnormalities in the system, the flowis perfect. The standard work conditions are determinedfor takt time, ergonomics, parts flow, maintenanceprocedures, and routines. Sharma (2001) provides adefinition of standard work:

“The best combination of machines and peopleworking together to produce a product or provide aservice at a particular point in time.”

Standard work is the documentation of each actionrequired to complete a specified task. Standard workshould always be displayed at the workplace. Ifabnormalities appear in the system, those items can bespotted and eliminated.



VIII-25 (869)

Standard Work (Continued)

The elements that comprise the standard workoperations are:

C Cycle time: the time allowed to make a piece ofproduction. This will be based on the takt time. Theactual time will be compared to the required takttime to see if improvements are needed.

C Work sequence: the order of operations that theworker must use to produce a part: grasp, move,hold, remove, delay, etc. The same order of workmust be done every time.

C Standard inventory: the minimum allowable in-process material in the work area, including theamount of material on the machinery, needed tomaintain a smooth flow. For continuous flow, onepiece in the machine and one piece for hand offs isoptimal. (Shingo, 1986), (Sharma, 2001)



VIII-26 (870)

SMED

SMED is an acronym for single minute exchange of dies.The concept is to take a long setup change of perhaps4 hours in length and reduce it to 3 minutes. Singleminute exchange of dies does not literally require diechanges or changeover of tooling to be performed inonly one minute. It merely implies that die changes areto be accomplished under a single digit of time. Nineminutes or less to change a die will qualify.There are 3 myths regarding setup times:

C The skill for setup changes comes from practice C Long production runs are more efficientC Long production runs are economically better

(Robinson, 1990)


VIII. IMPROVEMENT TECHNIQUESIMPROVEMENT TOOLS

VIII-27 (871)

Theory of Constraints

The theory of constraints (TOC) is a system developedby E. Goldratt. Goldratt describes the theory ofconstraints as an intuitive framework for managingbased on the desire to continually improve a company.Using TOC, a definition of the goals of the company areestablished along with metrics for critical measures.

(Goetsch, 2000)

The Goal reminds readers that there are three basicmeasures to be used in the evaluation of a system.

C ThroughputC InventoryC Operational expenses

These measures are more reflective of the true systemimpact than machine efficiency, equipment utilization,downtime, or balanced plants.



VIII-27 (872)

Theory of Constraints (Continued)

A few of the most widely used TOC concepts aredetailed below:

C Bottleneck resources are: “resources whosecapacity is equal to or less than the demand placedupon it.” If a resource presents itself as abottleneck, then things must be done to lighten theload.

C Balanced plants are not always a good thing. Donot balance capacity with demand, but “balance theflow of product through the plant with demand fromthe market.” The idea is to make the flow throughthe bottleneck equal to market demand.

C Dependent events and statistical fluctuations areimportant. A subsequent event depends upon theones prior to it. A bottleneck will restrain the entirethroughput.



VIII-28 (873)


C Throughput is: “the rate at which the systemgenerates money through sales.” The finishedproduct must be sold before it generates money.

C Inventory is: “all the money that the system hasinvested in purchasing things which it intends tosell.” This can also be defined as sold investments.

C Operational expenses are: “all the money (that) thesystem spends in order to turn inventory intothroughput.” This includes depreciation, lubricatingoil, scrap, carrying costs, etc.

C The terms throughput, inventory and operationalexpenses define money as: “incoming money,money stuck inside, and money going out.”

Goldratt (1986)



VIII-28 (874)


Goldratt (1990) provides more TOC details using thefollowing 5 step method:

1. Identify the system’s constraints

2. Decide how to exploit the system’s constraints

3. Subordinate everything else to the abovedecisions

4. Elevate the system’s constraints to keepimproving the system

5. Back to step 1



VIII-29 (875)

Total Quality Management

Total quality management is a management style basedupon producing quality service as defined by thecustomer. TQM is defined as a quality centered,customer focused, fact based, team driven, seniormanagement led process to achieve an organization’sstrategic goals through continuous processimprovement.

The word “total” in total quality management means thateveryone in the organization must be involved in thecontinuous improvement effort, the word “quality”shows a concern for customer satisfaction, and theword “management” refers to the people and processesneeded to achieve the quality.

Total quality management is not a program; it is asystematic, integrated, and organizational way-of-lifedirected at the continuous improvement of anorganization.



VIII-29 (876)

Total Quality Management (Continued)

Total quality management differs from othermanagement styles in that it is more concerned withquality during production than it is with the quality ofthe result of production. Other management styles havedifferent concerns.

Total quality management requires an organizationaltransformation - a totally new and different way ofthinking and behaving. This transformation is not easyto achieve.

Dr. Armand Feigenbaum championed the concept oftotal quality control at General Electric in the 1940s.



VIII-30 (877)

Total Quality Management (Continued)

Before total quality management implementation, uppermanagement must first determine the organization’scommon purpose or focus. Once an organizationdetermines its focus, it must begin empowering itsemployees.

TQM advocates using the cumulative skills andexpertise of employees to solve problems and improveservice quality. It calls for all members of a organizationto share authority, responsibility, accountability, anddecision making. Although it emphasizes group effort,a leader may be needed to keep the group on track.

In a routine TQM improvement process, a steeringcommittee is first made aware of a problem by inputfrom employees or customers. If it deems the problemworthy of further study, it charters an action team toanalyze the problem in detail and solve it.

Total quality management requires extensive statisticalanalysis to study processes and improve quality.



VIII-31 (878)

Continuous Quality Improvement

Continuous quality improvement may be a stand alonequality methodology, or it may be incorporated into, orwith, any number of other approaches, such as TQM, sixsigma, lean manufacturing, the Juran Quality Trilogy, orbenchmarking.

In most cases, the process of quality improvementattacks what Juran (1993) calls sporadic (special cause)or chronic (common cause) problems. The classicJapanese solution to many of these problems is calledkaizen. This technique is discussed later in this PrimerSection. It involves teamwork and a variety of tools,such as:

C Reduced material handlingC Standard operating procedures C Visual display managementC Just-in-time principlesC Value added activitiesC Workplace organizationC Elimination of wasteC Mistake proofing



VIII-31 (879)

Continuous Quality Improvement (Cont’d)

Problems that are chronic (common cause) requiretrained teams, with adequate resources, using anestablished problem solving methodology, andmanagement endorsement. Juran (1993) states thateffective improvement is accomplished on a project-by-project basis and in no other way.

This contains a variety of quality, quality management,planning, and statistical tools to assist an improvementteam. Carrying out each project involves:

C Verifying the project needC Diagnosing the causesC Providing a remedy and proving its effectivenessC Dealing with any resistance to changeC Instituting controls to hold the gains



VIII-32 (880)

Reengineering

The definition of reengineering by Lowenthal (1994) is:

“The fundamental rethinking and redesign ofoperating processes and organizational structure,focused on the organization’s core competencies toachieve dramatic improvements in organizationalperformance.”

Since most reengineering projects will involve severalfunctional departments, a senior executive is needed tohead up the effort. A process owner and areengineering cross functional team are needed. Nocompany can reengineer all of its processessimultaneously. Lowenthal (1994) recommends that aselection criteria be used on one or more of the majorprocesses in an organization:

C Which process is in trouble?C Which process has the greatest impact?C Which process can be successful redesigned?

The redesign should be a dramatic or breakthroughprocess for the company. A competitive advantage willoften be gained by this effort.


VIII. IMPROVEMENT TECHNIQUESCORRECTIVE & PREVENTIVE ACTIONS

VIII-33 (881)

Corrective and Preventive Actions

Six sigma methodology as well as ISO 9001:2000 andISO/TS 16949 require corrective and preventive actionsto prevent defect occurrence. Companies buyingproducts recognize that sorting usually doesn’t catch alldefects and only adds to their purchase price as well.

ISO 9001:2000 requires organizations to eliminate thecause of nonconformities in order to prevent theirrecurrence. Corrective actions shall be appropriate totheir potential effects. Documented procedures shouldbe established to define requirements for:

C Reviewing nonconformitiesC Determining the causes of nonconformitiesC Evaluating the need for actionC Determining and implementing the necessary actionC Maintaining records of the results of action takenC Reviewing the results of corrective actions taken

Many companies and organizations now require at leasttwo improvement activity responses for each correctiveaction request; temporary (short-term), and permanent(long-term).



VIII-34 (882)

Corrective Actions

ISO/TS 16949 (2002) has the following additionalcorrective action requirements:

C An organization have a defined process forproblem-solving, including root causedetermination and elimination.

C If a customer prescribed problem solving formatexists, this prescribed method must be used.

C An organization shall use error proofing methods intheir corrective action process.

C Any nonconformity related corrective action shallbe extended to similar processes and products.

C Rejected parts shall be analyzed. Records of thisanalysis shall be maintained.

C The cycle time of this rejected part analysis shall beminimized.



VIII-34 (883)

Preventive Actions

ISO 9001:2000 states that an organization shalldetermine actions to eliminate the causes of potentialnonconformities to prevent their occurrence. Preventiveactions shall be appropriate to their potential effects.Documented procedures shall be established to definerequirements for:

C Determining potential nonconformities and theircauses

C Evaluating the need for action to prevent theiroccurrence

C Determining and implementing the necessary action

C Maintaining records of the results of preventiveactions taken

C Reviewing the results of preventive actions taken



VIII-35 (884)

Corrective Action Definitions

The following definitions are important:

CAR: An acronym meaning corrective action request.

CAT: An acronym meaning corrective action team.

Containment action: Measures taken to screen andeliminate defective products via such techniques asinspection and removal. This should be viewed as atemporary fix and not a management philosophy.

Corrective action: An action taken to reduce or eliminatethe causes of an existing nonconformity, defect or otherundesirable situation. Often implied is the extension ofthis activity to one of preventing recurrence.

Preventive action: Measures taken to prevent theoccurrence of a quality deficiency.

Root cause analysis: The review necessary to determinethe original or true cause of a product or processnonconformance. This effort extends beyond the effectsof a problem to discover its most fundamental cause.



VIII-36 (885)

Corrective Action Procedure

There are countless varieties of corrective andpreventive action procedures.

An example is shown on Primer pages VIII - 36/37.



VIII-38 (886)

Corrective Action Request Form

CORRECTIVE ACTION REQUESTCAR#_________

TO:________________________________________________________ DATE_________

FROM:_____________________________________________________

THE FOLLOWING CONDITION IS BROUGHT TO YOUR ATTENTION FOR CORRECTIVEACTION. PLEASE INDICATE THE CAUSE AND CORRECTIVE ACTION IN THE SPACESBELOW INCLUDING SCHEDULED COMPLETION DATES. PLEASE SIGN AND DATE YOURRESPONSE AND RETURN THIS FORM TO THE SENDER WITHIN ______ WORKING DAYS.

DISCREPANT CONDITION AND APPARENT CAUSE_____________________________________________________________________________________________________________________________________________________________________________________________________________________

INVESTIGATIVE PORTIONROOT CAUSE_____________________________________________________________________________________________________________________________________________________________________________________________________________________

ACTION TO CORRECT OBSERVED DISCREPANCY (AND SIMILAR DISCREPANCIES)_____________________________________________________________________________________________________________________________________________________________________________________________________________________

ACTION TO PREVENT RECURRENCE_____________________________________________________________________________________________________________________________________________________________________________________________________________________

SCHEDULED COMPLETION DATE _____________________________________________

SIGNATURE______________________________DATE____________________________

REVIEW SIGNATURE_________________________

APPROVED DISAPPROVED DATE________________

PROJECT NAME PART NAME PART NO. MRR NO.



VIII-39 (887)

Corrective Action Commitment

Upper management is responsible for developing andimplementing a corrective action program. Most chronicsystem’s problems cannot be solved by simpletroubleshooting. The corrective action proceduretypically follows the following sequence:

C Assignment of responsibilityC Evaluation of potential importanceC Investigation of possible causesC Analysis of the problemC Corrective (or preventive) actionC Follow-up to ensure that corrective (preventive)

action is effective

The principal corrective action sources include thefollowing:

C Internal inspection and audit resultsC Customer returnsC Customer complaintsC Employee interviews and commentsC System and management audits



VIII-39 (888)

Customer Returns

All quality systems should have customer satisfactionas the ultimate goal. Therefore, any indication ofcustomer dissatisfaction should be treated with utmostgravity. A return should be viewed for what it is, anindictment of the quality system. After all, the qualitysystem is supposed to protect the customer fromunsatisfactory materials.

Customer Complaints

Customer complaints are the second most importantsource of quality system effectiveness information.Most customers don’t complain, they just quit doingbusiness with your company. Therefore, a complaintprobably represents many more similar complaints thatare unreported. Each complaint should be recorded,then investigated until the root cause is established.



VIII-40 (889)

Types of Corrective Action

As indicated earlier, many companies require two orthree step corrective action responses.

The three step corrective action process entails:

C Immediate actions(Actions taken to stop the problem immediately.)

C Temporary actions(Actions taken to stop the problem in the near term.)

C Permanent actions(Actions taken to stop the problem forever.)

When a floor level employee takes care of a problem, theactions are usually limited to “immediate actions.”Temporary and permanent actions are missed.



VIII-41 (890)

Corrective Action Planning

A company should have a documented procedure forcorrective and preventive action. The procedure shouldassign responsibilities for short-term, immediate actionto contain a product or process nonconformity.Permanent corrective actions must address the rootcause and strive to eliminate it.

Short-term, containment activities are concerned withdetection, segregation, and disposition. Guidelines forshort-term containment activities include the following:

C Clearly define the problemC Present the problem to team membersC Develop an immediate action planC Determine the following:C How to contain? How to repair? How to inspect?C What tools or gages are needed?C Who will perform sorting, and/or repairing?

C Put the short-term plan into effect quickly C Document the containment activity and resultsC Notify the appropriate personnel



VIII-41 (891)

Corrective Action Planning (Continued)

Long-term actions may take a more in-depth approach.The following steps represent the process:

C Organize the appropriate team members or expertsC Investigate and verify the problemC Clearly define the problem statementC Inform the team of any short-term activitiesC Present all known evidenceC Brainstorm and reach consensus on cause(s)C Delegate problem solving activitiesC Perform investigation (gather evidence or data)C Perform an analysis and present resultsC Perform any further investigation if neededC Clearly define the suspect root cause(s)C Determine action(s) to correct the root cause C Implement action to correct root cause(s)C Verify the effects of corrective action(s)C Report the results to management



VIII-42 (892)

Corrective Action Planning (Continued)

When the result is ineffective:

Check the method of corrective action implementation.If unsatisfactory, repeat the process. Seek assistancefrom other problem solving sources.

When the result is effective:

Assign follow-up verification using periodic checks.Check for similar process applications and implementthe same solution where applicable. The results may bepresented in a meeting with upper management.

The corrective action plans, the subject system(s) orprocess(es), assigned personnel, commitment dates,and any standardization must be documented on thecorrective action request form.



VIII-42 (893)

Root Cause Analysis

An individual or team is given the responsibility ofdetermining the root cause of a deficiency andcorrecting it. The solution to some problems may becomplex and difficult. In other cases, the solution maybe known but considerable time will be required toimplement it. The proposed action may take severalsteps. See the illustration below:

Situation ImmediateAction

IntermediateAction

Root Cause Action

The damleaks

Plug it Patch the dam Find out what caused theleak so it won't happenagain. Then rebuild the dam.

Parts areoversized

100%Inspection

Put an oversizekickout device in

line

Analyze the process and takeaction to eliminate theproduction of oversize parts.



VIII-43 (894)

Root Cause Analysis (Continued)

Most of us tend to focus on a downstream symptom ofan upstream problem. To help locate the system’s trueproblem, a variety of problem solving tools are available.Some 24 commonly used techniques are listed in thePrimer.

When permanent corrective action is proposed,management must determine if:

C The root cause analysis has identified the full extentof the problem

C The corrective action is satisfactory to eliminate orprevent recurrence

C The corrective action is realistic and maintainable



VIII-43 (895)

Standardizing Corrective Actions

Standardization is the act of identifying other systems orprocesses with similar nonconformance problems (orthe potential for similar problems) and applying thesame corrective action, once it has been proveneffective. A company must prevent similar problemsfrom occurring by means of such preventive actions.

Make the most of the solution by extending the fix. Ask,“what other situations or parts might benefit from thisfix?” Additionally, one should extend the cause. Ask,“what other things could have been affected by thiscause?”, and “are there other similar situations wheretrouble is waiting to happen?”



VIII-44 (896)

Mistake Proofing

Shigeo Shingo (1986) is widely associated with aJapanese concept called poka-yoke (pronounced poker-yolk-eh) which means to mistake proof the process. Thesuccess of poka-yoke is to provide some interventiondevice or procedure to catch the mistake before it istranslated into nonconforming product.

There are numerous adaptive approaches. Gadgets ordevices can stop machines from working if a part oroperation sequence has been missed by an operator. Aspecialized tray or dish can be used prior to assembly toensure that all parts are present. In this case, the dishacts as a visual checklist. Other service orientedchecklists can be used to assist an attendant in the caseof interruption.

Numerous mechanical screening devices can be used infabrication. The author has seen applications based onlength, width, height, and weight. Obviously, mistakeproofing is a preventive technique.



VIII-44 (897)

Mistake Proofing (Continued)

Other than eliminating the opportunity for errors,mistake proofing is relatively inexpensive to install andengages the operator in a contributing way. Work teamscan often contribute by brainstorming potential ways tothwart error prone activities. A disadvantage is thattechnical or engineering assistance is often required.

Other design improvements to “error proof” the processinclude:

C Elimination of error-prone componentsC Amplification of human sensesC Ergonomic design to optimize human responseC Redundancy in design (back up systems)C Simplification by using fewer componentsC Consideration of environmental factorsC Providing failsafe cut-off mechanismsC Enhancing product producibility and maintainabilityC Selecting proven components and circuits



VIII-45 (898)

Prevention Activities

A prevention activity is an effort to prevent a product orservice failure. Examples include:

C Applicant screeningC Capability studiesC Pilot projectsC Controlled storageC Design reviewsC Procedure writingC Maintenance and repairC Prototype testingC Field testingC Safety reviewsC ForecastingC SurveysC HousekeepingC Time and motion studiesC Job descriptionsC Training and educationC Market analysisC Personnel reviewsC Vendor evaluation and selection



VIII-45 (899)

Other Activities

Preventive and corrective improvement activities alsoinclude topics covered elsewhere in this and otherSections of the Primer. Examples include:

C BenchmarkingC ReengineeringC Kaizen techniquesC Cycle time reductionC Trend analysisC Check sheetsC DFSS techniquesC FMEA/FMECAC Automated controlsC Lean techniquesC Six sigma techniquesC Control plansC Creative prob lem solving tools


VIII. IMPROVEMENT TECHNIQUESQUESTIONS

VIII-49 (900)

8.2. A lowered rejection rate following corrective action:

a. Gives positive indication that one cause of nonconformance hasbeen removed

b. May be unrelated to the corrective actionc. Indicates that the corrective action was directly related to the

problemd. Has no significance

8.6. Modifying or redesigning a product would most likely occur duringwhich two of the PDCA phases?

a. Plan and dob. Check and actc. Do and actd. Plan and act

8.8. When comparing breakthrough achievement with Kaizen techniques,which of the following statements is true?

a. Kaizen techniques provide more rapid improvementb. Breakthrough achievement is generally less expensivec. Breakthrough achievement would be used for low tech productsd. Kaizen techniques are more easily applied at the floor level

Answers: 8.2. b, 8.6. c, 8.8. d



VIII-50 (901)

8.11. The theory of constraints is concerned with the basic measures ofthroughput, inventory, and operational expenses, which can beexpressed as all of the following, EXCEPT:

a. Incoming moneyb. Money on holdc. Money stuck insided. Money going out

8.14. Using a PDCA process to design a customer survey whileimplementing a customer feedback and improvement process is anexample of:

a. The critical path methodb. A customer driven companyc. A PDCA process within a PDCA processd. A reactive versus a proactive approach

8.17. Which of the following actions or techniques is most useful indetermining the original fundamental cause of a product or processnonconformance?

a. Continuous improvementb. Pareto analysisc. Root cause analysisd. Corrective action

Answers: 8.11. b, 8.14. c, 8.17. c



VIII-51 (902)

8.21. What is the best definition of takt time?

a. It is a calculated time element that equals customer demandb. It is the speed at which parts must be manufactured in order to

satisfy demand C. It is the heartbeat of any lean systemd. It is the application of kaizen to continuous flow manufacturing

8.27. Corrective action is complete when:

a. The customer is satisfiedb. The action taken is determined to be effectivec. The quality manager signs off on itd. The production department agrees to the change

8.29. Which of the following is a non-value added activity?

a. Design reviewsb. Vendor assessmentsc. Inventory reductionsd. Receiving inspection

Answers: 8.21. a, 8.27. b, 8.29. d



VIII-52 (903)

8.31. It’s obvious that a corrective action needs follow-up attention whenthe result is unsatisfactory. Which of the following is the best reasonfor corrective action follow-up when the result is very satisfactory?

a. To recognize the corrective action team for their achievementb. To assign the CAT members to the most difficult problems in the

futurec. To make the most of the solution by extending the fix to other

products or servicesd. To develop standardized approaches to solving all future corrective

actions

8.32. Using the DMAIC approach to six sigma improvement, at what stepwould the root causes of defects be identified?

a. Measureb. Controlc. Improved. Analyze

8.35. Lean enterprise may be summarized as:

a. An entire organization involved with improvementb. Implementation of SMED cycle time techniquesc. Poka-yoke techniques in actiond. Ergonomic principles in the workplace

Answers: 8.31. c, 8.32. d, 8.35. a


IX. BASIC STATISTICS

IX-1 (904)

DO NOT PUT YOUR FAITH INWHAT STATISTICS SAY UNTILY O U H A V E C A R E F U L L YCONSIDERED WHAT THEY DONOT SAY.

WILLIAM W. WATT


IX. BASIC STATISTICSCOLLECTING DATA / TYPES OF DATA

IX-2 (905)

Basic Statistics

Basic Statistics is presented in the following topicareas:C Collecting and summarizing dataC Quantitative conceptsC Probability distributions

Collecting and Summarizing Data

Collecting and Summarizing Data is presented in thefollowing topic areas:

C Types of dataC Measurement scalesC Data collection methodsC Data accuracyC Descriptive statisticsC Graphical relationshipsC Graphical distributions



IX-2 (906)

Types of Data

The three types of data are attribute data, variable data,and locational data. Of these three, attribute andvariable data are more widely used.

Attribute Data

Attribute data is discrete. This means that the datavalues can only be integers, for example, 3, 48, or 1029.Counted data or attribute data would be the answer toquestions like “how many,” “how often,” or “what kind.”In some situations, data will only occur as counted data.



IX-3 (907)

Variable Data

Variable data is continuous. This means that the datavalues can be any real number, for example, 1.037, -4.69,or 84.35. Variable data is the answer to questions like“how long,” “what volume,” “how much time,” and “howfar.” This data is generally measured with someinstrument or device.

Variable data is regarded as being better than counteddata. It is more precise and contains more information.For example, one would certainly know much moreabout the climate of an area, if they knew how much itrained each day, rather than how many days it rained.

Locational Data

The third type of data does not fit into either categoryabove. This data is known as locational data, whichsimply answers the question “where.” Charts that utilizelocational data are often called measles charts orconcentration charts.



IX-4 (908)

Data Comparison

Variable AttributeCharacteristics measurable

continuousmay derive fromcounting

countablediscrete units oroccurrencesgood/bad

Types of data lengthvolumetime

no. of defectsno. of defectivesno. of scrap items

Examples width of a door lug nut torquefan belt tension

audit points lostpaint chips per unitdefective lamps

Data examples 1.7 inches32.06 psi10.542 seconds

10 scratches6 rejected parts25 paint runs

A Comparison of Variable and Attribute Data



IX-5 (909)

Family of Numbers

Complex Numbers

Imaginary Numbers Real Numbers

Rational Numbers Irrational Numbers

Integers

Whole Numbers

Natural Numbers

Prime Numbers



IX-6 (910)

Mathematical Definitions

Denominator The divisor in a fraction.Exponent A symbol indicating the raising to a

power. In 23, 3 is the exponent.Factors Numbers used in multiplication, e.g. 8

(factor) x 6 (factor) = 48 (product).Inequality An expression that contains a sign:

=/ < > >_ etc.Irrationalnumber

A number that is not the quotient of twointegers, e.g. .

Numerator In 3/4, the numerator is 3.Pi (B) Ratio of the circumference of a circle to

its diameter. B is approximately 3.1416.Primenumber

Any number that cannot be obtained bymultiplying smaller whole numbers, e.g.are: 2, 3, 5, 7, 11, 13

Rationalnumber

A number that is the quotient of twointegers.

Reciprocal Two numbers are reciprocals if theirproduct is 1. 3/4 x 4/3 = 1

Scientificnotation

A number which is the product of anumber between 1 and 10 and a powerof 10. 7.1 X 106 is 7,100,000.


IX. BASIC STATISTICSCOLLECTING DATA / MEASUREMENT SCALES

IX-7 (911)

Measurement Scales

Level Description ExampleNominal Data consists of names

or categories only. Noordering scheme ispossible.

A bag of candycontained the followingcolors: Brown 17,Yellow 11, Red 10, Tan6, Orange 5, Green 7

Ordinal Data is arranged in someorder but differencesbetween values cannotbe determined or aremeaningless.

Product defects aretabulated as follows:A 16, B 32, C 42, D 30,where, A defects aremore critical than D.

Interval Data is arranged in orderand differences can befound. However, there isno inherent starting pointa n d r a t i o s a r emeaningless.

The temperatures ofthree aluminum ingotswere 200°F, 400°F and600°F. Note, that threetimes 200°F is not thesame as 600°F.

Ratio An extension of theinterval level thatincludes an inherent zerostarting point. Bothdifferences and ratiosare meaningful.

Product A costs $300and product B costs$600. Note, that $600is twice as much as$300.


IX. BASIC STATISTICSCOLLECTING DATA / MEASUREMENT SCALES

IX-8 (912)

Measurement Scales (Continued)

Level CentralLocation

Dispersion Significance Tests

Nominal Mode InformationOnly

Chi-square

Ordinal Median Percentages Sign or Run Test

Interval ArithmeticMean

Standard orAverageDeviation

t testF test

CorrelationAnalysis

Ratio Geometricor Harmonic

Mean

PercentVariation

(many intervalmeasures are useful

for ratio data)

Statistical Measures for Measurement Levels


IX. BASIC STATISTICSCOLLECTING DATA / DATA COLLECTION METHODS

IX-9 (913)

Data Collection Methods

To ensure that the collected data is relevant to theproblem, some prior thought must be given. Manualdata collection requires a data form. Some datacollection guidelines are:

C Formulate a clear statement of the problemC Define precisely what is to be measuredC List all the important characteristics to be measuredC Carefully select the right measurement techniqueC Construct an uncomplicated data formC Decide who will collect the dataC Arrange for an appropriate sampling methodC Decide who will analyze and interpret the resultsC Decide who will report the results



IX-10 (914)

Automatic Measurement

Computer controlled measurement systems may offerdistinct advantages over their human counterparts.(Improved test quality, shorter inspection times, loweroperating costs, automatic report generation, improvedaccuracy, and automatic calibration). Automatedmeasurement systems have the capacity and speed tobe used in high volume operations.

Automated systems have the disadvantages of higherinitial costs, and a lack of mobility and flexibilitycompared to humans. Automated systems may requiretechnical malfunction diagnostics. When used properly,they can be a powerful tool to aid in the improvement ofproduct quality.



IX-10 (915)

Automatic Measurement (Continued)

Applications for automatic measurement and digitalvision systems are quite extensive. The followingincomplete list is intended to show examples:

C Error proofing a process C Avoiding human boredom and errorsC Sorting acceptable from defective partsC Detecting flaws, surface defects, or foreign materialC Creating CAD drawings from an objectC Building prototypes by duplicating a modelC Making dimensional measurementsC Performing high speed inspectionsC Machining, using laser or mechanical methodsC Marking and identifying partsC Inspecting solder joints on circuit boardsC Verifying and inspecting packagingC Providing bar code recognitionC Identifying missing componentsC Controlling motionC Assembling componentsC Verifying color



IX-11 (916)

Data Coding

The efficiency of data entry and analysis is frequentlyimproved by data coding.

Coding by adding or subtracting a constant or bymultiplying or dividing by a factor:

Let the subscript, lowercase c, represents a codedstatistic; the absence of a subscript represents rawdata; uppercase C indicates a constant; and lowercasef represents a factor. Then:

Coding by substitution: Consider a dimensionalinspection procedure in which the specification isnominal plus and minus 1.25". The measurementresolution is 1/8 of an inch and inspectors, using a ruler,record plus and minus deviations from nominal.

Coding by truncation of repetitive place values:Measurements such as 0.55303, 0.55310, 0.55308, inwhich the digits 0.553 repeat in all observations, can berecorded as the last two digits expressed as integers.


IX. BASIC STATISTICSCOLLECTING DATA / DATA ACCURACY

IX-12 (917)

Data Accuracy

Bad data is costly to capture and corrupts the decisionmaking process. Data accuracy and integrity techniquesinclude:

C Avoid emotional bias relative to targets ortolerances when measuring or recording data.

C Avoid unnecessary rounding.

C If data occurs in time sequence, record it in order.

C If an item characteristic changes over time, recordthe measurement as soon as possible and againafter a stabilization period.

C To apply statistics which assume a normalpopulation, determine if the data can be representedby at least 8 to 10 resolution increments. If not, thedefault statistic may be the count of observations.

C Screen data to detect and remove data entry errors.

C Use objective statistical tests to identify outliers.

C Each important classification identification shouldbe recorded along with the data.


IX. BASIC STATISTICSCOLLECTING DATA / DESCRIPTIVE STATISTICS

IX-13 (918)

Descriptive Statistics

Numerical descriptive measures create a mental pictureof a set of data. These measures which are calculatedfrom a sample are numerical descriptive measures,called statistics. When these measures describe apopulation, they are called parameters. The two mostimportant measures are measures of central tendencyand measures of dispersion.



IX-13 (919)

Measures of Central Tendency

The Mean (X-bar, )

The mean is the sum total of all data values divided bythe number of data points.

X6 is the meanX represents each number3 means summationn is the sample size

The arithmetic mean is the most widely used measure ofcentral tendency.



IX-14 (920)

MEAN = MEDIAN = MODE

Measures of Central Tendency (Cont.)

The Mode

The mode is the most frequently occurring number in adata set. It is possible for groups of data to have morethan one mode.

The Median (Midpoint)

The median is the middle value when the data isarranged in ascending or descending order. For aneven set of data, the median is the average of the middletwo values.

For a Normal Distribution For a Skewed Distribution

Comparison of Central Tendency ina Normal and a Right Skewed Distribution



IX-16 (921)

The Central Limit Theorem

If a random variable, X, has mean µ, and finite varianceF2, as n increases, X6 approaches a normal distributionwith mean µ and variance . Where, and n isthe number of observations on which each mean isbased.

Distributions of Individuals Versus Means



IX-16 (922)

The Central Limit Theorem States:

C The sample means X6 i will be more normallydistributed around : than individual readings Xj.The distribution of sample means approachesnormal regardless of the shape of the parentpopulation. This is why X6 - R control charts work!

C The spread in sample means X6 i is less than Xj withthe standard deviation of X6 i equal to the standarddeviation of the population (individuals) divided bythe square root of the sample size. SX6 is referred toas the standard error of the mean:

Example: Assume the following are weight variationresults: X6 = 20 grams and F = 0.124 grams. Estimate FX6for a sample size of 4:

Solution:



IX-17 (923)

Population Distribution Population Distribution Population Distribution Population Distribution

Sampling Distribution of X Sampling Distribution of X Sampling Distribution of X Sampling Distribution of X

n = 2

n = 4

n = 2

n = 25

n = 4

n = 2

n = 25

n = 4

n = 2

n = 25

n = 4

n = 2

n = 25

Illustration of Central Tendency

The significance of the central limit theorem on controlcharts is that the distribution of sample meansapproaches a normal distribution.



IX-18 (924)

Measures of Dispersion

Other than central tendency, the other importantparameter to describe a set of data is spread ordispersion. Three main measures of dispersion will bereviewed: range, variance, and standard deviation.

Range (R)

The range of a set of data is the difference between thelargest and smallest values.

Example: Find the range of the following data:

5 3 7 9 8 5 4 5 8

Answer: 9 - 3 = 6

Variance (F2, s2)

The variance, F2 or s2, is equal to the sum of the squareddeviations from the mean, divided by the sample size.The formula for variance is:

The variance is equal to the standard deviation squared.



IX-18 (925)

Measures of Dispersion (Continued)

Standard Deviation (F, s)

The standard deviation is the square root of thevariance.

Note: N is used for a population, and n - 1 for a sample(to remove bias in small samples - less than 30)

Coefficient of Variation (COV)

The coefficient of variation equals the standarddeviation divided by the mean and is expressed as apercentage.



IX-19 (926)

Other Ways to Get Standard Deviation

The long and short cut methods of determining standarddeviation are illustrated in the Primer. No one usesthese techniques these days. The student should befamiliar with determining standard deviation using astatistical calculator or variable control chartinformation.



IX-20 (927)

Determine and s Using a Calculator

Formerly this Primer attempted to instruct the studenton how to determine X6 and standard deviation on aSharp calculator. However, many varieties of TexasInstrument, Casio, Hewlett Packard, and Sharpcalculators can accomplish this task. The functions onall of these calculators are subject to change. Mosttechnical people determine the mean and dispersion fora set of data using a calculator. The following generalprocedures apply:

1. Turn on the calculator. Put it in statistical mode.

2. Enter all observation values following the modelinstructions.

3. Determine the sample mean ( ).

4. Determine the population standard deviation F, orthe sample standard deviation, s.



IX-21 (928)

Standard Deviation from Control Charts

Standard deviation can be estimated from control chartsusing R6. This technique is discussed in Section X ofthis Primer, and relates to the determination of processcapability.

The control chart method of estimating standarddeviation makes the big assumption that the processbeing charted is in control and many processes aren’t.Using a calculator or software program to determine sfrom individual data is often more accurate.



IX-21 (929)

Tchebysheff's Theorem

Given a number, K, which is greater or equal to 1 and forany set of n measurements, at least (1-1/K2) of themeasurements will lie within K standard deviations oftheir mean. Tchebysheff's theorem applies to any set ofmeasurements. The distribution need not be normal.

If the mean and standard deviation of a sample of 25measurements are 75 and 10 respectively:

C At least 3/4 of the measurements will lie in theinterval ± 2S = 75 ± 20.

C At least 8/9 of the measurements will lie in theinterval ± 3S = 75 ± 30.

The theorem is very conservative because it applies toall distributions. In most situations, the fraction ofmeasurements falling in the specified interval willexceed 1 - 1/K2.



IX-22 (930)

Days a Defect Report is Open2 4 6 8 10 12 14 16 18 20 22 24

0

1

2

3

4

5

6

2

5

1112

15

8

65

Days a Defect Report is Open

0

2

4

6

8

10

12

14

16

3 6 9 12 15 18 21 24

Selected Distributions

Shown below are various ways to display distributions.

A Simple Ungrouped Distribution

A Grouped Frequency Polygon (Histogram)



IX-23 (931)

86

76

59

38

9398

100

75

50

25

40

30

20

10

A B C D E F G

CATEGORIES

Cumulative Line

Selected Distributions (Continued)

A Simple Pie Chart

A Grouped Column Chart


IX. BASIC STATISTICSCOLLECTING DATA / GRAPHICAL RELATIONSHIPS

IX-24 (932)

Graphical Methods

The average human brain is not good at comparingmore than a few numbers at a time. Therefore, a largeamount of data is often difficult to analyze, unless it ispresented in some easily digested format. Graphs,charts, histograms, tallies and Pareto diagrams are usedto analyze and present data. Graphical methods arescattered throughout the CQE Primer. Only a fewexamples are shown here.



IX-24 (933)

Boxplots

The boxplots technique is credited to John W. Tukey.The data median is a line dividing the box. The upperand lower quartiles define the ends of the box. Theminimum and maximum are drawn as points at the endof lines (whiskers) extending from the box.

Boxplots can be notched to indicate variability of themedian. Boxplots can have variable widths proportionalto the log of the sample size. Outliers are identified aspoints (asterisks).

Simple Boxplot Complex Boxplots



IX-25 (934)

02468

101214

Frequency

41# 43# 45# 47# 49# 51# 53#

Strength

Stem and Leaf Plots

The stem and leaf diagram consists of grouping the databy class intervals, as stems, and the smaller dataincrements as leaves.

Example: Shear Strength, 50 observations given in thePrimer.

Shear Strength Histogram



IX-26 (935)

52

53869 87091688591

5146449668 6212408644

Leaf 2 48245068302Stem 0123456789012

4444444444555

Stem and Leaf Plots (Continued)

Example: Show the previous data in a stem and leafdiagram.

Shear Strength Stem and Leaf Plot



IX-27 (936)

Value of $ Stage Corrective Action$<1 Infant mortality Additional screening or burn-in$=1 Random failure Failure are inherent

$>1 and <4 Early wearout Perform preventative maintenance$>4 Old age wearout Requires design changes to improve

100001000

999590807060504030

20

10

5

3 2

1

Cycles to Failure

Cum

ulat

ive

Per

cent

%

Shape 1.667Correlation 0.998

Weibull Probability Plot

The Weibull distribution can be used for a variety ofapplications. The Weibull distribution can begraphically represented on chart paper.

The graph indicates that $ = 1.667. This indicates thatthe slide has entered the period of early wearout. Thescale, characteristic life, 0, is the point at which 63.2% ofthe slides have failed (at 9,421 cycles).



IX-29 (937)

Probability Density Function

The probability density function, f(x), describes thebehavior of a random variable. The area under theprobability density function must equal one.

Histogram with Overlaid Model

For continuous distributions with f(x) >_ 0:

For discrete distributions for all values of n with f(x) >_ 0:

150

155

160

165

170

175

180

185

190

195

200

205

210

215

220

225

230

235

240

245

2500

20

40

60

80

100

Length

Freq

uenc

y



IX-30 (938)

155 159 163 167 171 175 179 183 187 191 195 199 203 207 211 215 219 223 227 231 235 239 2430.000

0.005

0.010

0.015

0.020

0.025

0.030

Length

155 159 163 167 171 175 179 183 187 191 195 199 203 207 211 215 219 223 227 231 235 239 2430.000

0.200

0.400

0.600

0.800

1.000

Length

Cumulative Distribution Function

The cumulative distribution function, F(x), denotes thearea beneath the probability density function to the leftof x.

The cumulative distribution function is equal to theintegral of the probability density function to the left ofx.



IX-30 (939)

Normal Probability Plots

A normal probability plot places observed data valueson the vertical axis and plots them with theircorresponding values from a standard normal table onthe horizontal axis. The purpose of this activity is todetermine if the data follows a normal, or near normal,distribution. The steps used in constructing a normalprobability plot are:

1. Place the values in the data set in ascending order2. Find the corresponding standardized normal values3. Plot the matching values on a two dimensional chart4. Evaluate the resulting chart for normalcy

In finding the standardized normal values, a standardnormal or Z table is used. The first value is the Z valuebelow which the proportion 1/(n+1) of the area under thenormal curve is found. This procedure continues untilthe nth (and largest) Z value is obtained, using thecalculation n/(n+1).



IX-31 (940)

Normal Probability Plots (Continued)

To illustrate the Z value determinations for variousdistributions of data, refer to the Table below. This ishypothetical data.

Class Test Scores Corresponding Z valuesA B C D

48 47 47 38 - 1.6552 54 48 41 - 1.2855 58 50 44 - 1.0457 61 51 47 - 0.8458 64 52 50 - 0.6760 66 53 53 - 0.5261 68 53 56 - 0.3962 71 54 59 - 0.2564 73 55 62 - 0.1365 74 56 65 0.0066 75 57 68 0.1368 76 59 71 0.2569 77 62 74 0.3970 77 64 77 0.5272 78 66 80 0.6773 79 69 83 0.8475 80 72 86 1.0478 82 76 89 1.2882 83 83 92 1.65

CQE Test Scores and Corresponding Z Values



IX-32 (941)

Z Value-1.8 -1.4 -1 -0.6 -0.2 0.2 0.6 1 1.4 1.8

30

40

50

60

70

80

90

Normaldistribution

Z Value-1.8 -1.4 -1 -0.6 -0.2 0.2 0.6 1 1.4 1.8

30

40

50

60

70

80

90

Positive skeweddistribution

Z Value-1.8 -1.4 -1 -0.6 -0.2 0.2 0.6 1 1.4 1.8

30

40

50

60

70

80

90

Negative skeweddistribution

Z Value-1.8 -1.4 -1 -0.6 -0.2 0.2 0.6 1 1.4 1.8

30

40

50

60

70

80

90

100

Rectangulardistribution

Normal Probability Plots (Continued)

The data sets for classes A, B, C, and D were organizedto respectively represent normal, negative skewed (tailpointed left), positive skewed, and rectangulardistributions. The corresponding probability plots areshown below.


IX. BASIC STATISTICSQUANTITATIVE CONCEPTS / TERMINOLOGY

IX-33 (942)

Quantitative Concepts

Quantitative Concepts is presented in the followingtopic areas:

C TerminologyC Drawing statistical conclusionsC Probability terms and concepts

Statistical Terminology

Continuousdistribution

A distribution containing infinite(variable) data points that may bedisplayed on a continuous measurementscale. Examples: normal, exponential,and Weibull distributions.

Discretedistribution

A distribution resulting from countable(attribute) data that has a finite number ofpossible values. Examples: binomial,Po isson , and hypergeometr icdistributions.



IX-33 (943)

Statistical Terminology (Continued)

Expectedvalue

The mean, :, of a probability distributionis the expected value, E(x), of its randomvariable.

Parameter The true numeric population value, oftenunknown, estimated by a statistic.

Population All possible observations of similar itemsfrom which a sample is drawn.

Statistic A numerical data value taken from asample that may be used to make aninference about a population.



IX-34 (944)

Expected Value

Bernoulli stated that the “Expected value equals thesum of the values of each of a number of outcomesmultiplied by the probability of each outcome relative toall the other possibilities.”

If E represents the expected value operator and Vrepresents the variance operator, such that:

If x is a random variable and c is aconstant, then:

1. E(c) = c

2. E(x) =

3. E(cx) = cE(x) = c

4. V(c) = 0

5. V(x) =

6. V(cx) =


IX. BASIC STATISTICSQUANTITATIVE CONCEPTS / STATISTICAL CONCLUSIONS

IX-35 (945)

Enumerative Statistics

Enumerative data is data that can be counted. Usefultools for tests of hypothesis conducted on enumerativedata are the chi-square, binomial, and Poissondistributions.

Deming (1986) defined a contrast between enumerationand analysis:

Enumerative study A study in which action will betaken on the universe.

Analytic study A study in which action will betaken on a process to improveperformance in the future.



IX-35 (946)

Robustness

A statistical procedure is considered robust when it canbe used even when the basic assumptions are violatedto a moderate degree. The normal distribution isexplained by two facts:

C The central limit theorem shows the standard errorof sample means from any continuous datadistribution to be approximately normal.

C A number of commonly used statistical proceduresare robust to deviations from theoretical normalcy.

Tests of means such as the t test and ANOVA are ratherinsensitive to the normality assumption. ANOVAassumes the means are normally distributed andvariances equal.

Variance: Whether normal or not, the mean value of s2

is F2. If the population is normal, the variance of s2 is:

When not normal, the variance of s2 is:



IX-37 (947)

Conditions for Probability

The probability of any event (E) lies between 0 and 1.The sum of the probabilities of all possible events (E) ina sample space (S) = 1.

Simple Events

An event that cannot be decomposed is a simple event(E). The set of all sample points for an experiment iscalled the sample space (S).

If an experiment is repeated a large number of times, (N),and the event (E) is observed nE times, the probability ofE is approximately:



IX-38 (948)

Compound Events

Compound events are formed by a composition of twoor more events. They consist of more than one point inthe sample space. EA = A and EB = B.

I. Composition.

A. Union of A and B - If A and B are two events in asample space (S), the union of A and B (A c B)contains all sample points in event A or B or both.

B. Intersection of A and B - If A and B are two eventsin a sample space (S), the intersection of A and B(A 1 B) is composed of all sample points that arein both A and B.

Venn Diagrams of Union and Intersection



IX-39 (949)

Compound Events (Continued)

II. Event Relationships.

A. Complement of an Event - The complement of anevent A is all sample points in the sample space(S), but not in A. The complement of A is 1-PA.

Example: If PA (cloudy days) is 0.3, the complement of Awould be 1 - PA = 0.7 (clear).

B. Conditional Probabilities - The conditionalprobability of event A given that B has occurredis:



IX-39 (950)


Example: If event A (rain) = 0.2, and event B(cloudiness) = 0.3, what is the probability of rain on acloudy day? (Note that it will not rain without clouds)

Two events A and B are said to be independent if either:

P(A|B) = P(A) or P(B|A) = P(B)

However for this example:

P(A|B) = 0.67 and P(A) = 0.2= no equality, andP(B|A) = 1.00 and P(B) = 0.3 = no equality

Therefore, the events are said to be dependent.



IX-40 (951)


C. Mutually Exclusive Events - If event A contains nosample points in common with event B, then theyare said to be mutually exclusive.

D. Testing for Event Relationships

Example: Refer to the data on page 38.

Event A: E1, E2, E3 Event B: E1, E3, E5

Are A and B, mutually exclusive, complementary,independent or dependent? A and B contain twosample points in common so they are not mutuallyexclusive. They are not complementary because B doesnot contain all points in S that are not in A.

By definition, events A and B are dependent.



IX-41 (952)

The Additive Law

If the two events are not mutually exclusive:

1. P (A c B) = P(A) + P(B) - P (A 1 B)

Note that P (A c B) is shown in many texts as P (A + B)and is read as the probability of A or B.

Example: If one owns two cars and the probability ofeach car starting on a cold morning is 0.7, what is theprobability of getting to work?

P (A c B) = 0.7 + 0.7 - (0.7 x 0.7)= 1.4 - 0.49= 0.91 = 91 %



IX-41 (953)

The Additive Law (Continued)

If the two events are mutually exclusive:

2. P (A c B) = P(A) + P(B) also P (A + B) = P(A) + P(B)

Example: If the probability of finding a black sock in adark room is 0.4 and the probability of finding a bluesock is 0.3, what is the chance of finding a blue or blacksock?

P (A c B) = 0.4 + 0.3 = 0.7 = 70 %



IX-42 (954)

( ) ( )( ) ( ) ( ) ( )P A B

P A|B = and P A B = P A|B P BP B∩

∩

( ) 30 29 870P A B = x = = 0.088 100 99 9900

∩

The Multiplicative Law

If events A and B are dependent, the probability of Ainfluences the probability of B. This is known asconditional probability and the sample space is reduced.

For any two events A and B such that P(B) =/ 0:

1.

Note in some texts P (A 1 B) is shown as P(A C B) and isread as the probability of A and B. P(B|A) is read as theprobability of B given that A has occurred.

Example: If a shipment of 100 T.V. sets contains 30defective units and two samples are obtained, what isprobability of finding both defective?

P(A 1 B) = 8.8 %



IX-42 (955)

The Multiplicative Law (Continued)

If events A and B are independent:

2. P (A 1 B) = P(A) X P(B)

Example: One relay in an electric circuit has aprobability of working equal to 0.9. Another relay inseries has a chance of 0.8. What's the probability thatthe circuit will work?

P (A 1 B) = 0.9 X 0.8 = 0.72P (A 1 B) = 72 %



IX-43 (956)

Permutations

An ordered arrangement of n distinct objects is called apermutation. The number of ways of ordering n distinctobjects taken r at a time are designated by the symbols:

Pnr or P(n,r) or nPr

Counting Rule for Permutations

The number of ways that n distinct objects can bearranged taking them r at a time is:

Note: 0! = 1

Example: Three lottery numbers are drawn from a totalof 50. How many arrangements can be expected?



IX-44 (957)

Combinations

The number of distinct combinations of n distinctobjects taken r at a time are denoted by the symbols:

Cnr, or nCr, or C(n,r), or (n

r)

Counting Rule for Combinations

The number of different combinations that can beformed from n distinct objects taken r at a time is:

Example: A set of gages contains 81 blocks. How many3 stack combinations exist?

Example: In the question above, how many 4 stackcombinations exist?


IX. BASIC STATISTICSPROBABILITY DISTRIBUTIONS / CONTINUOUS DISTRIBUTIONS

IX-46 (958)

Probability Distributions are presented in the followingtopic areas:

C Continuous DistributionsC Discrete DistributionsC Sampling Distributions

Common Continuous Distributions

Normal (Gaussian)

: = MeanF = Standard deviatione = 2.718



IX-47 (959)

Common Continuous Distributions (Cont.)

Exponential

or

: = 2 = MeanX = X axis reading8 = failure rate

Weibull

0 = 1$=1/2

$=1

0 = Scale parameter$ = Shape parameter $=3( = Location parameter



IX-47 (960)

Normal Distribution

When a sample of several random measurements areaveraged, distribution of such repeated sampleaverages tends to be normally distributed regardless ofthe distribution of the measurements being averaged.Mathematically, if:

the distribution of X6s becomes normal as n increases.If the set of samples being averaged have the samemean and variance then the mean of the X6s is equal tothe mean (:) of the individual measurements, and thevariance of the X6s is:



IX-47 (961)

-3 -2 -1 0 1 2 30.0

0.1

0.2

0.3

0.4

X

Prob

abili

ty D

ensi

tyNormal Distribution (Continued)

The normal probability density function is:

Where : is the mean and F is the standard deviation.

The Standard Normal Probability Density Function

2121( ) ,

2

x

f x e xμ

σ

σ

−⎛ ⎞− ⎜ ⎟⎝ ⎠= −∞ < < ∞

Π



IX-48 (962)

(a + x)(2a)

0 if x<-a

CDF(x) = if -a x +a

1 if x>+a

⎧ ⎫⎪ ⎪⎪ ⎪⎨ ⎬⎪ ⎪⎪ ⎪⎩ ⎭

≤ ≤

1(2a)

0 if x<-a

PDF(x) = if -a x +a

0 if x>+a

⎧ ⎫⎪ ⎪⎪ ⎪⎨ ⎬⎪ ⎪⎪ ⎪⎩ ⎭

≤ ≤

as = 3

Uniform Distribution

A uniform distribution is also called a rectangulardistribution and may be either continuous or discrete.

Probability Density Function

Cumulative Density Function

The continuous uniform distribution is used when onlythe variation limits are known and the probability isconstant. For a discrete uniform distribution:



IX-49 (963)

Bivariate Normal Distribution

The joint distribution of two variables is called abivariate distribution. Bivariate distributions may bediscrete or continuous. There may be totalindependence of the two independent variables, or theremay be a covariance between them.

The bivariate normal density is:

:1 and :2 are the two meansF1 and F2 are the two variances and are each > 0D is the correlation coefficient

Bivariate Normal Distribution Surface



IX-50 (964)

X

Prob

abili

ty D

ensi

tyExponential Distribution

The exponential distribution is used to model items witha constant failure rate. If a random variable, x, isexponentially distributed, 1/x follows a Poissondistribution. The exponential probability densityfunction is:

8 is the failure rate and 2 is the meanIt can be seen that 8 = 1/2.

Exponential Probability Density Function

The variance of the exponential distribution is:



IX-51 (965)

21 lnx21f(x) e , x 0

x 2

−μ⎛ ⎞− ⎜ ⎟σ⎝ ⎠= >σ Π

X

Prob

abili

ty D

ensi

ty

σ = 2

σ = 1

σ = 0.25

σ = 0.5

Lognormal Distribution

The most common transformation is made by taking thenatural logarithm, but any base logarithm, also yields anapproximate normal distribution. The natural logarithmdenoted as “ln”.

The standard lognormal probability density function is:

: is the location parameter. F is the scale parameter.

Lognormal Probability Density Function



IX-53 (966)

Weibull Distribution

The Weibull distribution is one of the most widely useddistributions in reliability and statistical applications.Common versions are the two parameter and threeparameter. The three parameter Weibull has a locationparameter when there is some non-zero time to firstfailure.

The three parameter Weibull probability densityfunction:

$ is the shape parameter2 is the scale parameter* is the location parameter

The three parameter Weibull distribution can also beexpressed as:

$ is the shape parameter0 is the scale parameter( is the non-zero location parameter



IX-54 (967)

0 50 100 150 2000.000

0.005

0.010

0.015

0.020

0.025

X

Prob

abili

ty D

ensi

ty

β = 0.8

β = 1

β = 6

β = 2

β = 3.6

0 50 100 150 2000.000

0.005

0.010

0.015

0.020

X

Prob

abili

ty D

ensi

ty

β = 1θ = 50

β = 2.5θ = 50

β = 2.5θ = 100

β = 1θ = 100


Effect of ShapeParameter, $with 2 = 100and * = 0

Effect of ScaleParameter



IX-55 (968)


Effect ofLocationParameter

The mean of the Weibull distribution is:

The variance of the Weibull distribution is:

The variance of the Weibull distribution decreases asthe value of the shape parameter increases. The gamma' value comes from a gamma function table.

0 50 100 1500.000

0.005

0.010

0.015

X

Prob

abili

ty D

ensi

ty

δ = 0δ = 30



IX-56 (969)

( )

( )/ 2 1 x /2

/2x ef(x) , x 02 / 2

ν − −

ν= >Γ ν

0 5 10 15 200.00

0.10

0.20

0.30

0.40

X

Prob

abili

ty D

ensi

ty

ν=1ν=2

ν=5

ν=10

2 2 2 21 2 3 ny = z + z + z + ... + z

Chi-Square Distribution

The chi-square distribution is formed by summing thesquares of standard normal random variables. Forexample, if z is a standard normal random variable, thenthe following is a chi-square random variable with ndegrees of freedom.

The chi-square probability density function where < isthe degrees of freedom, and '(x) is the gamma functionis:

Chi-square Probability Density Function



IX-57 (970)

1

2

X /FY /

ν=

ν

( )

1

1

1 2

/ 21 2

/2 12

/21 2 1

2

2 xf(x) , x 0x12 2

ν

ν −

ν +ν

⎛ ⎞⎛ ⎞⎛ ⎞ν + ν ν⎛ ⎞ ⎜ ⎟⎜ ⎟Γ⎜ ⎟⎜ ⎟ν⎝ ⎠ ⎜ ⎟⎜ ⎟⎝ ⎠= >⎜ ⎟⎜ ⎟ν ν⎛ ⎞ ⎛ ⎞ ⎛ ⎞νΓ Γ ⎜ ⎟⎜ ⎟⎜ ⎟ ⎜ ⎟ +⎜ ⎟⎜ ⎟ ⎜ ⎟⎝ ⎠ ⎝ ⎠ ν⎝ ⎠⎝ ⎠ ⎝ ⎠

F Distribution

If X is a chi-square random variable with <1, degrees offreedom and Y is a chi-square random variable with <2degrees of freedom and if X and Y are independent, thenthe following is an F distribution with <1 and <2 degreesof freedom:

The F distribution is used extensively to test for equalityof variances from two normal populations.

The F probability density function is:



IX-58 (971)

0 0.5 1 1.5 2 2.5 30.00

0.20

0.40

0.60

0.80

1.00

X

Prob

abili

ty D

ensi

ty

v1=1, v2=1v1=1, v2=10

v1=10, v2=1

v1=15, v2=15

F Distribution (Continued)

F Probability Density Function

Most texts only give one tail, and require the other tail tobe computed using the expression:

Example: Given F0.05 with <1 = 8 and <2 = 10 is 3.07, findthe value of F0.95 with <1 = 10 and <2 = 8.



IX-59 (972)

2

zt = Χν

( )( )

- ( + 1)/22 + 1 / 2 xf(x) = 1 + , - < x < /2

ντ ν ⎛ ⎞

∞ ∞⎜ ⎟ντ ν πν ⎝ ⎠

-4 -2 0 2 40.00

0.10

0.20

0.30

0.40

X

Prob

abili

ty D

ensi

ty

ν=1

ν=3

ν=10Standard Normal

Student’s t Distribution

If z is a standard normal random variable, and P2 is a chi-square random variable with < degrees of freedom, thena random variable with a t-distribution is:

The t probability density function with < degrees offreedom is:

t Probability Density Function



IX-60 (973)

2 = 0 = , 3- 2ν

μ σ ν ≥ν

Student’s t-Distribution (Continued)

The mean and variance of the t-distribution are:

From a random sample of n items, the probability that:

falls between any two specified values is equal to thearea under the t-probability density function between thecorresponding values on the x-axis with n-1 degrees offreedom.

Example: The burst strength of 15 randomly selectedseals has a mean of 495.13 and a sample standarddeviation of 8.467. What is the probability that the burststrength of the population is greater than 500? The areaunder the t probability density function, with 14 degreesof freedom, to the left of -2.227 is 0.0214.


IX. BASIC STATISTICSPROBABILITY DISTRIBUTIONS / DISCRETE DISTRIBUTIONS

IX-61 (974)

r

p=0.1

p=0.3p=0.5

n=30p=0.1

p=0.3p=0.5

n=30

r

p=0.1

p=0.3

p=0.5

n=30p=0.1

p=0.3

p=0.5

n=30

r

p=0.1p=0.3

p=0.5

N=60n=30p=0.1

p=0.5

N=60n=30

Common Discrete Distributions

Poisson

n = sample sizer = number of occurrencesp = probabilitynp6 = : = average

Binomial

n = sample sizer = number of occurrencesp = probabilityq = 1 - p

Hypergeometric

n = sample sizer = number of occurrencesd = occurrences in populationN = population size



IX-62 (975)

Binomial Probability Distribution

The binomial distribution applies when the population islarge (N > 50) and the sample size is small compared tothe population. Generally, n is less than 10% of N. It ismost appropriate to use when proportion defective isequal to or greater than (0.1).

Example: A random sample of 10 units is taken from asteady stream of product. Past experience has shown10% defective parts. Find the probability of exactly onebad part.

n = 10 r = 1 p = 0.1

Solve for 2 bad parts (Answer = 19.37%).Solve for 0 bad parts (Answer = 34.87%)



IX-63 (976)

Binomial Probability Distribution (Cont.)

Example: A continuous process averaged 6%defectives. In a sample of 300 units, 22 defective unitswere found. What is the expected sample average and3 sigma variation?

n = 300 p = 22/300 = 0.073 1 - p = 0.927

Sigma =

Limits = p ± 3S = 0.073 ± 0.045 = 0.028 and 0.118



IX-64 (977)

Poisson Probability Distribution

The Poisson distribution can be used to model defectcounts and an approximation to the binomial, whenp <_ 0.1 and the sample size is fairly large.

Example: A continuous process is running a 2%defective rate. What is the probability that a 100 piecesample will contain exactly 2 defectives?

: = np6 = (100)(0.02) = 2, r = 2

Solve for r = 0 Answer 0.135 (13.5%)Solve for r = 1 Answer 0.27 (27%)Solve for r = 3 Answer 0.18 (18%)

The Poisson distribution average and sigma are:



IX-66 (978)

Hypergeometric Probability Distribution

The hypergeometric distribution applies when thepopulation is small compared to the sample size.Sampling is done without replacement.

Example: From a group of 20 products, 10 are selectedat random. What is the probability that the 10 selectedcontain the 5 best units?

N = 20, n = 10, d = 5, (N-d) = 15 and r = 5



IX-67 (979)

Multinomial Distribution

Let events E1, E2, ... Ek occur with probabilitiesp1, p2, ... pk respectively. Then, the probability thatthose events will occur n1, n2, ... nk times respectively is:

N = n1 + n2 + ... + nk and p1 + p2 + ... + pk = 1

The multinomial distribution is a generalization of thebinomial distribution. It is the general term in themultinomial expansion (p1 + p2 + ... + pk)N.

Example: An inspection of units over time reveals fourdefective causes A, B, C, and good quality G.Historically, pA=0.03, pB = 0.05, pC =0.06 and pG =0.86. Ifa sample of 170 units was drawn from the population,what would be the probability of: nA=9, nB=7, nC=16 andnG=138?

P(A=9, B=7, C=16, G=138) =


IX. BASIC STATISTICSQUESTIONS

IX-69 (980)

9.2. Which of the following statements is NOT true regarding a probabilitydensity function?

a. f(x) must be greater than, or equal to, zero for all values of xb. The integral of f(x) over all x is equal to 1, if f(x) represents a

continuous distributionc. The sum of f(x) over all values of x is equal to 1, if f(x) represents a

discrete distributiond. The cumulative distribution function is the probability of being

greater than 0 and less than x

9.5. Which of the following distributions does NOT require the use of thenatural logarithmic base for probability calculations?

a. Normalb. Poissonc. Weibulld. Binomial

9.8. The hypergeometric distribution is:

a. A continuous distributionb. Used to describe sampling from a finite population without

replacementc. The limiting distribution of the sum of several independent discrete

random variablesd. A special case of the Poisson distribution

Answers: 9.2. d, 9.5. d, 9.8. b



IX-70 (981)

9.10. What is the most widespread use of the F distribution?

a. To model discrete data when the population size is small comparedto the sample size

b. To test for equality of variances from two normal populationsc. To compensate for error in the estimated standard deviation for small

sample sizesd. To construct confidence intervals by summing the squares of random

variables

9.13. Calculate the standard deviation of the following complete set ofdata:

52, 20, 24, 31, 35, 42

a. 10.8b. 11.8c. 12.8d. 13.8

9.14. The equation for joint probability of two fault events under anycircumstance is given by:

If event A does not enhance occurrence of event B in any way, theprobability of occurrence, when P(A) = 0.1, P(B) = 0.05, is given by:

a. 0.00025b. 0.10000c. 0.05000d. 0.00500

Answers: 9.10. b, 9.13. a, 9.14. d

P(A B) = P(A|B) x P(B)∩



IX-71 (982)

9.19. A set of measurements is arranged in order of magnitude with afrequency associated with each measurement. This action describes:

a. A grouped frequency distributionb. A cumulative frequency distributionc. An ungrouped frequency distributiond. A histogram

9.24. When performing calculations on sample data:

a. The cumulative relative frequency graph that is often used is calleda histogram

b. Rounding the data has no effect on the mean and standard deviationc. Coding the data has no effect on the mean and standard deviationd. Coding and rounding affect both the mean and standard deviation

9.28. The distribution of a characteristic is negatively skewed. Thesampling distribution of the mean for large samples is:

a. Negatively skewedb. Approximately normalc. Positively skewedd. Lognormal

Answers: 9.19. c, 9.24. d, 9.28. b



IX-72 (983)

9.31. Defining the sample space S as rock, book, cigar, guitar, dog, whatis the complement of cigar, dog?

a. rock, book, cigar, guitar, dogb. cigar, guitar, dogc. dogd. rock, book, guitar

9.32. The hypergeometric distribution should be used instead of thebinomial distribution when:

a. There are more than 2 outcomes on a single trialb. Each trial is independentc. Sampling does not involve replacementd. There is a fixed number of trials

9.34. A sample of n observations has a mean X-bar and standard deviationSx > 0. If a single observation, which equals the value of the samplemean X-bar is removed from the sample, which of the following istrue?

a. X6 and Sx both changeb. X6 and Sx remain the samec. X6 remains the same but Sx increasesd. X6 remains the same but Sx decreases

Answers: 9.31. d, 9.32. c, 9.34. c


X. STATISTICAL APPLICATIONS

X-1 (984)

A STATE OF STATISTICALCONTROL IS NOT A NATURALSTATE FOR A MANUFACTURINGPROCESS. IT IS INSTEAD ANACHIEVEMENT, ARRIVED AT BYELIMINATING ONE BY ONE, BYDETERMINED EFFORT, THESPECIAL CAUSES OF EXCESSIVEVARIATION.

W. EDWARDS DEMING


X. STATISTICAL APPLICATIONSSPC / OBJECTIVES AND BENEFITS

X-2 (985)

Statistical Applications

Statistical Applications are reviewed in two topicareas:

C Statistical process controlC Process and performance capability

Statistical Process Control (SPC)

Statistical Process Control (SPC) is presented in thefollowing topic areas:

C Objectives and benefitsC Common and special causesC Selection of variableC Rational subgroupingC Control chartsC Control chart analysisC Pre-control chartsC Short-run SPC


X. STATISTICAL APPLICATIONSSPC / OBJECTIVES AND BENEFITS

X-2 (986)

Objectives and Benefits

Statistical process control (SPC) is a technique forapplying statistical analysis to measure, monitor, andcontrol processes. The major component of SPC is theuse of control charting methods. The basic assumptionmade in SPC is that all processes are subject tovariation. This variation may be classified as one of twotypes, chance cause variation and assignable causevariation. When assignable cause variation does occur,the statistical analysis facilitates identification of thesource so it can be eliminated.

Statistical process control also provides the ability todetermine process capability, monitor processes, andidentify whether the process is operating as expected,or whether the process has changed and correctiveaction is required.


X. STATISTICAL APPLICATIONSSPC / COMMON AND SPECIAL CAUSES

X-4 (987)

Common and Special Causes

An important consideration, on the road to processimprovement, is the differentiation between special andcommon causes. Refer to the Figure on the left. Whenthe circled special (bad) events occur, most of theavailable company resources converge on the process,fix the problem, and then go back to sleep.

A process improvement team is required to investigatethe reasons for the multitudes of chance causes, and torecommend an improved system. The resultingperformance chart might look like the figure on the right.It appears that the process has been improved, and it isboth better and sustainable at the lower rate.


X. STATISTICAL APPLICATIONSSPC / COMMON AND SPECIAL CAUSES

X-5 (988)

Common and Special Causes (Continued)One of the best ways to illustrate what happens when a stablesystem is inappropriately adjusted is the Nelson funnel. Amoveable funnel is placed over a grid and a ball is droppedthrough the funnel creating a “mark.”

LIFEEXAMPLES

C WORKERSTWEAKING THEMACHINE

C MANAGERSTAMPERING WITHWORKERPERFORMANCE

LIFE LIFEEXAMPLES EXAMPLES

C US TAX C WORKER TRAINING POLICY WORKER

C SOME C USING PAINT CORPORATE MATCHES FROM“ RIGHT SIZING” PRIOR RUN

C SOME CORPORATE CULTURES


X. STATISTICAL APPLICATIONSSPC / SELECTION OF VARIABLE

X-7 (989)

Selection of Variable

Given the benefits of control charting, one might betempted to control chart every characteristic or processvariable. The risk of charting many parameters is thatthe operator will spend so much time and effortcompleting the charts, that the actual process becomessecondary.

Some considerations for the selection of a control chartvariable include:

C Items that protect human safetyC Items that protect the environment or community C Items that are running at a high defective rateC Key process variables that impact the productC Major sources of customer complaintsC Items that show adherence to applicable standardsC Items that are requested by key customersC Variables that have caused processing difficultiesC Variables that can be measured by the operatorC Items that can be counted by the person chartingC Items that contribute to high internal costsC Variables that help control the process


X. STATISTICAL APPLICATIONSSPC / SELECTION OF VARIABLE

X-7 (990)

Selection of Variable (Continued)

In an ideal case, one process variable is so critical thatit is indicative of the process as a whole. Key processinput variables (KPIVs) may be analyzed to determinethe degree of their effect on a process. Key processoutput variables (KPOVs) are ideal for determiningprocess capability and for process monitoring usingcontrol charts.


X. STATISTICAL APPLICATIONSSPC / RATIONAL SUBGROUPING

X-8 (991)

Rational Subgrouping

A control chart provides a statistical test to determine ifthe variation from sample-to-sample is consistent withthe average variation within the sample. The key idea inthe Shewhart control chart is the division ofobservations into what are called rational subgroups.The success of charting depends in large measure onthe selection of these subgroups.

Generally, subgroups are selected in a way that makeseach subgroup as homogeneous as possible, and thatgives the maximum opportunity for variation from onesubgroup to another.

In production control charting, it is very important tomaintain the order of production.



X-8 (992)

Rational Subgrouping (Continued)

Where order of production is used as a basis forsubgrouping, two fundamentally different approachesare possible:

C The first subgroup consists of product produced asnearly as possible at one time. This method followsthe rule for selection of rational subgroups bypermitting a minimum chance for variation within asubgroup and a maximum chance for variation fromsubgroup to subgroup.

C Another subgroup option consists of productintended to be representative of all the productionover a given period of time. Product may accumulateat the point of production, with a random samplechosen from all the product made since the lastsample.

The choice of subgroup size should be influenced, inpart, by the desirability of permitting a minimum chancefor variation within a subgroup.



X-9 (993)

Sources of Variability

Much of the discussion of process capability willconcentrate on the analysis of sources of variability. Itis therefore worthwhile to consider the possible sourcesof variation in a manufactured product.



X-10 (994)

Breakdown of Variation


X. STATISTICAL APPLICATIONSSPC / CONTROL CHARTS

X-11 (995)

Control Charts

Control charts are the most powerful tools to analyzevariation in most processes - either manufacturing oradministrative. Control charts were originated by WalterShewhart (1931). A process which is in statisticalcontrol is characterized by plot points that do notexceed the upper or lower control limits. When aprocess is in control, it is predictable. There are manyvariations of possible control charts. The two primarytypes are variables and attributes.



X-11 (996)

Control Charts for Variables

Plots specific measurements of a process characteristic(temperature, size, weight, sales volume, shipments,etc.).

Types

C X6 - R charts (when data is readily available)C Run charts (limited single point data)C MX6 - MR charts (moving average/moving range)C X - MR charts (or I - MR charts) (limited data)C X6 - s charts (when sigma is readily available)C Median chartsC CuSum charts (cumulative sum)C Moving averageC EWMA charts (exponentially weighted moving

average)

Charts for variables are costly since each measuredvariable must have data gathered and analyzed. This isalso the reason they are the most valuable and useful.



X-11 (997)

Control Charts for Attributes

Control charts for attributes plot a general measurementof the total process (the number of complaints per order,number of orders on time, absenteeism frequency,number of errors per letter, etc.).

Types

C p charts (fraction defective)C np charts (number of defectives)C c charts (number of defects)C u charts (number of defects per unit)

In some cases, the relatively larger sample sizesassociated with attribute charts can prove to beexpensive. There are short run varieties of these fourtypes.



X-12 (998)

and R Chart Terms

n Sample size (subgroup size)

X A reading (the data)

Average of readings in a sample

Average of all the s. It is the value of thecentral line on the chart.

R The range. The difference between the largestand smallest value in each sample.

Average of all the Rs. It is the value of thecentral line on the R chart.

UCL Upper and lower control limits. The controlLCL boundaries for 99.73 % of the population. They

are not specification limits.



X-12 (999)

XAverage

RRange

1 5 10 15 20 25 30

1 5 10 15 20 25 30

20.5

20.0

19.5

19.0

18.5

18.0

17.5

UCLX = 20.0

X = 18.9

LCLX = 17.8

UCLR = 4.0

R = 1.9

LCLR = 1.9

4.54.03.5

3.02.52.01.51.00.5

0

Typical - R Control Chart



X-13 (1000)

- R Charts Control Limits

- R Charts Factors

n A2 D3 D4 d2

2 1.88 0 3.27 1.133 1.02 0 2.57 1.694 0.73 0 2.28 2.065 0.58 0 2.11 2.336 0.48 0 2.00 2.53



X-15 (1001)

- R Control Charts



X-16 (1002)

X-Bar and Sigma Charts

X-bar ( ) and sigma (S) charts are often used forincreased sensitivity to variation (especially when largersample sizes are used). These charts may be moredifficult to work with manually than the - R charts dueto the tedious calculation of the sample standarddeviation (S). Often, S comes from automated processequipment so the charting process is much easier.

The control limit for the average chart formulas are:

The control limits for the sigma (S) chart are calculatedusing the following formulas and table:

is the average sample standard deviation and is thecenterline of the sigma chart.



X-16 (1003)

Sigma Chart Factors

n 2 3 4 5 6 7 8 9 10 25B4 3.27 2.57 2.27 2.09 1.97 1.88 1.82 1.76 1.72 1.44B3 * * * * 0.03 0.12 0.18 0.24 0.28 0.56A3 2.66 1.95 1.63 1.43 1.29 1.18 1.10 1.03 0.98 0.61

*The lower control limit for a sigma chart when (n) isless than 6 is zero.



X-17 (1004)

4

sˆ = C

σ

Capability from X-S Charts

The estimated standard deviation, called sigma hat, canbe calculated by:

If both and S charts are in control, and the individualmeasurements are normally distributed, processcapability can be assessed.

n 2 3 4 5 6 7 8 9 10C4 0.798 0.886 0.921 0.940 0.952 0.959 0.965 0.969 0.973



X-17 (1005)

Median Control Charts

There are several varieties of median control charts.One type plots only the individual measured data on asingle chart. The middle value is circled. Median chartsmay use an odd number of readings to make the medianvalue more obvious.

Another variety records the data and plots the medianvalue and range on two separate charts. Minimalcalculations are needed for each subgroup. The controllimits for the median chart are calculated using the sameformulas as the - R chart:

The values are somewhat different than the A 2 valuesfor the - R chart since the median is less efficient andtherefore exhibits more variation.

n 2 3 4 5 6 1.88 1.19 0.80 0.69 0.55



X-17 (1006)

Median Control Charts (Continued)

The range factors (D3 and D4) and process standarddeviation factor (d2) are the same as used for the - Rchart. The specific advantages of a median chart are:

C It is easy to use and requires fewer calculationsC It shows the process variationC It shows both the median and the spread



X-18 (1007)

MX6-MR Charts

MX6-MR (moving average-moving range) charts are usedwhere data is less readily available. An example forn = 3 is shown below. Control limits are calculatedusing the X6-R formulas and factors.



X-20 (1008)

X-MR Charts

Control charts plotting individual data points on onegraph and a moving range on another (similar to X-bar-R) are the most common and most applicable charts forcalibration and testing. Usually single data aremeasured for each required point.

The X-MR chart (for individuals and moving ranges) isthe only control chart which may have specificationlimits shown. However, there are some drawbacks inthe interpretation and use of X-MR charts:

C All interpretation is faulty if the data is not normal

C X-MR charts do not separate piece to piecerepeatability of the process

C Averages and limits can have wide variability until 80-100 readings are taken

C X-MR charts are not as sensitive to process changesas the X6-R chart



X-20 (1009)

X-MR Charts (Continued)

The control limits for the X-MR charts are calculatedusing the formulas and factor table below.

n 2 3 4 5D4 3.27 2.57 2.28 2.11D3 0 0 0 0E2 2.66 1.77 1.46 1.29

The control limits for the range chart are calculatedexactly as for the X6-R chart.



X-21 (1010)

DateTime

Product NameVariable

ProcessSpecification Limit

Chart No.Units of Measure

Operator

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25

1

45

SampleMeasurements

Range, RNotes

23

Apple StrudelT85, High 88, Low 82

7 youGrams

80

90

85

95

75

5

10

15

0

868785 77 83 84 87 90 84 89 82 84 86 88 85 90 83 84 87 872 6 3 63 2 2 31

860 9 1 5 7 2 5 17 3 0

X = 85.4MR = 3.4

UCL=11.1

MR = 3.4LCL = 0

LCL = 76.4

X = 85.4

UCL = 94.4

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25

Stick WeightsLine A

Measurement, X

4/16/03

Mea

sure

men

tR

ange

X - MR Chart Example



X-22 (1011)

CuSum Control ChartsCumulative sum (CuSum) control charts have beenshown to be more efficient in detecting small shifts inthe mean of a process than Shewhart charts. They arebetter to detect 2 sigma or less shifts in the mean.

To create a CuSum chart, collect m sample groups, eachof size n, and compute the mean of each sample.Determine Sm or S'm from the following equations:

Where :0 is the estimate of the in-control mean and F X6is the known (or estimated) standard deviation of thesample means. The CuSum control chart is formed byplotting Sm or S'm as a function of m. If the processremains in control, centered at :0, the CuSum plot willshow variation in a random pattern centered about zero.

A visual procedure proposed by Barnard, known as theV-Mask, may be used to determine whether a process isout of control. A V-Mask is an overlay V shape that issuperimposed on the graph of the cumulative sums.

As long as all the previous points lie between the sidesof the V, the process is in control.



X-22 (1012)

CuSum Control Charts (Continued)

The behavior of the V-Mask is determined by thedistance k (which is the slope of the lower arm) and therise distance h. Note that we could also specify d andthe vertex angle (or, as is more common in the literature,q = 1/2 the vertex angle).

For an alpha and beta design approach, we mustspecify:

C ", the probability of concluding that a shift in theprocess has occurred, when in fact it did not.

C $, the probability of not detecting that a shift in theprocess mean has, in fact, occurred.

C * (delta), the detection level for a shift in theprocess mean, expressed as a multiple of thestandard deviation of the data points.

Assume a process has an estimated mean of 5.000 withh set at 2 and k at 0.5. As h and k are set to smallervalues, the V-Mask becomes sensitive to smallerchanges in the process average. Consider the following16 data points, each of which is average of 4 samples(m=16, n=4).



X-23 (1013)

CuSum Control Charts (Continued)

The CuSum control chart with 16 data groups andshows the process to be in control.

If data collection is continued until there are 20 datapoints (m=20, n=4), the CuSum control chart shows theprocess shifted upward, as indicated by data points 16,17 and 18 below the lower arm of the V-Mask.



X-25 (1014)

Moving Average

Past data may be summarized by computing the meanof successive sets of data. Single moving average is amethod of smoothing the data and is then used as anestimate of future values. Single moving average is:

X are individual data values, t is the current time period,and N is the moving group size

Moving average is best used when the process mean isstable, but is a poor predictor when the process exhibitstrends.

Single Moving Average with N = 3



X-26 (1015)

Exponentially Weighted MovingAverage (EWMA)

The exponentially weighted moving average (EWMA) isa statistic for monitoring a process by averaging thedata in a way that gives less and less weight to data asthey are further removed in time.

By the choice of a weighting factor, 8, the EWMA controlprocedure can be made sensitive to a small or gradualdrift in the process. The statistic that is calculated is:

EWMA t = 8 Y t + ( 1- 8 ) EWMA t-1 for t = 1, 2, ..., n

C EWMA 0 is the mean of historical data (target) C Y t is the observation at time t C n is the number of observations to be monitored,

including EWMA 0 C 0 < 8 # 1 is a constant that determines the depth of

memory of the EWMA

The parameter, 8 determines the rate at which “older”data enters into the calculation of the EWMA statistic.A large value of 8 gives more weight to recent data anda small value of 8 gives more weight to older data. Thevalue of 8 is usually set between 0.2 and 0.3 althoughthis choice is somewhat arbitrary.



X-26 (1016)

EWMA (Continued)

The estimated variance of the EWMA statistic isapproximately:

when t is not small, and where s is the standarddeviation calculated from the historical data.

The center line for the control chart is the target value orEWMA 0 . The control limitsare:

UCL = EWMA 0 + ks EWMALCL = EWMA 0 - ks EWMA

Where the factor k is either set equal to 3 or chosenusing the Lucas and Saccucci tables. The data areassumed to be independent and these tables alsoassume a normal population.



X-27 (1017)

EWMA (Continued)

Example: Parameters calculated from historical data:

EWMA 0 = 50, s = 2.0539, and 8 = 0.3UCL = 50 + 3 (0.4201)(2.0539) = 52.5884LCL = 50 - 3 (0.4201) (2.0539) = 47.4115

EWMA Plot of Example Data

The process is in control however, there seems to be atrend upwards for the last 5 sample periods.

The EWMA is often superior to the CuSum chartingtechnique for detecting “larger” shifts.



X-29 (1018)

Attribute ChartsAn attribute chart plots characteristics. Attributes arediscrete, counted data. Unlike variables charts, only onechart is plotted for attributes. There are four types ofattribute charts, as summarized below:

Chart Records Subgroup sizep Fraction Defective Varies

np Number of Defectives Constantc Number of Defects Constantu Number of defects per unit Varies

100p* Percent Defectives Varies

The best use of an attribute chart is to:

C Follow trends and cyclesC Evaluate any change in the process

* The p chart reflected in percentage.



X-29 (1019)

Attribute Charts (Continued)Key points to consider when using attribute charts:

C Normally the subgroup size is greater than 50 (for pcharts).

C The average number of defects/defectives is equalto or greater than 4 or 5.

C If the actual p chart subgroup size varies by morethan ± 20 % from the average subgroup size, thedata point must either be discarded or the controllimits calculated for the individual point.

C The most sensitive attribute chart is the p chart.The most sensitive and expensive chart is the - R.

C The defects and defectives plotted in attributecharts are often categorized in Pareto fashion todetermine the vital few. To actually reduce thedefect or defective level, a fundamental change inthe system is often necessary.



X-30 (1020)

Attribute Chart FormulasDefectives (Binomial Distribution)

p Chart%Defectives

np ChartDefectives

k = number of samples

Defects (Poisson Distribution)

u ChartAverage Number of Defects

c ChartNumber of Defects

k = number of samples

Sample Size Varies Sample Size Fixed



X-32 (1021)

p Chart Example

Note the change at plot point 15.



X-34 (1022)

p np c u

: 0

2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 251

10

7 3

0

4

2

8

14

12

10

6

Attributes Control Chart Form

100 Units Fixed

9 6 3 4 6 3 3 4 4 6 4 5 2 3 2 8 4 3 2 3 4 8 6

1925

UCL = 10.7np

LCL = 0np

np = 4.5

Any DefectiveYou

SPC ChecklistDESCRIPTION:

AVERAGE:

CHARACTERISTIC: DATE:OPERATOR: INSPECTOR:SOURCE:

UCL

PART

Sample

(np,c)

(n)

Date/Time

Notes

%(p,u)

Number

Fraction

: 9/25 - 10/1

LCL:Binding Department

Encyclopedia

np Chart Example



X-36 (1023)

p np c u

Sample

Number(np,c)

(n)

Fraction

Date/Time

Notes

%(p,u)

2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 251

One Fixed Standard Sample

ShiftChange

101

5 8 7 5 7 3 3 4 2 2 3 3 2 3 1 9 6 7 7 4 7 1 6 5 4

0

4

2

8

14

12

10

6

UCL = 11

LCL = 0

Attributes Control Chart Form

c = 4.6

: 0You

SPC ChecklistDESCRIPTION:

AVERAGE:

CHARACTERISTIC: DATE:OPERATOR: INSPECTOR:SOURCE:

UCL

PART :

LCL:

Defects 10/1 Binding Department

Encyclopedia

c Chart Example

Is the shift between plot points 15 and 16 significant?



X-37 (1024)

Out-of-controlIf a process is “out-of-control,” then special causes ofvariation are present in either the average chart or rangechart, or both. These special causes must be found andeliminated in order to achieve an in-control process. Aprocess out-of-control is detected on a control charteither by having any points outside the control limits orby unnatural patterns of variability.

± 1S = 68.26 %

± 2S = 95.46 %

± 3S = 99.73 %

Upper Control Limit

Grand Average

Lower Control Limit



X-37 (1025)

Out-of-control (Continued)Because there are two components to every controlchart -- the average chart and the range chart -- fourpossible conditions could occur in the process.

1. Average Out-of-ControlRange In-Control

2. Average In-Control ProcessRange Out-of-Control Out-of-Control

3. Average Out-of ControlRange Out-of-Control

4. Average In-Control ProcessRange In-Control In-Control



X-38 (1026)

1. Average Out-of-controlAverage ShiftingVariation Stable

2. Variation Out-of-controlAverage StableVariation Changing



X-39 (1027)

3. Average & Variation Out-of-controlAverage ShiftingVariation Changing

4. Process In-controlAverage StableVariation Stable



X-40 (1028)

Control Chart InterpretationFive Common Rules

Other Unusual Patterns



X-41 (1029)

Process In-control with Chance Variation

This is an example of a process which is in-control. Notice that it looksgood, but not too good.



X-41 (1030)

Trends

CHART CAUSESX R CHART CAUSES

C Deterioration of machineC Tired operatorC Tool wear

C Change in operator skillC Tired operatorC Change in incoming material quality

CORRECTIVE ACTION

C Repair or use alternate machine if availableC Discuss operation with operator to find causeC Rotate operatorC Change, repair, or sharpen toolC Investigate material



X-42 (1031)

Jumps in Process Level

CHART CAUSES R CHART CAUSESX

C Changes in proportions of materialscoming from different sources

C New operator or machineC Modification of production method or

processC Change in inspection device or

method

C Change in materialC Change in methodC Change in operatorC Change in inspection

CORRECTIVE ACTION

C Keep material supply consistentC Investigate source of materialC Check out machine capabilityC Examine operator methods and instructionC Check calibration of measurement device



X-42 (1032)

Recurring Cycles


C Physical environmentC TemperatureC Humidity

C Tired operatorC Regular rotation of machine or operator

C Scheduled maintenanceC Tired operatorC Tool wear

CORRECTIVE ACTION

C If environment is controllable, adjust itC Service equipmentC Rotate operatorsC Evaluate machine maintenanceC Replace, sharpen, or repair tool



X-43 (1033)

Points Near or Outside Limits


C Over controlC Large systematic differences in

material qualityC Large systematic differences in

test methods or equipment

C Mixture of material ofdistinctly different quality

CORRECTIVE ACTION

C Check control limitsC Investigate material variationC Evaluate test proceduresC Evaluate inspection frequency or methodsC Eliminate operator over adjustment of the process



X-43 (1034)

Lack of Variability


C Incorrect calculation of controllimits

C Improvement in process sincelimits were calculated

C Employee may not be makingchecks

C Collecting in eachsample a number ofmeasurements from widely differing lots

C Improvement inprocess since limitswere calculated

CORRECTIVE ACTION

C Check control limitsC Validate rational sample subgroupingsC Verify checking procedure, gages, etc.C Verify proper employee measurementC Congratulate someone for improvement



X-44 (1035)

Runs Test for RandomnessA run is a sequence of data that exhibit the samecharacteristic. The subject of time sequence analysiscan apply to both variable and attribute data.

To perform a runs test the following sequence should befollowed:

1. Determine the value of n1 and n 2 (either the totalof two attributes or the readings above and belowthe center line on a run or control chart).

2. Determine the number of runs (R).

3. Consult a critical value table or calculate a teststatistic (Refer to the non-parametric runs test).



X-44 (1036)

Critical Value Table for Number of RunsConsult the Critical Value Table below for the expectednumbers of runs. Note that the expected number ofruns can be approximated by adding the smallest andlargest values together and dividing by two.

n 1 +n 2Plotted Points

Smallest Run Limit

Average# Runs

Largest Run Limit

8 1 5 9 (not possible)10 2 6 1012 3 7 1114 3 8 1316 4 9 1418 5 10 1520 6 11 1622 7 12 1724 7 13 1926 8 14 2028 9 15 2130 10 16 2234 11 18 2540 14 21 2850 20 26 32



X-45 (1037)

5 10 15 20 24

11

8

5

6

7

9

10

Runs Test Example

For the 24 plot points, one should expect between 8 and18 total runs. Since there are 5 runs, one can say with95% confidence that non-random variation exists.


X. STATISTICAL APPLICATIONSSPC / PRE-CONTROL CHARTS

X-46 (1038)

The Pre-Control TechniqueAn easy method of controlling the process average is known as“pre-control.” Pre-control was developed in 1954 by a group ofconsultants (including Dorin Shainin) in an attempt to replacethe control chart. Pre-control is most successful withprocesses which are inherently stable and not subject to rapidprocess drifts once they are set up. Pre-control cannot only actas a guide in setting process aim, but can also be used tomonitor the continuing process.

The idea behind pre-control is to divide the total tolerance intozones. The two boundaries within the tolerance are called pre-control lines. The location of these lines is halfway between thecenter of the specification and specification limits. It can beshown that 86 % of the parts will be inside the P-C lines with 7% in each of the outer sections, if the process is normallydistributed and the Cpk = 1. Usually, the process will occupymuch less of the tolerance range, so this extreme case will notapply.



X-46 (1039)

A Pre-Control Schematic

The chance that two parts in a row will fall outside either P-Cline is 1/7 (0.14) times 1/7 (0.14), or 1/49. This means that onlyonce in every 49 pieces can one expect to get two pieces in arow outside the P-C lines just due to chance. There is a muchgreater chance (48/49) that the process has shifted.



X-47 (1040)

Pre-Control RulesC Set-up: The job is OK to run if five pieces in a row are inside

the target

C Running: Sample two consecutive pieces:

C If the first piece is within target, run (don’t measure thesecond piece)

C If the first piece is not within target, check the secondpiece

C If the second piece is within target, continue to run

C If both pieces are out of target, adjust the process, go backto set up

C Any time a reading is out-of-specification, stop and adjust

The ideal frequency of sampling is 25 checks until a reset isrequired. Sampling can be relaxed if the process does not needadjustment in greater than 25 checks. Sampling must beincreased if the opposite is true. To make pre-control eveneasier to use, gauges for the target area may be painted green.Yellow is used for the outer zones and red for out-of-specification.



X-47 (1041)

Pre-Control AdvantagesThe advantages of pre-control include:

C Shifts in process centering or increases in process spreadcan be detected

C The % non-conforming product will not exceed apre-determined level

C No recording, calculating or plotting is required

C Attribute or visual characteristics can be used

C Can serve as a set-up plan for short runs

C The specification tolerance is used directly

C Very simple instructions are needed for operators



X-47 (1042)

Pre-Control DisadvantagesThe disadvantages of pre-control include:

C There is no permanent paper record of adjustments

C Subtle changes in process capability cannot be calculated

C It will not work for an unstable process

C It will not work effectively if the process spread exceedsthe tolerance


X. STATISTICAL APPLICATIONSSPC / SHORT-RUN SPC

X-48 (1043)

Short Run SPC

Most traditional SPC techniques require long,reasonably stable production runs. Short run chartingmay be desirable when the production lot size isextremely small (10-20) pieces or when the sample size,under typical operating conditions, is small. Two limiteddata charts have already been discussed:

X - MR ChartsM - MR Charts

Various techniques have been suggested by a numberof authors. However, the recommendations of some arenot without controversy. The emphasis has been onshort runs and multiple variables per chart, as this isincreasingly the greatest need in an era ofcustomization.

An example is illustrated in the Primer.


X. STATISTICAL APPLICATIONSCAPABILITY / CAPABILITY STUDIES

X-53 (1044)

Process and Performance Capability

Process and Performance Capability is presented inthe following topic areas:

C Capability studiesC Performance vs. specificationsC Capability indicesC Performance indices



X-53 (1045)

Process Capability Studies

The determination of process capability requires apredictable pattern of statistically stable behavior. Acapable process is a process whose spread on the bell-shaped curve is narrower than the tolerance range orspecification limits. USL is the upper specification limitand LSL is the lower specification limit.

A process capability study includes three steps:

C Planning for data collectionC Collecting dataC Plotting and analyzing the results



X-54 (1046)

Process Capability Studies (Continued)

The objective of process quality control is to establisha state of control over the manufacturing process andthen maintain that state of control through time. Whenthe natural process limits are compared with thespecification range, any of the following possiblecourses of action may result:

C Do nothing. If the process limits fall well within thespecification limits, no action may be required.

C Change the specifications. The specification limitsmay be unrealistic.

C Center the process. An adjustment to the centeringof the process may bring the bulk of the productwithin specifications.

C Reduce variability. This is often the most difficultoption to achieve.

C Accept the losses. In some cases, managementmust be content with a high loss rate.



X-54 (1047)

Process Capability Studies (Continued)

Other capability applications:

C Provide set-up-data for a variables control chartC Evaluate new equipmentC Review tolerances based on process variationC Assign more capable equipment to tougher jobsC Perform routine process performance auditsC Determine the effects of adjustments

(Juran, 1999)



X-55 (1048)

Machine Capability

Machine capability is a measure of the inherent bestshort-term capability of a machine or process. Thecalculations for machine capability are exactly asdiscussed previously for process capability with a fewexceptions:

C Historical data from a control chart should not beused. Other forms of variation may be included inthis data.

C If multiple machines are producing the same part,then the capability of each machine should bedetermined independently.

C Machine capability should come from consecutivepart measurements from the same machine at ornear the same time (perhaps 20 to 40 parts).



X-55 (1049)

Machine Capability (Continued)

What normally results from a machine capability studyis:

What a machine capability study is trying to determineis the inherent process (machine) variation by excludingelements like batch-to batch, stream-to-stream, andtime-to-time variation and trying to minimize themeasurement factors (operator and equipment), piece-to-piece variation, and within piece variation. This cannever truly be achieved, but can be approximated.



X-56 (1050)

Process Performance vs. Specifications

In the figure below, one can see that the control limitsare determined by process average values. One canalso see the process spread of the individual values.This process spread can be predicted, and will indicatethe range of the individuals being produced.

If the R-bar is known from a control chart, then:


X. STATISTICAL APPLICATIONSCAPABILITY / PERFORMANCE VS. SPECIFICATION

X-57 (1051)

Calculating Performance vs. Specification

All processes are not centered. For this reason, thecustomer may want to know the Cpk, since thiscalculation takes centerness into account.

Aim



X-58 (1052)

68.26%

95.46%

99.73%:-3F :-2F :-1F : :+1F :+2F :+3F

The Normal Distribution

When all special causes of variation are eliminated,many variable data processes, when sampled andplotted, produce a bell-shaped distribution. If the baseof the histogram is divided into six (6) equal lengths(three on each side of the average), the amount of datain each interval exhibits the following percentages:



X-58 (1053)

The Z Value

The area outside of specification for a normal curve canbe determined by a Z value.

The Z transformation formula is:

Where: x = Data value (The value of concern) : = Mean

F = Standard deviation

This transformation will convert the original values tothe number of standard deviations away from the mean.The result allows one to use a standard normal table.



X-60 (1054)

Z Value Examples

To illustrate the z value, consider the followingexamples of typical 10th grade student weights. Theweights are normally distributed with a mean : = 150 lbsand standard deviation F = 20.



X-60 (1055)

0 1

.1587

Z Value Examples (Continued)

Example: What is the probability of a student weighingmore than 170 lbs.?

P(z=1 to + ∞) = 0.1587. 15.87 % of the students willweigh more than 170 lbs.



X-61 (1056)

150100


Example: What is the probability of a student weighingless than 100 lbs.?

Since the normal table has values about the mean, a Zvalue of - 2.5 can be treated as 2.5.

P(z = - ∞ to -2.5) = 0.0062. That is, 0.62 % of the studentswill weigh less than 100 lbs.



X-61 (1057)

150 160120


Example: What is the probability a student weighingbetween 120 and 160 lbs?

The best technique to solve this problem using thestandard normal table in this Primer would be todetermine the tail area values, and to subtract them fromthe total probability of 1.



X-62 (1058)

.3085

150 160

.0668

120 150


Example (Continued). First, determine the z value andprobability below 120 lbs.

P(z = - ∞ to -1.5) = 0.0668

Second, determine the z value and probability above 160lbs.

P(z = 0.5 to + ∞) = 0.3085



X-62 (1059)


Example (Continued)

Third, the total probability - below - above = probabilitybetween 120 and 160 lbs.

1 - 0.0668 - 0.3085 = 0.6247

Thus, 62.47 % of the students will weigh more than 120lbs., but less than 160 lbs.



X-63 (1060)

Process Capability from Control Charts

Process capability (using Z value determinations) can begenerated from a control chart as shown on Primer pageX - 63.


X. STATISTICAL APPLICATIONSCAPABILITY / CAPABILITY INDICES

X-64 (1061)

Capability Index Failure Rates

There is a direct link between the calculated Cp (and Ppvalues) with the standard normal (Z value) table. A Cp of1.0 is the loss suffered at a Z value of 3.0 (doubled, sincethe table is one sided). Refer to the table below.

CpZ

value ppm

0.33 1.00 317,3110.67 2.00 45,5001.00 3.00 2,7001.10 3.30 9671.20 3.60 3181.30 3.90 961.33 4.00 631.40 4.20 271.50 4.50 6.81.60 4.80 1.61.67 5.00 0.571.80 5.40 0.0672.00 6.00 0.002



X-64 (1062)

Capability Index Failure Rates (Continued)

In the prior table, ppm equals parts per million ofnonconformance (or failure) when the process:

C Is centered on C Has a two-tailed specificationC Is normally distributedC Has no significant shifts in average or dispersion

When the Cp, Cpk, Pp, and Ppk values are 1.0 or less, Zvalues and the standard normal table can be used todetermine failure rates. With the drive for increasinglydependable products, there is a need for failure rates inthe Cp range of 1.5 to 2.0.



X-65 (1063)

Process Capability Indices

To determine process capability an estimation of sigmais necessary:

FR is an estimate of process capability sigma and comesfrom a control chart.



X-65 (1064)

Process Capability Indices (Continued)

The capability index is defined as:

As a rule of thumb:

The capability ratio is defined as:

As a rule of thumb:



X-66 (1065)

Process Capability Indices (Continued)

Cpk is the ratio giving the smallest answer between:

Example: For a process with = 12, FR = 2 an USL = 16and LSL = 4, determine Cp and Cpk min:



X-66 (1066)

Cpm Index

The Cpm index is defined as:

Where: USL = Upper specification limit LSL = Lower specification limit

: = process mean T = target value F = process standard deviation

Cpm is based on the Taguchi index, which places moreemphasis on process centering on the target.


X. STATISTICAL APPLICATIONSCAPABILITY / PERFORMANCE INDICES

X-67 (1067)

Cpm Index Exercise

Example: For a process with : = 12, F = 2, T = 10, USL =16 and LSL = 4, determine Cpm:


X. STATISTICAL APPLICATIONSCAPABILITY / PERFORMANCE INDICES

X-67 (1068)

Process Performance Indices

To determine process performance an estimation ofsigma is necessary:

Fi is a measure of total data sigma and generally comesfrom a calculator or computer.

The performance index is defined as:

The performance ratio is defined as:

Ppk is the ratio giving the smallest answer between:


X. STATISTICAL APPLICATIONSQUESTIONS

X-69 (1069)

10.1. Which of the following charts have upper control limits, butfrequently have lower control limits of zero?

a. X-bar and individual chartsb. c charts and u chartsc. p charts and np chartsd. R and sigma charts

10.5. The spread of individual observations from a normal processcapability distribution may be expressed numerically as:

a. 6 /d2b. 2 x A2c. /d2d. D4

10.6. Pre-control starts a process specifically centered between:

a. Process limitsb. Specification limitsc. Normal distribution limitsd. Three sigma control limits

Answers: 10.1. d, 10.5. a, 10.6. b



X-70 (1070)

10.10. An and R chart was prepared for an operation using twentysamples with five pieces in each sample; was found to be 33.6and was 6.20. During production, a sample of five was taken andthe pieces measured 36, 43, 37, 25, and 38. At the time, thissample was taken:

a. Both the average and range were within control limitsb. Neither the average nor range were within control limitsc. Only the average was outside control limitsd. Only the range was outside control limits

10.13. A quality engineer wants to chart the package weights on a highlyautomated food processing line. The recommended control chartis an X-bar - S chart and not the typical X-bar - R chart, in wide usethroughout the facility. The most logical reason for this switch iswhich of the following?

a. The X-bar control limits will be tighterb. The supervisor obviously wants some variety in control chart usagec. Only one control chart will be requiredd. The X-bar and S values will come automatically from a weight

checker

10.14. Select the INCORRECT statement. If the ODs of a certain bushingare normally distributed with a mean of 2.00", then the proportionof bushings with ODs greater than 1.90" is:

a. Greater than the proportion with ODs less than 1.90"b. Greater than the proportion with ODs less than 2.20"c. Greater than 50%d. Greater than the proportion with ODs greater than the median

Answers: 10.10. d, 10.13. d, 10.14. b



X-71 (1071)

10.17. In which one of the following would the use of an and R chart bethe most helpful as a tool to control a process:

a. The machine capability is wider than the specificationb. The machine capability is equal to the specificationc. The machine capability is somewhat smaller than the specificationd. The machine capability is very small compared to the specification

10.18. Given = 51.0, = 4.0, n = 5; assuming statistical control, whatproportion of the population will meet specifications of 50 ± 3.0?

a. 87%b. 88%c. 91%d. 93%

10.20. An and R chart with n=5 has been plotted for some time and hasdemonstrated random variation. Upon review of the last 30 plotpoints, the expected number of runs around the center line on the chart is expected to be approximately which of the following?

a. 4b. 9c. 12d. 16

Answers: 10.17. c, 10.18. a, 10.20. d



X-72 (1072)

10.26. The lengths of a certain bushing are normally distributed withmean . How many standard deviation units symmetrical about will include 80% of the lengths?

a. ±1.04b. ±0.52c. ±1.28d. ±0.84

10.28. One looks at a process and notes that the chart for averages hasbeen in control. If the range suddenly and significantly increases,the mean will:

a. Usually increaseb. Stay the samec. Always decreased. Occasionally show out of control of either limit

10.31. During variable control charting a trend of four consecutive pointsis noted on both the average and range charts. The average chartis increasing and the range chart is decreasing. One may makewhich of the following conclusions?

a. No conclusions may be made yetb. The nominal measurement is increasingc. The variability is decreasingd. The process is improving

Answers: 10.26. c, 10.28. d, 10.31. a


XI. ADVANCED STATISTICS

XI-1 (1073)

MOST PEOPLE WOULD RATHERLIVE WITH A PROBLEM THEYCAN'T SOLVE, THAN ACCEPT ASOLUTION THEY CAN'TUNDERSTAND.

R. E. D. WOOLSEY AND H. S. SWANSON


XI. ADVANCED STATISTICSSTATISTICAL DECISION MAKING

XI-2 (1074)

Advanced Statistics

Advanced Statistics is presented in the following topicareas:

C Statistical decision makingC Analysis of variance (ANOVA)C Relationships between variablesC Design and analysis of experiments

Statistical Decision Making

Statistical Decision Making is presented in thefollowing topic areas:

C Point estimates C Paired-comparison testsC Confidence intervals C Goodness-of-fit testsC Hypothesis testing C Contingency tables


XI. ADVANCED STATISTICSSTATISTICAL DECISION MAKING

XI-2 (1075)

Statistical Inference

The objective of statistical inference is to drawconclusions about population characteristics based onthe information contained in a sample. The stepsinvolved in statistical inference are:

C Precisely define the problem objective

C Formulate a null and an alternate hypothesis

C Decide if the problem will be evaluated by a one-tailor two-tail test

C Select a test distribution and a critical value for thetest statistic

C Calculate a test statistic from the sample

C Make a inference by comparing the calculated andthe critical values

C Report the findings


XI. ADVANCED STATISTICSSTATISTICAL DECISION MAKING / POINT ESTIMATES

XI-3 (1076)

n

ii = 1

X X =

nμ ≈

∑

n

ii = 1

X 28.7 + 27.9 + 29.2 + 26.5 X = = = 28.08 psin 4

μ ≈∑

Point Estimate for Population Mean

In analyzing sample values to arrive at populationprobabilities, two major estimators are used: pointestimates and confidence intervals.

A point estimate of the population mean, μ, is thesample mean, X.

Example: Given the following tensile strength readingsfrom 4 piano wire segments: 28.7, 27.9, 29.2, and 26.5psi, calculate the point estimation of the populationmean.

28.08 psi is the point estimate for the populationmean.


XI. ADVANCED STATISTICSSTATISTICAL DECISION MAKING / POINT ESTIMATES

XI-3 (1077)

( ) ( )

( ) ( )

n n2 2

i i2 2i = 1 i = 1

n n2 2

i ii = 1 i = 1

X - X X - s = =

n - 1 N

X - X X - s = =

n - 1 N

μσ

μσ

∑ ∑

∑ ∑

Point Estimate for Population Variance

The sample variance, s2, is the best point estimate of thepopulation variance, σ2. The sample standard deviation,s, is the best point estimate of the population standarddeviation, σ.


XI. ADVANCED STATISTICSSTATISTICAL DECISION MAKING / CONFIDENCE INTERVALS

XI-4 (1078)

X X/2 /2X - Z X + Z

n nα α

σ σ≤ μ ≤

Confidence Interval for the Mean

Continuous Data - σ Known

The confidence interval of the population mean, μ, whenthe population standard deviation, σ, is known, iscalculated using the sample mean, X, the populationstandard deviation, σ, the sample size, n, and the normaldistribution.

From sample data one can calculate the interval withinwhich the population mean, μ, is predicted to fall.Confidence intervals are always estimated forpopulation parameters. A confidence interval is a two-tail event and requires critical values based on analpha/2 risk in each tail.



XI-4 (1079)

/2, n-1 /2, n-1

s sX - t X + tn n

6 618 - 2.064 18 + 2.06425 25

15.52 20.48

α α≤ μ ≤

≤ μ ≤

≤ μ ≤

/2, n-1 /2, n-1

s sX - t X + tn nα α≤ μ ≤

Continuous Data - σ Unknown

The confidence interval of the population mean, μ, whenthe population standard deviation, σ, is unknown, iscalculated using the sample mean, X, the samplestandard deviation, s, the sample size, n, and the tdistribution.

Example: The average of 25 samples is 18 with asample standard deviation of 6. Calculate the 95%confidence interval for the population mean.



XI-5 (1080)

( ) ( )s s s ss /2 s /2

p 1 - p p 1 - pp - Z p p + Z

n nα α≤ ≤

Confidence Interval for Proportion

For large sample sizes, with np and n(1-p) greater thanor equal to 5, the binomial distribution can beapproximated by the normal distribution to calculate aconfidence interval for population proportion.

ps = sample proportion, p = population proportion, n = sample size



XI-6 (1081)

( ) ( )2 22X X

2 2/2, n - 1 1 - /2, n - 1

n - 1 s n - 1 s α α

≤ σ ≤Χ Χ

( ) ( )2 2X X

2 2/2, n - 1 1 - /2, n - 1

n - 1 s n - 1 s α α

≤ σ ≤Χ Χ

Confidence Interval for Variance

The confidence interval or interval estimate for thepopulation variance, σ2, is given by:

s2 = sample variancen = sample sizen - 1 = degrees of freedom

Confidence Interval for Standard Deviation

The confidence interval for the population standarddeviation, σ, is given by:


XI. ADVANCED STATISTICSSTATISTICAL DECISION MAKING / HYPOTHESIS TESTING

XI-7 (1082)

Hypothesis Testing

Hypothesis testing is a type of statistical inference inwhich a null hypothesis and alternative hypothesis arestated. The null hypothesis is a statement about thevalue of a population parameter such as the mean, andmust contain the condition of equality.

The alternative hypothesis is a statement that must betrue if the null hypothesis is false.

A null hypothesis can only be rejected, or fail to berejected, it cannot be accepted because of a lack ofevidence to reject it.

As an example of hypothesis tests for a populationmean, there are only three possible forms, where μ isthe population mean and μ0 is a specified value:

H0: μ = μ0 H0: μ <_ μ0 H0: μ >_ μ0H1: μ =/ μ0 H1: μ > μ0 H1: μ < μ0



XI-7 (1083)

Hypothesis Testing (Continued)

The steps of hypothesis testing are:

C State the null and alternative hypothesis

C Specify the level of significance, α

C Determine the critical values separating the rejectand nonrejection areas

C Determine the sampling distribution and teststatistic

C Determine if the test statistic is in the reject ornonrejection area

C Conclude if the null hypothesis is rejected or failedto be rejected

C State the statistical decision in terms of the originalproblem



XI-8 (1084)

Types of Errors

When formulating a conclusion regarding a populationbased on observations from a small sample, two typesof errors are possible:

C Type I error: This error results when the nullhypothesis is rejected when it is, in fact, true. Theprobability of making a type I error is called α(alpha) or producer’s risk.

C Type II error: This error results when the nullhypothesis is not rejected when it should berejected. This error is called the consumer’s riskand is denoted by the symbol β (beta).

The degree of risk (α) is normally chosen by theconcerned parties (α is often taken as 5%) in arriving atthe critical value of the test statistic. Increasing thesample size can reduce both the α and β risks.



XI-8 (1085)

Types of Errors (Continued)

The types of errors are shown in the Figure below:

The Decision

Made

Null Hypothesis

True False

Fail toReject

H0

Reject H0

p = 1 - αCorrect

Decision

p = βType II Error

p = αType IError

p = 1- βCorrect

Decision

Error Matrix



XI-9 (1086)

ENTIRE " = 5%

:0 = 35 HOURS0

One-Tail Test

If a null hypothesis is established to test whether asample value is smaller or larger than a populationvalue, then the entire α risk is placed on one end of adistribution curve. This constitutes a one tail-test.

H0: new <_ to present H1: new > present

Determine if the true mean is within the α critical region.



XI-10 (1087)

" = 0.0252

:0 0

" = 0.0252

+1.96-1.96

Two-Tail Test

If a null hypothesis is established to test whether apopulation shift has occurred, in either direction, then atwo-tail test is required. The allowable α error isgenerally divided into two equal parts.

H0: levels are = H1: levels are =/

Determine if the true mean is withineither the upper or lower α critical regions.



XI-11 (1088)

2 2/2

2

Zn = Eα σ

( ) ( )( )

2/2

2

Z p 1 - pn =

pα

Δ

Required Sample Size

The sample size, n, needed for hypothesis testingdepends on:

C The desired type I (α) risk and type II (β) riskC The minimum value to be detected between the

population means (μ - μ0)C The variation in the characteristic being measured

(s or σ)

The sample size equation for variable data is:

n = Sample sizeZ = The appropriate Z valueE = The desired mean intervalσ = The population standard deviation

For binomial data, use the following formula:

Z = The appropriate Z valuep = Proportion rateΔp = The desired proportion interval



XI-12 (1089)

0 0

XX

X - X - Z = =

n

μ μσσ ⎛ ⎞

⎜ ⎟⎝ ⎠

Hypothesis Tests for Means

Z Test

When the population follows a normal distribution andthe population standard deviation, σX, is known, then thehypothesis tests for comparing a population mean, μ,with a fixed value, μ0, are given by the following:

H0: μ = μ0 H0: μ <_ μ0 H0: μ >_ μ0H1: μ =/ μ0 H1: μ > μ0 H1: μ < μ0

The null hypothesis is denoted by H0 and the alternativehypothesis is denoted by H1. The test statistic is givenby:

Where the sample average is X, the number of samplesis n and the standard deviation of means is σX. If n > 30,the sample standard deviation, s, is often used as anestimate of the population standard deviation, σX.



XI-12 (1090)

0

X

X - 4.95 - 5.00Z = = = -1.180.12

n 8

μσ⎛ ⎞ ⎛ ⎞

⎜ ⎟ ⎜ ⎟⎝ ⎠ ⎝ ⎠

Hypothesis Tests for Means (Continued)

Z Test (Continued)

Example: The average vial height from an injectionmolding process has been 5.00" with a standarddeviation of 0.12". An experiment is conducted usingnew material which yielded the following vial heights:5.10", 4.90", 4.92", 4.87", 5.09", 4.89", 4.95", and 4.88".Can one state, with 95% confidence, that the newmaterial is producing shorter vials?

H0: μ >_ μ0 H1: μ < μ0H0: μ >_ 5.00" H1: μ < 5.00"

X = 4.95", n = 8, σX = 0.12". The test statistic is:

It is a left, one-tailed test and with a 95% confidence, thelevel of significance, α = 0.05. Z0.05 = -1.645. Since thetest statistic, -1.18, does not fall in the reject region, thenull hypothesis cannot be rejected. There is insufficientevidence to conclude that the vials made with the newmaterial are shorter.



XI-13 (1091)

0

X

X - t = sn

μ⎛ ⎞⎜ ⎟⎝ ⎠


Student’s t Test

The student’s t distribution is used for makinginferences about a population mean when thepopulation variance σ2 is unknown and the sample sizen is small. A sample size of 30 is normally the crossoverpoint between the t and Z tests. The test statisticformula is:

X = The sample meanμ0 = The target value or population meansx = The sample standard deviationn = The number of test samples

The null and alternative hypotheses are the same aswere given for the Z test. The degrees of freedom isdetermined by the number of samples, n, and is simply:

d.f. = n - 1



XI-14 (1092)

0

X

X - 900 - 880t = = = 5.0s 20n 25

μ⎛ ⎞ ⎛ ⎞⎜ ⎟ ⎜ ⎟⎝ ⎠ ⎝ ⎠


Student’s t Test (Continued)

Example: The average daily yield of a chemical processhas been 880 tons (μ = 880 tons). A new process hasbeen evaluated for 25 days (n = 25) with a yield of 900tons (X) and sample standard deviation, s = 20 tons.Can one say, with 95% confidence, that the process haschanged?

H0: μ = μ0 H1: μ =/ μ0H0: μ = 880 tons H1: μ =/ 880 tons

The test statistic calculation is:

With a 95% confidence, the level of significance, α =0.05. Since it is a two-tailed test, α/2 is used todetermine the critical values. The degrees of freedom,d.f. = n - 1 = 24. The critical values in a t distributiontable, are t0.025 = -2.064 and t0.975 = 2.064. Since the teststatistic, 5.0, falls in the right-hand reject (or critical)region, the null hypothesis is rejected. One concludes,with 95% confidence, that the process has changed.



XI-17 (1093)

t Distribution Table

d.f. t0.100 t0.050* t0.025** t0.010 t0.005 d.f.123456789

1011121314151617181920212223242526272829inf.

3.0781.8861.6381.5331.4761.4401.4151.3971.3831.3721.3631.3561.3501.3451.3411.3371.3331.3301.3281.3251.3231.3211.3191.3181.3161.3151.3141.3131.3111.282

6.3142.9202.3532.1322.0151.9431.8951.8601.8331.8121.7961.7821.7711.7611.7531.7461.7401.7341.7291.7251.7211.7171.7141.7111.7081.7061.7031.7011.6991.645

12.7064.3033.1822.7762.5712.4472.3652.3062.2622.2282.2012.1792.1602.1452.1312.1202.1102.1012.0932.0862.0802.0742.0692.0642.0602.0562.0522.0482.0451.960

31.8216.9654.5413.7473.3653.1432.9982.8962.8212.7642.7182.6812.6502.6242.6022.5832.5672.5522.5392.5282.5182.5082.5002.4922.4852.4792.4732.4672.4622.326

63.6579.9255.8414.6044.0323.7073.4993.3553.2503.1693.1063.0553.0122.9772.9472.9212.8982.8782.8612.8452.8312.8192.8072.7972.7872.7792.7712.7632.7562.576

123456789

1011121314151617181920212223242526272829inf.

* One tail 5% α risk ** Two tail 5% α risk



XI-18 (1094)

( )0

0 0

x - npZ = np 1 - p

Hypothesis Tests for Proportions

p Test

When testing a claim about a population proportion, wemay use a p test. When np < 5 or n(1-p) < 5, the binomialdistribution is used to test hypotheses relating toproportion.

If conditions that np >_ 5 and n(1-p) >_ 5 are met, then thebinomial distribution of sample proportions can beapproximated by a normal distribution. The hypothesistests for comparing a sample proportion, p, with a fixedvalue, p0, are given by the following:

H0: p = p0 H0: p <_ p0 H0: p >_ p0H1: p =/ p0 H1: p > p0 H1: p < p0


The number of successes is x and the number ofsamples is n. Z is compared with a critical value Zα orZα/2, which is based on a significance level, α, for a one-tailed test or α/2 for a two-tailed test.



XI-19 (1095)

Hypothesis Tests for Variance

Chi-square (Χ2) Test

It was discussed earlier that standard deviation (orvariance) is fundamental in making inferences regardingthe population mean. In many practical situations,variance (σ2) assumes a position of greater importancethan the population mean.

The standardized test statistic is called the chi-square(Χ2) test.

Population variances are distributed according to thechi-square distribution. Therefore, inferences about asingle population variance will be based on chi-square.

The chi-square test is widely used in two applications.

Case I. Comparing variances when the variance ofthe population is known.

Case II. Comparing frequencies of test outcomeswhen there is no defined population variance(attribute data).



XI-20 (1096)

( ) 22 X

20

n - 1 s = Χσ

Hypothesis Tests for Variance (Cont.)

Chi-square (Χ2) Test (Continued)

When the population follows a normal distribution, thehypothesis tests for comparing a population variance,σ2

X, with a fixed value, σ20, are given by the following:

H0: σ2X = σ2

0 H0: σ2X <_ σ2

0 H0: σ2X >_ σ2

0H1: σ2

X =/ σ20 H1: σ2

X > σ20 H1: σ2

X < σ20


Where the number of samples is n and the samplevariance is s2

X. The test statistic, Χ2, is compared with acritical value Χ2

α or Χ2α/2 which is based on a significance

level, α, for a one-tailed test or α/2 for a two-tailed testand the number of degrees of freedom, d.f.

The degrees of freedom is determined by the number ofsamples, n, and is simply:

d.f. = n - 1



XI-20 (1097)



If the H1 sign is =/ , it is a two-tailed test. If the H1 sign is>, it is a right, one-tailed test, and if the H1 sign is <, it isa left, one-tailed test.

The Χ2 distribution looks like:

Left tail Right tail

f(Χ2) f(Χ2)

0 Χ21-α 0 Χ2

α

Chi-square Distribution Tail Areas



XI-21 (1098)

( ) ( ) ( )( )

222 X

220

n - 1 s 8 - 1 8 psi = = = 1.9915 psi

Χσ

Hypothesis Tests for Variance (Cont.)Chi-square (Χ2) Test (Continued)

Chi-square Case I. Population Variance Is Known.

Example: The R & D department claims that the newsteel alloy will show a four sigma tensile variation lessthan or equal to 60 psi 95 % of the time. An eightsample test yielded a standard deviation of 8 psi. Can areduction in tensile strength variation be validated with95 % confidence? The best range of variation expectedis 60 psi. This translates to a sigma of 15 psi (anapproximate 4 sigma spread covering 95.44 % ofoccurrences).

H0: σ2X >_ σ2

0 or H0: σ2X >_ (15)2

H1: σ2X < σ2

0 or H1: σ2X < (15)2

This is a left-tail test. Using d.f. = n - 1 = 7, the chi-square critical value for 95 % confidence is 2.17.

Since 1.99 is to the left of 2.17, and is in the critical area,the null hypothesis must be rejected. The decreasedvariation in the new steel alloy tensile strength supportsthe R & D claim.



XI-22 (1099)

X2.95 X2

.05

Critical Values of theChi-square (Χ2) Distribution

d.f. Χ20.99 Χ2

0.95 Χ20.90 Χ2

0.10 Χ20.05 Χ2

0.01

1 0.00016 0.0039 0.0158 2.71 3.84 6.632 0.0201 0.1026 0.2107 4.61 5.99 9.213 0.115 0.352 0.584 6.25 7.81 11.344 0.297 0.711 1.064 7.78 9.49 13.28 5 0.554 1.15 1.61 9.24 11.07 15.096 0.872 1.64 2.20 10.64 12.59 16.817 1.24 2.17 2.83 12.02 14.07 18.488 1.65 2.73 3.49 13.36 15.51 20.099 2.09 3.33 4.17 14.68 16.92 21.67

10 2.56 3.94 4.87 15.99 18.31 23.2111 3.05 4.57 5.58 17.28 19.68 24.7312 3.57 5.23 6.30 18.55 21.03 26.2213 4.11 5.89 7.04 19.81 22.36 27.6914 4.66 6.57 7.79 21.06 23.68 29.1415 5.23 7.26 8.55 22.31 25.00 30.5816 5.81 7.96 9.31 23.54 26.30 32.0018 7.01 9.39 10.86 25.99 28.87 34.8120 8.26 10.85 12.44 28.41 31.41 37.5724 10.86 13.85 15.66 33.20 36.42 42.9830 14.95 18.49 20.60 40.26 43.77 50.8940 22.16 26.51 29.05 51.81 55.76 63.6960 37.48 43.19 46.46 74.40 79.08 88.38

120 86.92 95.70 100.62 140.23 146.57 158.95



XI-23 (1100)



Chi-square Case II. Comparing Observed and ExpectedFrequencies of Test Outcomes. (Attribute Data)

This application of chi-square is called the contingencytable or row and column analysis. The procedure is asfollows:

1. State the null hypothesis and alternativehypothesis:

Null hypothesis: There is no difference amongthe treatment probabilities.

Alternative hypothesis: At least one of theprobabilities is different.

H0: p1 = p2 = p3 = ... = pnH1: p1 =/ p2 =/ p3 =/ ... =/ pn

2. The contingency table degrees of freedom = d.f.

d.f. = (rows - 1)(columns - 1) = (r - 1)(c - 1)



XI-24 (1101)

c

i ijj = 1

r

j iji = 1

r c

i ji = 1 j = 1

R = O

C = O

N = R = C

∑

∑

∑ ∑

i jij

R CE =

N

( ) ( )2 2

r cij ij2 2

i = 1 j = 1 ij

O - E O - E = or = E E

Χ Χ∑∑ ∑



3. Determine the observed frequencies Oij for thevarious conditions being compared.

4. Calculate all row totals, Ri, column totals, Ci, and thegrand total, N.

5. Calculate the expected frequencies Eij for eachcondition, under the assumption that no differenceexists among the processes.

6. Calculate the chi-square test statistic:

This is the most “famous” chi-square statistic.



XI-24 (1102)



7. Note that although the alternative hypothesis has =/ ,the Χ2 critical value for this Case II test is alwaysdetermined using the chi-square table with theentire level of significance, α, in the one-tail, rightside, of the distribution. Determine the Χ2 criticalvalue from a table using α and the degrees offreedom.

8. Compare the calculated test statistic and the criticalvalue. If the calculated test statistic exceeds thecritical value, then a significant difference exists, ata selected confidence level.



XI-25 (1103)



Example: An airport authority wanted to evaluate theability of three X-ray inspectors to detect key items. Atest was devised whereby transistor radios were placedin ninety pieces of luggage. Each inspector wasexposed to exactly thirty of the preselected and“bugged” items in a random fashion.

At a 95% confidence level, is there any significantdifference in the abilities of the inspectors?

Inspector Observed Results

Inspectors TreatmentTotals1 2 3

Radios detected 27 25 22 74Radios undetected 3 5 8 16Sample total 30 30 30 90



XI-25 (1104)



Example continued:1. Null hypothesis: There is no difference between the

inspectors. H0: p1 = p2 = p3

Alternative hypothesis: At least one of theinspectors is different.

H1: p1 =/ p2 =/ p3

2. Degrees of freedom = d.f.

d.f. = (rows - 1)(columns - 1) = (r - 1)(c - 1)d.f. = (2 - 1)(3 - 1) = 2

3. Determine the observed frequencies Oij for thevarious conditions being compared.

4. Calculate all row totals, Ri, column totals, Ci, and thegrand total, N. These are given in the previousTable.



XI-26 (1105)

i jij

R CE =

N

( )

( ) ( ) ( ) ( ) ( ) ( )

2r c

ij ij2

i = 1 j = 1 ij

2 2 2 2 2 2

2

2

O - E =

E

2.33 0.33 2.67 2.33 0.33 2.67 = + + + + + 24.67 24.67 24.67 5.33 5.33 5.33

= 2.89

Χ

Χ

Χ

∑∑

Inspectors TreatmentTotals1 2 3

Radios detected 24.67 24.67 24.67 74Radios undetected 5.33 5.33 5.33 16Sample total 30 30 30 90



Example continued:5. Calculate the expected frequencies Eij for each

condition, using the formula below, these are shownin the Table.

Inspector Expected Results

6. Calculate the chi-square test statistic:



XI-26 (1106)



Example continued:

7. The critical value from the Table or the AppendixTable VI using d.f. = 2, α = 0.05, right-tail, is Χ2 =5.99. There is only a 5% chance that the calculatedvalue of Χ2 will exceed 5.99.

8. Compare the calculated test statistic and the criticalvalue. Since the Χ2 calculated value of 2.89 is lessthan the critical value of 5.99, and this is a right-tailtest, the null hypothesis cannot be rejected. Thereis insufficient evidence to say with 95% confidencethat the abilities of the inspectors differ.



XI-27 (1107)

Practical Significance vsStatistical Significance

The hypothesis is tested to determine if a claim hassignificant statistical merit. Traditionally, levels of 5% or1% are used for the critical significance values. If thecalculated test statistic has a p-value below the criticallevel then it is deemed to be statistically significant.

More stringent critical values may be required whencatastrophic loss is involved. Less stringent criticalvalues may be advantageous when there are no suchrisks.

On occasion, some hypothesis is found to bestatistically significant, but may not be worth the effortto implement. This could occur if a large sample wastested and the result is statistically significant, butwould not have any practical significance.



XI-27 (1108)

Normal D istribution, μ = 71

00.050.1

0.150.2

0.250.3

0.350.4

0.45

68 69 70 71 72 73 74

X

Normal D istribution,μ = 70

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

67 68 69 70 71 72 73X

Normal Distribution, μ = 71

00.050.1

0.150.2

0.250.3

0.350.4

0.45

68 69 70 71 72 73 74

X

Normal Distribution,μ = 70

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

67 68 69 70 71 72 73X

.025.025

LCL UCL

$

Power of Test H0: μ = μ0

Consider a null hypothesis that a population has meanμo= 70.0 and σX = 0.80. The 95% confidence limits are 70±(1.96)(0.8) = 71.57 and 68.43. One accepts thehypothesis μ = 70 if Xs are between these limits. Thealpha risk is that sample means will exceed those limits.What if μ shifts to 71, would it be detected? There is arisk that the null hypothesis would be accepted even ifthe shift occurred. This risk is termed β.

Illustration of Beta (β) Risk



XI-29 (1109)

00.10.20.30.40.50.60.70.80.9

1

67 68 69 70 71 72 73μ

1-β

Power of Test H0: μ = μ0 (Continued)

To construct a power curve, 1 - β is plotted againstvalues of μ. A shift in a mean away from the nullincrease the probability of detection. In general, asalpha increases, beta decreases, and the power of 1 - βincreases.

A gain in power can be obtained by accepting a lowerlevel of protection from the alpha error. Increasing thesample size makes it possible to decrease both alphaand beta, and increase power.

1 - β = Probability of rejecting the null hypothesis giventhat the null hypothesis is false.

Power Curve, (1 - β) vs μ



XI-30 (1110)

Largesamples

Means X vs :

NormalX1 vs X2

Variances

S12 vs S2

2

S12 vs F2

Smallsamples

Means

X vs :

X1 vs X2

Welch-SatterthwaiteApproximation

Z = 6X - :F/ n

Z = 6X - :F/

F1 - x2

= F21

N1+F2

2

N2

Fx - x =21 +

22

Z =6X1 - 6X2F6X1 - 6X2

=6 - 66 - 6

X = (n - 1)s2

F

2 ( - 1) 2

2

F = S21

S 22

=21

t = 6X - :s/ n

t = 6X - :s/ n

S2 = (n1 - 1)s21 + (n - 1)s2

2n1 + n2 -

= ( - ) + ( - )- 2

F21 = F2

2F21 = F2

2

S61- 6X2

= S 1n1

%1n2

= %X

t =6X1 - 6X2S6X1 - 6 2

=6 - 6

6 1 - 6Xdf = n1 + n2 - 2= + -

A = S21 / n1

B = S22 / n2

/B = S /

d f = (A + B)A2

n1 - 1+ B2

n2 - 1

2

+

F21 … F

22F … F

S6x1-6x2= A + B6 6

2

Normal Distribution Hypotheses Tests



XI-31 (1111)

Binomial

p vs :

p1 vs p2

Poisson

c vs :

c vs cc = no. of defects

k = no. samples

Fp = 6 (1 -p)n

Fp = p 6 Z = p - 6pFp

Z = p - 6pFp

Fp1&p2= 6p(1 - 6p) 1

n1+ 1

n2

Fp1&p2= 6p(1 - 6p) 1

n1+ 1

n2

6p =n1 p1 + n2p2

n1 + n26p =

n1 p1 + n2p2

n1 + n2

F = cF =

X 2 =c 2

1

k1+

c 22

k2

k1 + k2

c1 + c2- (c1 + c2)X 2 =

c 21

k1+

c 22

k2

k1 + k2

c1 + c2- (c1 + c2)

Z = c - 6cZ = c - 6c

c

Z =p - pFp -p

Z =p

1- p2

Fp1

-p2

Attribute Hypotheses Tests (Continued)


XI. ADVANCED STATISTICSSTATISTICAL DECISION MAKING / PAIRED-COMPARISON TESTS

XI-32 (1112)

( ) ( )1 2

2 21 21 1 2 2

p n +n -21 2

p1 2

n - 1 s + n - 1 s X - Xs = t = n + n - 2 1 1s +

n n

Paired-comparison Hypotheses Tests

Two Mean, Equal Variance, t Test

Tests the difference between two population means, μ1and μ2, when σ1 and σ2 are unknown but consideredequal, and are normally distributed.

H0: μ1 = μ2 H1: μ1 =/ μ2

sp = pooled standard deviationd.f. = n1 + n2 - 2



XI-33 (1113)

( ) ( )

22 21 2

1 21 22 2 d.f. 2 22 2

1 21 2

1 21 2

1 2

s s + n n X - Xd.f. = t =

s ss s + n nn n +

n - 1 n - 1

⎛ ⎞⎜ ⎟⎝ ⎠

⎛ ⎞ ⎛ ⎞⎜ ⎟ ⎜ ⎟⎝ ⎠ ⎝ ⎠

Paired-comparison Tests (Continued)

Two Mean, Unequal Variance, t Test

Tests the difference between two population means, μ1and μ2, when σ1 and σ2 are unknown, and are notconsidered to be equal.

H0: μ1 = μ2 H1: μ1 =/ μ2



XI-34 (1114)

d

dt = sn

⎛ ⎞⎜ ⎟⎝ ⎠


Paired t Test

Tests the difference between two population means, μ1and μ2, when data is taken in pairs with the differencecalculated for each pair, and the populations arenormally distributed. Data from the samples areassumed to be related.

H0: μ1 = μ2 H1: μ1 =/ μ2

Note that paired t tests using H0: μ1 <_ μ2 and H1: μ1 > μ2or H0: μ1 >_ μ2 and H1: μ1 < μ2 may also be performed.

The paired t test method with dependent samples, ascompared to treating the data as two independentsamples, will often show a more significant differencebecause the standard deviation (sd) includes no sampleto sample variation.

In general, the paired t test is a more sensitive test thanthe comparison of two independent samples.



XI-35 (1115)


F Test

The need for a statistical method of comparing twopopulation variances is apparent. The F test, named inhonor of Sir Ronald Fisher, is usually employed. Ifindependent, random samples are drawn from twonormal populations with equal variances, the ratio of(s1)2/(s2)2 creates a sampling distribution known as theF distribution. The hypotheses tests for comparing apopulation variance, σ2

1, with another populationvariance, σ2

2, are given by the following:

H0: σ21 = σ2

2 H0: σ21 <_ σ2

2 H0: σ21 >_ σ2

2

H1: σ21 =/ σ2

2 H1: σ21 > σ2

2 H1: σ21 < σ2

2

The shape of the F distribution is non-symmetrical andwill depend on the number of degrees of freedomassociated with s2

1 and s22. The degrees of freedom are ν1

and ν2 respectively.



XI-35 (1116)

2122

sF = s


F Test (Continued)

The F statistic is the ratio of two sample variances (twochi-square distributions) and is given by the formula:

Where s21 and s2

2 are sample variances and ν1 is the d.f. inthe numerator.

Since the identification of the sample variances isarbitrary, it is customary to designate the larger samplevariance as s2

1 and place it in the numerator.



XI-36 (1117)

f(F)

f (")


F Test (Continued)

ν1

ν2

1 2 3 4 5 6 7 8 9 10

1 161.4 199.5 215.7 224.6 230.2 234.0 236.8 238.9 240.5 241.9

2 18.51 19.00 19.16 19.25 19.30 19.33 19.35 19.37 19.38 19.40

3 10.13 9.55 9.28 9.12 9.01 8.94 8.89 8.85 8.81 8.79

4 7.71 6.94 6.59 6.39 6.26 6.16 6.09 6.04 6.00 5.96

5 6.61 5.79 5.41 5.19 5.05 4.95 4.88 4.82 4.77 4.74

6 5.99 5.14 4.76 4.53 4.39 4.28 4.21 4.15 4.10 4.06

7 5.59 4.74 4.35 4.12 3.97 3.87 3.79 3.73 3.68 3.64

8 5.32 4.46 4.07 3.84 3.69 3.58 3.50 3.44 3.39 3.35

9 5.12 4.26 3.86 3.63 3.48 3.37 3.29 3.23 3.18 3.14

10 4.96 4.10 3.71 3.48 3.33 3.22 3.14 3.07 3.02 2.98

F Critical Values (α = 0.05)



XI-37 (1118)

At Start One Year LaterNo. of tests 9 7

Product standarddeviation (psi) 900 300

( )( )

221

222

900sF = = = 9s 300


F Test (Continued)

Example: A materials laboratory wants to know if thereis an improvement in consistency of strength after agingfor one year (assume a 95% confidence level).

Solution: H0: σ12 <_ σ2

2 H1: σ12 > σ2

2 and ν1 = 8 ν2 = 6One is concerned with an improvement in variation;therefore, a one-tail test is used, with the entire α risk inthe right-tail. From the prior F Table, the critical value ofF is 4.15. The null hypothesis rejection area is equal toor greater than 4.15.

Since the calculated F value is in the critical region, thenull hypothesis is rejected. There is sufficient evidenceto indicate a reduced variance and more consistency ofstrength after aging for one year.



XI-38 (1119)

0 0

XX

X - X - Z = =

n

μ μσ σ⎛ ⎞

⎜ ⎟⎝ ⎠

0

X

X - t = sn

μ⎛ ⎞⎜ ⎟⎝ ⎠

1 2d.f. 2 2

1 2

1 2

X - Xt = s s + n n

Summary of Inference Tests

Type Test Statistic d.f. Application

Z N.A.Single sample mean.Standard deviation ofpopulation is known.

t test n - 1Single sample mean.Standard deviation ofpopulation unknown.

Twomeanequal

variancet test

n1+n2-2

2 sample means.V a r i a n c e s a r eu n k n o w n , b u tconsidered equal.

Twomean

unequalvariance

t test

*

2 sample means.V a r i a n c e s a r eu n k n o w n , b u tconsidered unequal.d.f. is determinedfrom the Welch-S a t t e r t h w a i t eapproximation.

1 2

1 2n +n -2

p1 2

X - Xt = 1 1s + n n

( ) ( )2 21 1 2 2

p1 2

n - 1 s + n - 1 ss =

n + n - 2



XI-38 (1120)

2122

sF = s

( )2r c

ij ij2

i = 1 j = 1 ij

O - E =

EΧ ∑∑

d

dt = sn

⎛ ⎞⎜ ⎟⎝ ⎠

( ) 22 X

20

n - 1 s = Χσ

Summary of Inference Tests (Continued)

Type Test Statistic d.f. Application

Pairedt test n - 1

2 sample means.Data is taken in pairs.A different d is

Χ2

σ2

knownn - 1

Tests sample variancea g a i n s t k n o w nvariance.

Χ2 (r-1)(c-1)Compares observeda n d e x p e c t e dfrequencies of testoutcomes.

F n1 - 1n2 - 1

Tests if two samplevariances are equal.


XI. ADVANCED STATISTICSSTATISTICAL DECISION MAKING / GOODNESS-OF-FIT TESTS

XI-39 (1121)

( ) ( )22k k

o e2 2i i

i = 1 i = 1i e

f - fO - E = or =

E fΧ Χ∑ ∑

Goodness-of-fit TestsThe chi-square goodness-of-fit (GOF) test can beapplied to any univariate distribution with a cumulativedistribution function.

H0: The data follow a specified distributionH1: The data do not follow the specified distribution

There observed frequency in each cell is Oi or fo and theexpected or theoretical frequency, Ei or fe. Any cellswhich have an expected frequency of less than 5, arecombined with an adjacent cell. Chi-square ( Χ2 ) is thensummed across all cells:

k is the number of cells after combining. c is thenumber of estimated population parameters for thedistribution plus 1. The calculated chi-square is thencompared to the chi-square critical value for thefollowing appropriate degrees of freedom.

GOF Distribution d.f. (k - c)Weibull (3 parameter) k - 4Normal k - 3Poisson k - 2Binomial k - 2Uniform k - 1



XI-40 (1122)

Spots fe fo (fe - fo)2 /fe

1 8 12 2.0002 8 7 0.1253 8 2 4.5004 8 7 0.1255 8 12 2.0006 8 8 0.000

Total = 48 48 8.750

Uniform Distribution (GOF)

Example: Is a game die honest and balanced, given thenumber of times each side has come up? A die wastossed 48 times with the following sample results:

1 spot 12 times, 2 spots 7 times, 3 spots 2 times4 spots 7 times, 5 spots 12 times, 6 spots 8 times

When a die is rolled, the expectation is that each sideshould come up an equal number of times. It is obviousthere will be random departures from this theoreticalexpectation even if the die is honest.

H0: The die outcomes follow a uniform distributionH1: The die outcomes do not follow a uniform

distribution



XI-40 (1123)

( )2ko e2

ei = 1

f - f = = 8.750

fΧ ∑

Uniform Distribution (GOF) (Cont.)

Example continued:

The calculated chi-square is 8.75. The critical chi-square Χ2

0.05,5 = 11.07. The calculated chi-square doesnot exceed critical chi-square. Therefore, thehypothesis of an honest die following a uniformdistribution cannot be rejected. The random departuresfrom theoretical expectation could well be explained bychance cause.

The student is encouraged to work through thefollowing examples given in the CQE Primer for:

C Normal distribution (GOF)

C Poisson distribution (GOF)

C Binomial distribution (GOF)


XI. ADVANCED STATISTICSSTATISTICAL DECISION MAKING / CONTINGENCY TABLES

XI-46 (1124)

( ) ( ) ( ) ( )2 2 2 2k

2 i i 1 1 2 2 n n

i = 1 i 1 2 n

O - E O - E O - E O - E = = + + ... +

E E E EΧ ∑

Contingency Tables

A two-way classification table (rows and columns)containing original frequencies can be analyzed todetermine whether the two variables (classifications) areindependent or have significant association. Acontingency coefficient (correlation) can be calculated.If the chi-square test shows a significant dependency,the contingency coefficient shows the strength of thecorrelation.

Results obtained in samples do not always agree exactlywith the theoretical expected results according to rulesof probability. A measure of the difference foundbetween observed and expected frequencies is suppliedby the statistic chi-square, Χ2, where:

If Χ2 = 0 observed and theoretical frequencies agreeexactly. If Χ2 > 0 they do not agree exactly. The largerthe value of Χ2, the greater the discrepancy betweenobserved and theoretical frequencies. The chi-squaredistribution is an appropriate reference distribution forcritical values when the expected frequencies are atleast equal to 5.



XI-47 (1125)

2

2C = + NΧ

Χ

k - 1Max C = k

Contingency Tables (Continued)

A contingency table example is shown in the CQEPrimer. The methodology is exactly like that presentedearlier for Chi-square Case II.

Coefficient of Contingency (C)

The degree of relationship, association or dependenceof the classifications in a contingency table is given by:

Where N equals the grand frequency total.

The maximum value of C is never greater than 1.0, andis dependent on the total number of rows and columns.The maximum coefficient of contingency is:

Where: k = min of (r, c) and r = rows, c = columns



XI-49 (1126)

( )2

= N k - 1

Χφ

Correlation of Attributes

Contingency table classifications often describecharacteristics of objects or individuals. Thus, they areoften referred to as attributes and the degree ofdependence, association or relationship is calledcorrelation of attributes. For (k = r = c) tables, thecorrelation coefficient, φ, is defined as:

The value of φ falls between 0 and 1. If the calculatedvalue of chi-square is significant, then φ is significant.In the example given in the CQE Primer, rows andcolumns are not equal and the correlation calculation isnot applied.


XI. ADVANCED STATISTICSANALYSIS OF VARIANCE

XI-50 (1127)

( )2X - X∑

Analysis of Variance (ANOVA)

In many investigations (such as experimental trials), it isnecessary to compare three or more population meanssimultaneously. The underlying assumptions inanalysis of variance of means are: the variance is thesame for all factor treatments or levels, the individualmeasurements within each treatment are normallydistributed and the error term is considered a normallyand independently distributed random effect.

The variability of a set of measurements is proportionalto the sum of squares of deviations used to calculate thevariance:

Analysis of variance partitions the sum of squares ofdeviations of individual measurements from the grandmean (called the total sum of squares) into parts: thesum of squares of treatment means plus a remainderwhich is termed the experimental or random error.

When an experimental variable is highly related to theresponse, its part of the total sum of the squares will behighly inflated. This condition is confirmed bycomparing the variable sum of squares with that of therandom error using an F test.



XI-50 (1128)

2 22X - ( X) /N total sum of squares= (variance) =

N - 1 total DF (degrees of freedom)Σ Σ σ

A Comparison of Three or More Means

An analysis of variance to detect a difference in three ormore population means first requires obtaining thesame summary statistics applied in the short cutformula for calculating variance of a set of data:

ΣX2 is called the crude sum of squares

(ΣX)2 / N is the CM (correction for the mean)

ΣX2 - (ΣX)2 / N is termed SS (total sum of squares, orcorrected SS)



XI-51 (1129)

Three or More Means (Continued)

One-Way ANOVA

In the one-way ANOVA, the total variation in the data hastwo parts: the variation among treatment means and thevariation within treatments.

ANOVA grand average = GM. The total SS is then:

Where Xi is any individual( )2

iTotal SS = X - GM∑measurement

Total SS = SST + SSE Where SST = treatment sum ofsquares and SSE is theexperimental error sum ofsquares.

Sum of the squared deviations( )2ttSST = n X - GM∑

of each treatment average fromthe grand average or grandmean.

Sum of the squared deviations( )2ttSSE = X - X∑

of each individual observationwithin a treatment from thetreatment average.



XI-51 (1130)


One-Way ANOVA (Continued)

For the ANOVA calculations:

( ) Each treatment total squaredTCM = Number of observations in that treatment∑ ∑

( )SST = TCM - CM∑

SSE = Total SS - SST (always obtained by difference)

Total DF = N - 1 (total degrees of freedom)

TDF = t -1 (treatment DF = number oftreatments minus 1)

EDF = (N-1) - (t - 1) = N - t (error DF, always obtainedby difference)

(mean square treatments)SST SSTMST = = TDF t - 1

(mean square error)SSE SSEMSE = = EDF N - t



XI-52 (1131)



To test the null hypothesis:

H0: μ1 = μ2 = ... = μt H1: At least one mean different

When F > Fα , reject H0MSTF = MSE

Example: The following coded results were obtainedfrom a single factor randomized experiment, in whichthe outputs of three machines were compared.Determine if there is a significant difference in theresults (α=0.05).

Machines Data Sum n Avg TCM =

A 5, 7, 6, 7, 6 31 5 6.2 192.2 195

B 2, 0, 1, -2, 2 3 5 0.6 1.8 13

C 1, 0, -2, -3, 0 -4 5 -0.8 3.2 14

Total 30 15 197.2 222



XI-52 (1132)

( ) ( )

( )( )

2

2 2

2

X = 30 N = 15 Total DF = N - 1 = 15 - 1 = 14GM = X N = 30 N = 2.0 X = 222

X 30CM = = = 60N 15

Total SS = X - CM = 222 - 60 = 162TCM = 197.2

SST = TCM - CM = 197.2 - 60 = 137

∑∑ ∑∑

∑∑

∑( ) ( ) ( ) ( )2 2 2 2

t t

.2 and

SST = n X - GM = 5 6.2 - 2 + 5 0.6 - 2 + 5 0.8 - 2SST = 82.2 + 9.8 + 39.2 = 137.2SSE = Total SS - SST = 162 - 137.2 = 24.8

∑

Source(of

variation) SS DF Mean

Square F 1 2, ,Fα ν ν

Machines 137.2 2 68.6 33.2 F0.05,2,12 = 3.89Error 24.8 12 2.067Total 162 14 e = 2.07 = 1.44σ



Example continued:

The completed ANOVA table is:



XI-53 (1133)



Example continued:

Since the computed value of F (33.2) exceeds the criticalvalue of F, the null hypothesis is rejected. Thus, thereis evidence that a real difference exists among themachine means.

σe is the pooled standard deviation of within treatmentsvariation. It can also be considered the processcapability sigma of individual measurements. It is thevariation within measurements which would still remainif the difference among treatment means wereeliminated.



XI-53 (1134)

Two-Way ANOVA

The two-way analysis procedure is an extension of thepatterns described in the one-way analysis. Recall thata one-way ANOVA has two components of variance:Treatments and experimental error. In the two-wayANOVA there are three components of variance: FactorA treatments, Factor B treatments, and experimentalerror.

Two Factor, Two-Way ANOVA Experiment

ANOVA Table for the Two-Factor, Two-Way Example

Source SS DF MS F 1 2, ,Fα ν ν

Columns(Matls) 872.44 2 436.22 20.8 F0.05,2,14 = 3.74

Rows(Instruct) 2005.6 1 2005.6 95.6 F0.05,1,14 = 4.60

Error 293.78 14 20.98 SIGtotal = 13.66

17 SIGe =

SIG total = 13.66



XI-55 (1135)

Two Factor, Two-Way ANOVAExperiment (Continued)

The null hypotheses: Instructor and study materialmeans do not differ.

Col F = ColMS/EMS = 436.22/20.98 = 20.79. This is largerthan critical F = 3.74. Therefore, the null hypothesis ofequal material means is rejected.

Row F = RowMS/EMS = 2005.56/20.98 = 95.59. This islarger than critical F = 4.60. Therefore, the nullhypothesis of equal instructor means is rejected.

The difference between total sigma (13.66) and errorsigma (4.58) is due to the significant difference ininstructor means and material means.

If the instructor difference and study materialdifferences were only due to chance cause, the sigmavariation in the data would be equal to SIGe, the squareroot of the Error Mean Square.



XI-56 (1136)

( ) ( )2SumCellCellSq = InterSqs = CellSq

k ∑

Two Factor ANOVAExperiment with Interaction

In the previous materials/instructor example, the datawas listed in six cells. That is, six experimentalcombinations. There were also 3 replications (students)in each cell (k = 3). When k is greater than 1 in a twofactor ANOVA, there is the opportunity to analyze for apossible interaction between the two factors.

Example continued: Examine the previous data forinteraction effects. A similar analysis pattern is notedhere. The data in each cell is summed, and that total isdivided by the number of observations in that cell.

InterSS = InterSqs - CM - ColSS - Row SS

InterSS = 81604 - 78672.22 - 872.44 - 2005.56 = 53.78

ErrorSS = TotSS - ColSS - RowSS - InterSS

ErrorSS = 3171.78 - 872.44 - 2005.56 - 53.78 = 240



XI-57 (1137)

Source SS DF MS F 1 2, ,Fα ν ν

Columns(Materials) 872.44 2 436.22 21.81 F0.05,2,12 = 3.89

Rows(Instruct) 2005.6 1 2005.56 100.3 F0.05,1,12 = 4.75

Interaction(Row/Col) 53.78 2 26.89 1.34 F0.05,2,12 = 3.89

Error 240 12 2017 SIGe = 20 = 4.47

SIG total = Total SS/(N-1) = 13.66

Two Factor ANOVA, Interaction (Cont.)

Example continued: The null hypothesis for theinteraction effect is that there is no interaction.

The interaction calculated F (1.34) is less than critical F(3.89). The null hypothesis of no interaction is notrejected.



XI-58 (1138)

ijk i j ij k(ij)X = + M + I + MI + μ ε

Components of Variance

An analysis of variance can be extended with adetermination of the COV (components of variance).The COV table uses the MS (mean square), F, and F(alpha) columns from the previous ANOVA table andadds columns for EMS (expected mean square),variance, adjusted variance and percent contribution todesign data variation. The model for the ANOVA is:

The model states that any measurement ( X ) representsthe combined effect of the population mean ( μ ), thedifferent materials ( M ), the different instructors ( I ), thematerials/instructor interaction ( M/I ), and theexperimental error ( ε ).

I represents materials at 3 levels, j representsinstructors at 2 levels, k represents cells with 3replications.



XI-58 (1139)

COV TABLE

MS F F(α) EMS VAR ADJVAR

% CONTR

436.22 21.81 3.89 2 2e M+ 6σ σ 69.37 69.37 22.21

2005.6 100.3 4.75 2 2e I+ 9σ σ 220.62 220.62 70.65

26.89 1.34 3.89 2 2e MI + 3σ σ 2.3 2.3 0.74

20 2eσ 20 20 6.4

Totals 312.39 100

Components of Variance (Continued)

Example continued:

Effect Variance = (Effect MS - Error MS)/(Variance Coefficient)

M Var = (436.22 - 20)/6 = 69.37 I Var = (2005.56 - 20)/9 = 220.62M/I Var = (26.89 - 20)/3 = 2.30 Error Var = 20

Material differences are significant and contribute22.21% of variation in the data. Instructor differencesare significant and contribute 70.65% of variation in thedata. The material/instructor interaction is notsignificant. Experimental error contributes only 6.40%of total variation.



XI-59 (1140)

ANOVA Table for anA x B Factorial Experiment

In a factorial experiment involving factor A at a levelsand factor B at b levels, total sum of squares can bepartitioned into:

Total SS = SS(A) + SS (B) + SS(AB) + SSE

ANOVA Table for an A x B Factorial ExperimentSource DF SS MS

Factor AFactor BInteraction ABError

(a-1)(b-1)

(a-1)(b-1)(n-ab)

SS(A)SS(B)

SS(AB)SSE

SS(A)/(a-1)SS(B)/(b-1)

SS(AB)/(a-1)(b-1)SSE/(n-ab)

Total (n-1) Total SS



XI-59 (1141)

ANOVA Table for aRandomized Block Design

The randomized block design implies the presence oftwo independent variables, “blocks” and “treatments.”The total sum of squares of the response measurementscan be partitioned into three parts; the sum of thesquares for the blocks, treatments, and error.

ANOVA Table for a Randomized Block Design

Source DF SS MS

BlocksTreatments

Error

b-1t-1

(b-1)(t-1)

SSBSSTSSE

MSB=SSB/(b-1)MST=SST/(t-1)

MSE=SSE/(b-1)(t-1)

Total bt-1 Total SS


XI. ADVANCED STATISTICS / RELATIONSHIPS BETWEENVARIABLES / LINEAR REGRESSION

XI-60 (1142)

Relationships Between Variables

Relationships between variables is presented in thefollowing topic areas:

C Linear regressionC Simple linear correlationC Time-series analysis



XI-60 (1143)

Linear Regression

Consider the problem of predicting the CQE test results(Y) for students based upon an input variable (X), theamount of preparation time in hours. A total of tenstudents were sampled in this fabricated example.

Student Study Time(Hours)

Test Results50 = 50%

123456789

10

60405065354050304555

67617380605562506170

An initial approach to the analysis of the data in thetable above is to plot the points on a graph known as ascatter diagram. Observe that Y appears to increase asX increases.



XI-61 (1144)

30 35 40 45 50 55 60 65Study Time (Hours), X

53

60

67

74

81

Linear Regression (Continued)

The mathematical equation of a straight line is:

Y = β0 + β1X

Where β0 is the Y intercept and β1 is the slope of the line.



XI-61 (1145)

( )

0 1

Mean value of Y forY = + random error

a given value of XY = + X +

⎛ ⎞⎜ ⎟⎝ ⎠β β ε

Linear Regression (Continued)

A random error is the difference between an observedvalue of Y and the mean value of Y for a given value ofX. One assumes that for any given value of X theobserved value of Y varies in a random manner andpossesses a normal probability distribution.

The probabilistic model for any particular observedvalue of Y is:

Variation in Y as a Function of X



XI-62 (1146)

i 0 1 iY = + Xβ β

i 0 1 iY = + Xβ β

81

74

67

60

53

30 35 40 45 50 55 60 65

Study Time (Hours), X

The Method of Least Squares

If one denotes the predicted value of Y obtained fromthe fitted line as , the prediction equation is:Y

Where: represent estimates of the true β0 and0 1 and β ββ1.

The principle of least squares is:

Choose, as the best fitting line, the line thatminimizes the sum of squares of the deviationsof the observed values of Y from thosepredicted.



XI-63 (1147)

( ) ( ) ( )2

2

2n n n

i i in n2 i = 1 i = 1 i = 1i XY i iX

i = 1 i = 1

XY1 0 1

X

X X YS = X - S = X Y -

n n

S = = Y - XS

β β β

∑ ∑ ∑∑ ∑

( )2n

iii = 1

SSE = Y - Y∑

i 0 1 iY = + Xβ β

The Method of Least Squares (Cont.)

Expressed mathematically, to minimize the sum ofsquared errors given by:

Substituting for one obtains the following expression:iY

Sum of squared errors = ( ) 2n

0 1i ii = 1

SSE = Y - + X⎡ ⎤β β⎣ ⎦∑

The least square estimator of β0 and β1 are calculated asfollows:

Once have been computed, substitute their0 1 and β βvalues into the equation of a line to obtain the leastsquares prediction equation, or regression line.

The prediction equation for is:Y

Where: represent estimates of the true β0 and β1.0 1 and β β



XI-65 (1148)

Xi Yi X2i XiYi Y2

i

60405065354050304555

67617380605562506170

3,6001,6002,5004,2251,2251,6002,500 9002,0253,025

4,0202,4403,6505,2002,1002,2003,1001,5002,7453,850

4,4893,7215,3296,4003,6003,0253,8442,5003,7214,900

Sum 470 639 23200 30805 41529

Least Squares Example

Example: Obtain the least squares prediction line forthe table data below:

Data Table for the Study Time/Test Score Example



XI-66 (1149)

( )

( ) ( )

2

2n

2ini = 12

iXi = 1

n n

i ini = 1 i = 1

XY i ii = 1

X470

S = X - = 23,200 - = 1,110n 10

X Y470 639

S = X Y - = 30,805 - = 772n 10

470 639X = = 47 Y = = 63.910 10

⎛ ⎞⎜ ⎟⎝ ⎠

⎛ ⎞ ⎛ ⎞⎜ ⎟ ⎜ ⎟⎝ ⎠ ⎝ ⎠

∑∑

∑ ∑∑

2

XY1

X

0 1

S 772 = = = 0.6955S 1,110

= Y - X = 63.9 - (0.6955)(47) = 31.2115

Y = 31.2115 + 0.6955 X

β

β β

Y = 31.2115 + (0.6955)(60)

Y = 72.9415 = 73%

Least Squares Example (Continued)

Example continued:

One may now predict Y for a given value of X forexample, if 60 hours of study time is allocated, thepredicted test score would be:



XI-67 (1150)

0 1Y = + X + β β ε

2 2 2e

SSE = is sometimes shown as sˆ ˆn - 2ε εσ σ

i 0 1 iY = + Xβ β

( ) ( )

( )

( ) ( )2 2

2

2

22n n

i 0 1i i ii = 1 i = 1

2

XY1 XYY Y

X

2n

in n2 2 i = 1i iY

i = 1 i = 1

SSE = Y - Y = Y - + X

SSSE = S - S = S -

S

YS = Y - Y = Y -

n

⎡ ⎤β β⎣ ⎦

β

∑ ∑

∑∑ ∑

Calculating s2e, an Estimator of σ2

ε

The model for Y assumes that Y is related to X:

If the least squares line is used:

A random error ε enters into the calculations of β0 andβ1. The random errors affect the error of prediction.

We estimate σ2ε from SSE (sum of squares for error)

based on (n - 2) degrees of freedom.



XI-68 (1151)

12

1

1 1

X

- ˆt = s = s S

εβ

β

β β σ

1

2

1 11 1

X

- - 0.6955 - 0t = = = = 5.18s 4.47ˆ

1,110Sβ ε

β β β β⎛ ⎞ ⎛ ⎞σ⎜ ⎟ ⎜ ⎟⎜ ⎟ ⎝ ⎠⎝ ⎠

Inferences Concerning theSlope β1 of a Line

The null hypothesis and alternative hypothesis are:

H0: β1 = 0 H1: β1 =/ 0

The test statistic is a t distribution with n - 2 degrees offreedom:

Example: From the data in Study Time/Test Scoreexample, determine if the slope results are significant ata 95% confidence level.

For a 95% confidence level, determine the critical valuesof t with α = 0.025 in each tail, using n - 2 = 8 degrees offreedom: t0.025, 8 = -2.306 and t0.025, 8 = 2.306. Reject thenull hypothesis if t > 2.306 or t < -2.306, depending onwhether the slope is positive or negative. In this case,the null hypothesis is rejected and we conclude thatβ1 =/ 0 and there is a linear relationship between Y and X.



XI-69 (1152)

2

2 2

1 /2, n-2

X

1 1/2, n-2 1 /2, n-2

X X

ˆ t thus,S

ˆ ˆ - t < < + tS S

εα

ε εα α

σβ ±

σ σβ β β

Confidence IntervalEstimate for the Slope β1

The confidence interval estimate for the slope β1 is givenby:


XI. ADVANCED STATISTICS / RELATIONSHIPS BETWEENVARIABLES / SIMPLE LINEAR CORRELATION

XI-70 (1153)

( )X,Y

X Y

cov X, Y = ρσ σ

( ) ( )( ) ( )2 2

n

i iXY i = 1

XY n n2 2X Y

i ii = 1 i = 1

X - X Y - YSr = = S S X - X Y - Y

∑

∑ ∑

Simple Linear Correlation

Correlation Coefficient

The population linear correlation coefficient, ρ,measures the strength of the linear relationship betweenthe paired X and Y values in a population. ρ is apopulation parameter. For the population, the Pearsonproduct moment coefficient of correlation, ρX,Y is givenby:

Where cov means covariance. Note that -1 < ρ < +1

The sample linear correlation coefficient, r, measuresthe strength of the linear relationship between the pairedX and Y values in a sample. r is a sample statistic. Fora sample, the Pearson product moment coefficient ofcorrelation, rXY is given by:

Note that -1 < r < +1



XI-71 (1154)

( )( )

2

2 2

2

n 2

iYi = 1

2

XY1 XYY Y

X

S = Y - Y

SSSE = S - S = S -

Sβ

∑

( ) ( )2 2

XYXY

X Y

S 772r = = = 0.878S S 1,110 696.9

Simple Linear Correlation (Continued)

Correlation Coefficient (Continued)

Example: Using the study time and test score datareviewed earlier, determine the correlation coefficient.

The coefficient of correlation r will assume exactly thesame sign as β1 and will equal zero when β1 = 0.

C A positive value for r implies that the line slopesupward to the right.

C A negative value indicates that it slopes downwardto the right.

Note that r = 0 implies no linear correlation, not simply“no correlation.” If X is of any value in predicting Y,then SSE, can never be larger than:



XI-71 (1155)

( )2

2 2 2 2

2

2 2 XYY

Y Y X Y

S - SSE SSSER = r = = 1 - = S S S S

( ) ( )( ) ( )

( )2 2

2 2

2 XY

X Y

22

S 772r = = = 0.771S S 1,110 696.9

or r = 0.878 = 0.771

Coefficient of Determination (R2)

The coefficient of determination is R2. The square ofthe linear correlation coefficient is r2. It can be shownthat: R2 = r2

The coefficient of determination is the proportion of theexplained variation divided by the total variation, whena linear regression is performed. r 2 lies in the interval of0 < r2 < 1. r2 will equal +1 or -1 only when all the pointsfall exactly on the fitted line.

Example: Using the data from the previous example,determine the coefficient of determination.

One can say that 77% of the variation in test scores canbe explained by variation in study hours.



XI-72 (1156)

MPG20

21

22

23

24

25

19

18

17

16

2000 3000 4000

CAR WEIGHT

AVERAGE 20 MPG

2 2 21 2 9

2 2 21 2 9

2

SST = D + D + . . . + DSSE = d + d + . . . + d

SSE SST - SSEr = 1 - = SST SST

∑∑

Simple Linear Correlation (Continued)

Correlation Example

Correlation Plot of Car Weight and MPG


XI. ADVANCED STATISTICS / RELATIONSHIPS BETWEENVARIABLES / TIME-SERIES ANALYSIS

XI-73 (1157)

UPWARD TREND

1 5 10 15 200

20

40

60

80

100DOWNWARD TREND

1 5 10 15 200

20

40

60

80

100PROCESS SHIFT

1 5 10 15 200

20

40

60

80

100

CYCLES

1 5 10 15 200

20

40

60

80

100UNUSUAL VALUES

1 5 10 15 200

20

40

60

80

100INCREASING VARIABILITY

1 5 10 15 200

20

40

60

80

100

Time-Series Analysis

Data can be presented in either summary (static) or timeseries (dynamic) fashion. Important elements of mostprocesses can change over time. For many businessactivities, trend charts will show patterns that indicate ifa process is running normally or whether desirable orundesirable changes are occurring.

It should be noted that normal convention has timeincreasing across the page (from left to right) and themeasurement value increasing up the page.

Time-Series (Trend) Charts


XI. ADVANCED STATISTICSDESIGN OF EXPERIMENTS / INTRODUCTION

XI-74 (1158)

Design and Analysis of Experiments

Design and analysis of experiments is presented inthe following topic areas:

C IntroductionC TerminologyC Planning experimentsC Simple experimentsC Block experimentsC Full-factorial experimentsC Fractional-factorial experimentsC Other experiments



XI-74 (1159)

Introduction to DOE

Many experiments focus on 1FAT (one factor at a time)at two or three levels and try to hold everything elseconstant (which is impossible to do in a complicatedprocess). When Design of Experiments (DOE) isproperly constructed, it can focus on a wide range ofkey input factors or variables and will determine theoptimum levels of each of the factors.

It should be recognized that the Pareto principle appliesto the world of experimentation. That is, 20% of thepotential input factors generally make 80% of the impacton the result.

Changing just one factor at a time, has shortcomings:

C Too many experiments are necessary

C The optimum values may never be revealed

C The factor interaction cannot be determined

C Conclusions may be wrong or misleading

C Non-statistical experiments are often inconclusive

C Time and effort may be wasted



XI-75 (1160)

Introduction to DOE (Continued)

Design of experiments is a methodology of varying anumber of input factors simultaneously in a carefullyplanned manner, such that their individual andcombined effects on the output can be identified.Advantages of DOE include:

C Many factors can be evaluated simultaneously

C Noise factors cannot be controlled, but other inputfactors can be controlled to make the outputinsensitive to noise factors

C In-depth, statistical knowledge is not necessary

C Important factors can be distinguished

C Since the designs are balanced, there is confidencein the conclusions drawn

C If important factors are overlooked, the results willindicate that they were overlooked

C Precise statistical analysis can be run usingstandard computer programs

C Quality can be improved without increased costs


XI. ADVANCED STATISTICSDESIGN OF EXPERIMENTS / TERMINOLOGY

XI-76 (1161)

A B C+ + -+ - +- + +- - -

AB AC BC+ - -- + -- - ++ + +

A B C- - +- + -+ - -+ + +

AB AC BC+ - -- + -- - ++ + +

Or

DOE Terminology

The CQE Primer lists a number of DOE terms. Thestudent is encouraged to review those definitions.

Alias An alias occurs when two factor effectsare confounded with each other.

Balanceddesign

A fractional-factorial design in which anequal number of trials is conducted foreach factor.

Block A subdivision of the experiment intorelatively homogenous experimentalunits.

Confounded When the effects of two factors are notseparable.

A is confounded with BCB is confounded with ACC is confounded with AB



XI-77 (1162)

DOE Terminology (Continued)

Correlationcoefficient(r)

A number between -1 and 1 that indicatesthe degree of linear relationship betweentwo sets of numbers. Zero (0) indicatesno linear relationship.

Curvature Refers to non-straight-line behaviorbetween one or more factors and theresponse. For example:

Y = B0 + B1X1 + B11 (X1 C X1) + εDegrees offreedom

The term used is DOF, DF, d.f. or ν. Thenumber of measurements that areindependently available for estimating apopulation parameter.

EVOP evolutionary operation, a term thatdescribes the way sequent ia lexperimental designs can be adapted bylearning from current results to predictfuture treatments.

Small response improvements may bemade via large sample sizes. Theexperimental risk is low because the trialsare conducted in vicinity of an alreadysatisfactory process.



XI-78 (1163)


Experiment A test undertaken to make animprovement in a process or to learnpreviously unknown information.

First-order The equation below is is first-order inboth X1 and X2.

Y = B0 + B1X1 + B2X2 + εFractionalfactorial

Fewer experiments than the full designare conducted. Three-factor two-level,half-fractional designs examples are:

A B C A B C- - - - - +- + + - + -+ - + + - -+ + - + + +



XI-79 (1164)


Fullfactorial

Experimental designs which contain allcombinations of all levels of all factors. Atwo-level, three-factor full-factorial designis:

A B C- - -- - +- + -- + ++ - -+ - ++ + -+ + +

Input factor An independent variable which may affecta (dependent) response variable and isincluded at different levels in theexperiment.

Inner array In Taguchi-style, fractional-factorialexperiments, these are the factors thatcan be controlled in a process.



XI-79 (1165)

No Interaction Interaction

Haveeaten

Haven’teaten

# Drinks # Drinks

No drugs

Drugs

2 4 6 8 0 1 2 3


Interaction Occurs when the effect of one input factoron the output depends upon the level ofanother input factor.

Level A given factor or a specific setting of aninput factor. Four levels of a heattreatment may be 100EF, 120EF, 140EF and160EF.

Main effect An estimate of the effect of a factorindependent of any other factors.

Mixtureexperi-ments

Experiments in which the variables areexpressed as proportions of the wholeand sum to 1.0.



XI-80 (1166)


Orthogonal A design is orthogonal if the main andinteraction effects can be estimatedwithout confounding the other maineffects or interactions.

Outer array In a Taguchi-style fractional-factorialexperiment, these are the factors thatcannot be controlled in a process.

Qualitative Descriptors of category and/or order, butnot of interval or origin.

Quanti-tative

Descriptors of order and interval (intervalscale) and possibly also of origin (ratioscale).

Random-ized trials

Frees an experiment from theenvironment and eliminates biases.

Repeatedtrials

Trials conducted to estimate the trial-to-trial experimental error. Also calledreplications.

Residualerror(ε) or (E)

The difference between the observed andthe predicted value for that result, basedon an empirically determined model.



XI-81 (1167)


Residuals The difference between experimentalresponses and predicted model values.

Resolution II An experiment in which some of themain effects are confounded.

Resolution III A fractional-factorial design in which nomain effects are confounded with eachother but the main effects andtwo-factor interaction effects areconfounded.

Resolution IV A fractional factorial design in whichthe main effects and two factorinteraction effects are not confounded,but the two factor effects may beconfounded with each other.

Resolution V A fractional-factorial design in which noconfounding of main effects and twofactor interactions occurs.

Responsesurfacemethodology(RSM)

The graph of a system response plottedagainst one or more system factors.Response surface methodologyemploys experimental design todiscover the “shape” of the responsesurface.



XI-82 (1168)


Responsevariable

The variable that shows the observedresults of an experimental treatment.Also output or dependent variable.

Robustdesign

Associated with the application ofTaguchi experimentation in which aresponse variable is considered immuneto input variables that may be difficult orimpossible to control.

Screeningexperiment

A technique to discover the mostimportant factors in an experimentalsystem. Most screening experimentsemploy two-level designs.

Sequentialexperiments

Experiments are done one after another,not at the same time.

Simplexdesign

A spatial design used to determine themost desirable variable combination(proportions) in a mixture.

Testcoverage

The percentage of all possiblecombinations of input factors in anexperimental test.

Treatments The various factor levels that describehow an experiment is to be carried out.



XI-83 (1169)

L L LH H H

Nointeraction

Moderateinteraction Very strong

interaction

Factor B Factor B Factor B

A LOW

A HIGH

L H

Stronginteraction

Factor B

Interactions

An interaction occurs when the effect of one input factoron the output depends upon the level of another inputfactor.

Interactions can be readily examined with full-factorialexperiments. Often, interactions are lost with fractional-factorial experiments.

The preferred DOE approach screens a large number offactors with highly fractional experiments. Interactionsare then explored or additional levels examined once thesuspected factors have been reduced.



XI-85 (1170)

Additive

70

6050

Additive

80

60

70

8090

60

70 80

9080

70

5060

70

80

90

8070

6050

X1 X1 X1

X2 X2X2 50

50

50

Response Surfaces

3-D Response Surface Matching Dome Contour

Comparison of 3-D and 2-D Response Surfaces

Rising Ridge Stationary Ridge Saddle Minimax

Contour Examples


XI. ADVANCED STATISTICSDESIGN OF EXPERIMENTS / PLANNED EXPERIMENTS

XI-86 (1171)

DOE Applications

Situations where experimental design can be effectivelyused include:

C Choosing between alternatives

C Selecting the key factors affecting a response

C Response surface modeling to:

C Hit a targetC Reduce variabilityC Maximize or minimize a responseC Make a process robustC Seek multiple goals



XI-87 (1172)

DOE Steps

Getting good results from a DOE involves a number ofsteps:

C Set objectives

C Select process variables

C Select an experimental design

C Execute the design

C Check that the data are consistent with theexperimental assumptions

C Analyze and interpret the results

C Use/present the results



XI-88 (1173)

A Typical DOE Checklist

The following checklist will be helpful for manyinvestigations.

C Define the objective of the experiment

C Learn many facts about the process

C Brainstorm the key variables with knowledgeablepeople

C Run “dabbling experiments” where necessary

C Assign levels to each independent variable

C Select, develop and review the DOE plan

C Run the experiments in random order

C Draw conclusions and verify them

The Iterative Approach to DOE

Instead of performing one big experiment, it is morecommon to perform several smaller experiments, witheach stage supplying a different kind of answer.



XI-89 (1174)

Experimental Objectives

Some experimental design objectives are:

1. Comparative objective

2. Screening objective

3. Response surface (method) objective

4. Optimizing responses when factors are proportionsof a mixture objective

5. Optimal fitting of a regression model objective



XI-90 (1175)

Select and Scale the Process Variables

Process variables include both inputs and outputs - i.e.factors and responses.

C Include all important factorsC Be bold, but not foolish, in choosing factor levelsC Avoid impractical factor settingsC Include all relevant responsesC Avoid using combined measurement responses

When choosing the range of settings for input factors,it is wise to avoid extreme values.

The most popular experimental designs are called two-level designs.



XI-90 (1176)

Design Guidelines

Factors ComparativeObjective

ScreeningObjective

ResponseSurfaceObjective

1 1-factorcompletelyrandomizeddesign

____ ____

2 - 4 Randomizedblock design

Full orfractional-factorial

Centralcomposite orBox-Behnken

5 ormore

Randomizedblock design

Fractional-factorial orPlackett-Burman

Screen firstto reducenumber offactors

The choice of a design depends on the amount ofresources available and the degree of control overmaking wrong decisions.



XI-91 (1177)

Experimental Assumptions

In all experimentation, one makes assumptions. Someof the engineering and mathematical assumptions anexperimenter makes include:

C Are the measurement systems capable for allresponses?

C Is the process stable?

C Are the residuals (the difference between the modelpredictions and the actual observations) wellbehaved?



XI-92 (1178)

,

X1

,

X2

,

X3

Experimental Assumptions (Continued)

Are the Residuals Well Behaved?

Residuals can be thought of as elements of variationunexplained by the fitted model. Residuals are expectedto be normally and independently distributed with amean of 0 and some constant variance.

These are the assumptions behind ANOVA and classicalregression analysis.

Residualssuggest theX1 model is

properlyspecified.

Residualssuggest thatthe variance

increases withX2

Residualssuggest theneed for a

quadratic termadded to X3.


XI. ADVANCED STATISTICSDESIGN OF EXPERIMENTS / SIMPLE EXPERIMENTS

XI-93 (1179)

C84%

A63%

69%B

79%A

A70%

B87%

83%B

D88%

E92%

71%A

94%E

91%E

69%A

88%C

96%D

pH

Concentration

Evolutionary Operations

EVOP emphasizes a conservative experimental strategyfor continuous process improvement. Tests arecentered on the best conditions from previousexperiments. Small incremental changes are made sothat little or no process scrap is generated.

EVOP Experimentation


XI. ADVANCED STATISTICSDESIGN OF EXPERIMENTS / BLOCK DESIGNS

XI-94 (1180)

Randomized Block Plans

One may be able to divide the experiment into blocks, orplanned homogeneous groups. When each group in theexperiment contains exactly one measurement on everytreatment, the experimental plan is called a randomizedblock plan.

A randomized incomplete block (tension response)design is shown below.

TreatmentBlock(Days)

A B C D

1 -5 Omitted -18 -102 Omitted -27 -14 -53 -4 -14 -23 Omitted4 -1 -22 Omitted -12



XI-95 (1181)

Latin Square Designs

In Latin square designs a third variable, theexperimental treatment, is applied to the sourcevariables in a balanced fashion. The Latin square planis restricted by two conditions:

C The number of rows, columns and treatments mustbe the same.

C There should be no interactions between row andcolumn factors, since these cannot be measured.

A Latin square design is essentially a fractional-factorialexperiment.



XI-95 (1182)

Latin Square Designs (Continued)

Consider the following 5 x 5 Latin square:

Carburetor TypeCar I II III IV V

1 A B C D E2 B C D E A3 C D E A B4 D E A B C5 E A B C D

In the above design, five automobiles and fivecarburetors are used to evaluate gas mileage by fivedrivers (A, B, C, D, and E). Note that only 25 of thepotential 125 combinations are tested. Thus, theresultant experiment is a one-fifth, fractional-factorial.

Similar 3 x 3, 4 x 4, and 6 x 6 designs may be utilized.



XI-96 (1183)

Graeco-Latin Designs

Graeco-Latin square designs are sometimes useful toeliminate more than two sources of variability in anexperiment. A Graeco-Latin design is an extension ofthe Latin square design, but one extra blocking variableis added for a total of three blocking variables.

Consider the following 4 X 4 Graeco-Latin Design:

Carburetor TypeCar I II III IV Drivers

1 Aα Bβ Cγ Dδ A,B,C,D2 Bδ Aγ Dβ Cα3 Cβ Dα Aδ Bγ Days4 Dγ Cδ Bα Aβ α,β,γ,δ



XI-96 (1184)

Hyper-Graeco-Latin Designs

A Hyper-Graeco-Latin square design permits the studyof treatments with more than three blocking variables.

Carburetor TypeCar I II III IV Drivers Tires

1 AαMφ BβNΧ CγOΨ DδPΩ A,B,C,D M,N,O,P2 BδNΩ AγMΨ DβPΧ CαOφ3 CβOΧ DαPφ AδMΩ BγNΨ Days Speeds4 DγPΨ CδOΩ BαNφ AβMΧ α,β,γ,δ φΧΨΩ


XI. ADVANCED STATISTICSDESIGN OF EXPERIMENTS / FULL-FACTORIAL EXPERIMENTS

XI-97 (1185)

Full-factorial Experiments

Suppose that pressure, temperature and concentrationare three key variables affecting the yield of a chemicalprocess which is currently running at 64%. In order tofind out the effect of all three factors and theirinteractions, conduct 2 3 = 8 experiments. This is calleda full-factorial experiment. The low and high levels ofinput factors are noted below by (-) and (+).

Exp. No. Temp. Press. Conc. % Yield1 - - - 552 + - - 773 - + - 474 + + - 735 - - + 566 + - + 807 - + + 518 + + + 73

Average 64

Temperature: (-) = 120EC (+) = 150ECPressure: (-) = 10 psi (+) = 14 psiConcentration: (-) = 10N (+) = 12N



XI-98 (1186)

( ) ( )77 + 73 + 80 + 73 - 55 + 47 + 56 + 51The temperature effect = = 23.54

( ) ( )47 + 73 + 51 + 73 - 55 + 77 + 56 + 80The pressure effect = = -64

( ) ( )56 + 80 + 51 + 73 - 55 + 77 + 47 + 73The concentration effect = = 24

( ) ( )55 + 73 + 56 + 73 - 77 + 47 + 80 + 51T x P interaction = = 0.54

( ) ( )

( ) ( )

( ) ( )

55 + 77 + 51 + 73 - 47 + 73 + 56 + 80P x C interaction = = 04

55 + 47 + 80 + 73 - 77 + 73 + 56 + 51T x C interaction = = -0.54

77 + 47 + 56 + 73 - 55 + 73 + 80 + 51T x P x C interaction = = -1.54

Full-factorial Experiments (Continued)



XI-99 (1187)


InteractionsEXP. T P C TXP PXC TXC TXPXC YIELD

1 - - - + + + - 552 + - - - + - + 773 - + - - - + + 474 + + - + - - - 735 - - + + - - + 566 + - + - - + - 807 - + + - + - - 518 + + + + + + + 73

The best combination of factors is: high temperature,low pressure, and high concentration.



XI-100 (1188)

( ) ( )

( ) ( )

( ) ( )

77 + 73 - 47 + 56The temperature effect = = 23.52

47 + 73 - 77 + 56The pressure effect = = -6.52

56 + 73 - 47 + 77The concentration effect = = 2.52


Comparison to a Fractional Factorial Design

Consider the following fractional factorial experiment, inwhich only the main effects can be determined.

Exp. T P C Yield2 + - - 773 - + - 475 - - + 568 + + + 73

The results are not identical, but, the same relativeconclusions as to the effects of temperature, pressure,and concentration on the final yield can be drawn.


XI. ADVANCED STATISTICS / DESIGN OF EXPERIMENTS /FRACTIONAL-FACTORIAL EXPERIMENTS

XI-101 (1189)

Two-Level Fractional Factorial Example

1. Select a process

2. Identify the output factors of concern

3. Identify the input factors and levels to beinvestigated

4. Select a design (from a catalogue, Taguchi, self-created, etc.)

5. Conduct the experiment under the predeterminedconditions

6. Collect the data (relative to the identified outputs)

7. Analyze the data and draw conclusions

A example of a two-level, fractional factorial CQE TestSuccess is given in the CQE Primer. Please note thatthe values given were arbitrarily chosen for thepurposes of the example, and are not based on factualdata.

The student is encouraged to work through thisexample.



XI-106 (1190)

FACTORG C A D B E F

0

10

20

30

40

50

60

70SUM OF SQUARES SCREE PLOT

CQE Test Success (Continued)

The significance of the CQE design results may beexamined using the sum of squares and a scree plot.

Note that( )2 valueSS =

8Δ

FACTOR Δ SSG 23 66.1C 20 50A 13 21.2D 5 3.1B 0 0E 0 0F 0 0



XI-107 (1191)

3.1MSE (Mean Square Error) = = 0.7754

CQE Test Success (Continued)The scree plot indicates that factors D, B, E, and F arenoise. The SS (sum of squares) for the error term is 3.1(3.1 + 0 + 0 + 0).

The maximum F table given in the CQE Primeraccommodates screening designs for runs of 8, 12, 16,20, and 24. p is the number of noise factors averaged toderive the MSE, and k is the number of factors.

The maximum F ratio for factor G is: 66.1 = 85.290.775

The critical max-F value for k-1=7, p=4 and α=0.05 is 73.Thus, factor G is important at the 95% confidence level.

The maximum F ratio for factor C is 50 = 65.420.775

The critical max-F value for k-1=7, p=4 and α=0.10 is 49.Thus, factor C is important at the 90% confidence level.

The maximum F ratio for factor A is 21.1 = 27.220.775

The critical max-F values for k-1=7, p=4 and α=0.10 is 49.Therefore, factor A is not considered important.


XI. ADVANCED STATISTICSDESIGN OF EXPERIMENTS / OTHER DESIGNS

XI-108 (1192)

Plackett-Burman Designs

Plackett-Burman designs are used for screeningexperiments. PB designs are very economical. The runnumber is a multiple of four rather than a power of 2.

PB geometric designs are two-level designs with 4, 8,16, 32, 64, and 128 runs and work best as screeningdesigns. Each interaction effect is confounded withexactly one main effect.

All other two-level PB designs (12, 20, 24, 28, etc.) arenon-geometric designs. In these designs a two-factorinteraction will be partially confounded with each of theother main effects in the study. Thus, the non-geometricdesigns are essentially “main-effect designs,” whenthere is reason to believe any interactions are of littlepractical importance. A PB design in 12 runs, forexample, may be used to conduct an experimentcontaining up to 11 factors.



XI-108 (1193)

Plackett-Burman Designs (Continued)

FactorsExp X1 X2 X3 X4 X5 X6 X7 X8 X9 X10 X11

1 + + + + + + + + + + +2 - + - + + + - - - + -3 - - + - + + + - - - +4 + - - + - + + + - - -5 - + - - + - + + + - -6 - - + - - + - + + + -7 - - - + - - + - + + +8 + - - - + - - + - + +9 + + - - - + - - + - +

10 + + + - - - + - - + -11 - + + + - - - + - - +12 + - + + + - - - + - -

Plackett-Burman Non-Geometric Design(12 Runs/11 Factors)

With a 20-run design, an experimenter can do ascreening experiment for up to 19 factors. As many as27 factors can be evaluated in a 28 run design.



XI-109 (1194)

TEMPERATURE

CONCENTRATION

( 200 )

( 100 )

( 000 ) ( 001 ) ( 002 )

( 222 )

( 122 )

( 022 )

( 012 )

PRESSURE

Three Factor, Three Level Experiments

A 1/3 fractional-factorial design, three factors, threelevels is shown below. Three level designs are alwaysrepresented as 0, 1, and 2.

EXPER. CONC. PRESS. TEMP.1 0 0 02 0 1 23 0 2 14 1 0 15 1 1 06 1 2 27 2 0 28 2 1 19 2 2 0



XI-110 (1195)

Taguchi Designs

The Taguchi philosophy emphasizes two tenets:

(1) reduce the variation of a product or processwhich reduces the loss to society

(2) use a proper development strategy tointentionally reduce variation

Orthogonal Arrays Degrees of Freedom

Let d.f. = degrees of freedom

Let k = number of factor levels

For factor A, d.f.A = kA - 1

For factor B, d.f.B = kB - 1

For A x B interaction, d.f.AB = d.f.A x d.f.B

d.f.min = Gd.f. all factors + Gd.f. all interactions of interest



XI-110 (1196)

Taguchi Designs (Continued)

Two - Level OAs

OAs can be used to assign factors and interactions.The simplest OA is an L4 (four trial runs).

ColumnsTrial 1 2 3

1 1 1 12 1 2 23 2 1 24 2 2 1

An L4 OA Design

Factors A and B can be assigned to any two of the threecolumns. The remaining column is the interactioncolumn. Assume a trial is conducted with two repeatruns for each trial. Assign factor A to column 1 andfactor B to column 2. The interaction is then assignedto column 3.



XI-111 (1197)

( ) ( )

( ) ( )

( )

2

T

2 2

A B

2

3

e T A B 3

e

39SS = 16 + 49 + 9 + 25 + 1 + 4 + 64 + 81 - = 58.8758

20 - 19 25 - 14SS = = 0.125 SS = = 15.1258 8

28 - 11SS = = 36.1258

SS = SS - SS - SS - SSSS = 58.875 - 0.125 - 15.125 - 36.125 = 7.5


Two - Level OAs (Continued)

Column Raw Data Simplified (Simplified)2

Trial 1 2 3 (y1) y1 - 40 (y1 - 40)2

1 1 1 1 44 47 4 7 16 492 1 2 2 43 45 3 5 9 253 2 1 2 41 42 1 2 1 44 2 2 1 48 49 8 9 64 81

Totals 39 249

Factor A GA1= 4+7+3+5 = 19 GA2= 1+2+8+9 = 20Factor B GB1= 4+7+1+2 = 14 GB2= 3+5+8+9 = 25A x B Interaction

G31= 4+7+8+9 = 28 G32= 3 + 5 + 1 + 2 = 11



XI-112 (1198)

21 3


Linear Graphs & Triangular Tables

Column 2 31 3 22 1

L4 Linear Graph L4 Triangular Table

The L4 linear graph shows that if the two factors areassigned to columns 1 and 2, the interaction will be incolumn 3. The L4 triangular table shows that if the twofactors are put in columns 1 and 3, the other point of thetriangle for the interaction is in column 2. If the twofactors are put in columns 2 and 3, the interaction will befound in column 1.



XI-112 (1199)

1

2

3

4

5

6

1

32

6

45

7

7


Linear Graphs & Triangular Tables (Cont.)

Type A Type BL8 Linear Graphs

The next level of linear graphs are for an L8 OA. Thelinear graphs in the Figure indicate that several factorscan be assigned to different columns and severaldifferent interactions may be evaluated in differentcolumns. If three factors (A, B and C) are assigned, theL8 linear graph indicates the assignment to columns 1,2 and 4 located at the vertices in the type A triangle.



XI-113 (1200)



ColumnNumbers

Column Numbers2 3 4 5 6 7

1 3 2 5 4 7 62 1 6 7 4 53 7 6 5 44 1 2 35 3 26 1

Triangular Table

The column assignment for the factors and theirinteractions are shown in the Table below. All maineffects and all interactions can be estimated, whichresults in a high-resolution experiment. This is also afull-factorial experiment.

Column Number1 2 3 4 5 6 7A B A x B C A x C B x C A x B x C

Column Assignments for an L8 Linear Graph



XI-114 (1201)



A number of Taguchi designs are available on the NISTwebsite and other internet locations. Examples include:

L4: 3 Factors - 2 LevelsL8: 7 Factors - 2 LevelsL9: 4 Factors - 3 Levels

L12: 11 Factors - 2 LevelsL16: 15 Factors - 2 Levels

L16b: 5 Factors - 4 LevelsL18: 1 Factor - 2 Levels and 7 Factors - 3 LevelsL25: 6 Factors - 5 LevelsL27: 13 Factors - 2 LevelsL32: 30 Factors - 2 Levels

L32b: 1 Factor - 2 Levels and 9 Factors - 4 LevelsL36: 11 Factors - 2 Levels and 12 Factors - 3 LevelsL50: 1 Factor - 2 Levels and 11 Factors - 5 LevelsL54: 1 Factor - 2 Levels and 25 Factors - 3 LevelsL64: 31 Factors - 2 Levels

L64b: 20 Factors - 4 LevelsL81: 40 Factors - 3 Levels

The above list represents the most common designs.



XI-115 (1202)

Taguchi vs. Modern DOE

Taguchi experiments are based on orthogonal arrays.They are usually identified with a name like, L8 toindicate an array with 8 runs. Modern experimentaldesigns are also based on orthogonal arrays. They areidentified with a superscript to indicate the number ofvariables. Thus, the design 23 also has eight runs. Bothmethods have different emphasis but are very similar.

To rotate the table on the following page, use thecommands:

<Shift><Ctrl><+> clockwise rotation

<Shift><Ctrl><-> counter clockwise rotation



XI-115 (1203)

Mod

ern

23 Des

ign

Tagu

chi L

8 Arr

ayFa

ctor

Inte

ract

ions

Col

umn

noR

unA

BC

AB

AC

BC

AB

C1

23

45

67

1-1

-1-1

11

1-1

11

11

11

12

1-1

-1-1

-11

11

11

22

22

3-1

1-1

-11

-11

12

21

12

24

11

-11

-1-1

-11

22

22

11

5-1

-11

1-1

-11

21

21

21

26

1-1

1-1

1-1

-12

12

21

21

7-1

11

-1-1

1-1

22

11

22

18

11

11

11

12

21

21

12

42

16

53

7C

BB

CA

AC

AB

AB

C

Taguchi vs. Modern DOE (Cont.)


XI. ADVANCED STATISTICSQUESTIONS

XI-117 (1204)

11.2. When finding a confidence interval for mean μ, based on a samplesize of n:

a. Increasing n increases the intervalb. Having to use Sx instead of n decreases the intervalc. The larger the interval, the better the estimate of μd. Increasing n decreases the interval

11.4. Determine whether the following two types of rockets havesignificantly different variances at the 5% level. Assume that thelarger variance goes in the numerator.

Rocket A Rocket B

61 readings 31 readings1,347 miles2 2,237 miles2

a. Significant difference because Fcalc < F tableb. No significant difference because Fcalc < F tablec. Significant difference because Fcalc > F tabled. No significant difference because Fcalc > F table

11.7. Given the data below is normally distributed, and the populationstandard deviation is 3.1, what is the 90% confidence interval for themean?

22, 23, 19, 17, 29, 25

a. 20.88 - 24.12b. 20.42 - 24.59c. 21.65 - 23.35d. 17.4 - 27.60

Answers: 2. d, 4. b, 7. b



XI-118 (1205)

11.12. A designed experiment has been conducted at three levels (A, B,and C) yielding the following "coded" data:

A B C6 5 33 9 45 1 22

As a major step in the analysis, the degrees of freedom for the "error"sum of squares is determined to be:

a. 7b. 9c. 6d. 3

11.13. The power of efficiency in designed experiments lies in the:

a. Random order of performanceb. Sequential procedure of conjecture, to design, and then to analysisc. Hidden replicationd. Large number of possible combinations of factors

11.18. A 2-level 5-factor experiment is being conducted to optimize thereliability of an electronic control module. A half replicate of thestandard full-factorial experiment is proposed. The number oftreatment combinations will be:

a. 10b. 16c. 25d. 32

Answers: 12. a, 13. c, 18. b



XI-119 (1206)

11.23. Which of the following is NOT true in regards to blocking?

a. A block is a dummy factor which doesn't interact with real factorsb. A blocking factor has 2 levelsc. A block is a subdivision of the experimentd. Blocks are used to compensate when run randomization is restricted

11.29. The difference between setting alpha equal to 0.05, and alphaequal to 0.01, in hypothesis testing is:

a. With alpha equal to 0.05, one is more willing to risk a type I errorb. With alpha equal to 0.05, one is more willing to risk a type II errorc. Alpha equal to 0.05 is a more "conservative" test of the null

hypothesis (H0)d. With alpha equal to 0.05, one is less willing to risk a type I error

11.31. A basic L4 Taguchi design is most similar to:

a. A two-factor, two-level, full-factorialb. A three-factor, two-level, one-half fractional-factorialc. A three-factor, two-level, full-factoriald. A test of a single variable at 4 levels

Answers: 23. b, 29. a, 31. b



XI-120 (1207)

11.33. Which of the following characteristics apply to the Latin squaredesign?

a. The number of treatments must equal 4 or 5b. Interest is centered determining interactionsc. The design is a full-factoriald. Each treatment appears once per row and per column

11.35. Which of the following is a valid null hypothesis?

a. p > 1/8b. mu < 98c. The mean of population A is not equal to the mean of population Bd. mu = 110

11.36. An experiment is being run with 8 factors. Two of the factors aretemperature and pressure. The levels for temperature are 25, 50,and 75. The levels for pressure are 14, 28, 42, and 56. How manydegrees of freedom are required to determine the effect of theinteraction between temperature and pressure?

a. 1b. 2c. 4d. 6

Answers: 33. a, 35. d, 36. d


XII. APPENDIX

XII-1 (1208)

INDEX LEARNING TURNS NOSTUDENT PALE, YET HOLDS THEEEL OF SCIENCE BY THE TAIL.

ALEXANDER POPE


XII. APPENDIX

XII-2 (1209)

Table I - Standard Normal Table

0 Z

Z X.X0 X.X1 X.X2 X.X3 X.X4 X.X5 X.X6 X.X7 X.X8 X.X9

0.00.10.20.30.4

0.5000 0.4602 0.4207 0.3821 0.3446

0.49600.45620.41680.37830.3409

0.49200.45220.41290.37450.3372

0.48800.44830.40900.37070.3336

0.48400.44430.40520.36690.3300

0.48010.44040.40130.36320.3264

0.47610.43640.39740.35940.3228

0.47210.43250.39360.35570.3192

0.46810.42860.38970.35200.3156

0.46410.42470.38590.34830.3121

0.50.60.70.80.9

0.3085 0.2743 0.2420 0.2119 0.1841

0.30500.27090.23890.20900.1814

0.30150.26760.23580.20610.1788

0.29810.26430.23270.20330.1762

0.29460.26110.22970.20050.1736

0.29120.25780.22660.19770.1711

0.28770.25460.22360.19490.1685

0.28430.25140.22060.19220.1660

0.28100.24830.21770.18940.1635

0.27760.24510.21480.18670.1611

1.01.11.21.31.4

0.1587 0.1357 0.1151 0.0968 0.0808

0.15620.13350.11310.09510.0793

0.15390.13140.11120.09340.0778

0.15150.12920.10930.09180.0764

0.14920.12710.10750.09010.0749

0.14690.12510.10560.08850.0735

0.14460.12300.10380.08690.0721

0.14230.12100.10200.08530.0708

0.14010.11900.10030.08380.0694

0.13790.11700.09850.08230.0681

1.51.61.71.81.9

0.0668 0.0548 0.0446 0.0359 0.0287

0.06550.05370.04360.03510.0281

0.06430.05260.04270.03440.0274

0.06300.05160.04180.03360.0268

0.06180.05050.04090.03290.0262

0.06060.04950.04010.03220.0256

0.05940.04850.03920.03140.0250

0.05820.04750.03840.03070.0244

0.05710.04650.03750.03010.0239

0.05590.04550.03670.02940.0233

2.02.12.22.32.4

0.0228 0.0179 0.0139 0.0107 0.0082

0.02220.01740.01360.01040.0080

0.02170.01700.01320.01020.0078

0.02120.01660.01290.00990.0075

0.02070.01620.01250.00960.0073

0.02020.01580.01220.00940.0071

0.01970.01540.01190.00910.0069

0.01920.01500.01160.00890.0068

0.01880.01460.01130.00870.0066

0.01830.01430.01100.00840.0064

2.52.62.72.82.93.0

0.0062 0.0047 0.0035 0.0026 0.0019 0.00135

0.00600.00450.00340.00250.0018

0.00590.00440.00330.00240.0018

0.00570.00430.00320.00230.0017

0.00550.00410.00310.00230.0016

0.00540.00400.00300.00220.0016

0.00520.00390.00290.00210.0015

0.00510.00380.00280.00210.0015

0.00490.00370.00270.00200.0014

0.00480.00360.00260.00190.0014


XII. APPENDIX

XII-3 (1210)

Table II - Six Sigma Failure RatesWith a 1.5 σ Process Shift With No Process Shift

Z ppm Z ppm Z ppm Z ppm

1.0 697,672.15 3.6 17,864.53 1.0 317,310.52 3.6 318.291.1 660,082.92 3.7 13,903.50 1.1 271,332.20 3.7 215.661.2 621,378.38 3.8 10,724.14 1.2 230,139.46 3.8 144.741.3 581,814.88 3.9 8,197.56 1.3 193,601.10 3.9 96.231.4 541,693.78 4.0 6,209.70 1.4 161,513.42 4.0 63.371.5 501,349.97 4.1 4,661.23 1.5 133,614.46 4.1 41.341.6 461,139.78 4.2 3,467.03 1.6 109,598.58 4.2 26.711.7 421,427.51 4.3 2,555.19 1.7 89,130.86 4.3 17.091.8 382,572.13 4.4 1,865.88 1.8 71,860.53 4.4 10.831.9 344,915.28 4.5 1,349.97 1.9 57,432.99 4.5 6.802.0 308,770.21 4.6 967.67 2.0 45,500.12 4.6 4.232.1 274,412.21 4.7 687.20 2.1 35,728.71 4.7 2.602.2 242,071.41 4.8 483.48 2.2 27,806.80 4.8 1.592.3 211,927.71 4.9 336.98 2.3 21,448.16 4.9 0.9602.4 184,108.21 5.0 232.67 2.4 16,395.06 5.0 0.5742.5 158,686.95 5.1 159.15 2.5 12,419.36 5.1 0.3402.6 135,686.77 5.2 107.83 2.6 9,322.44 5.2 0.2002.7 115,083.09 5.3 72.37 2.7 6,934.05 5.3 0.1162.8 96,809.10 5.4 48.12 2.8 5,110.38 5.4 0.0672.9 80,762.13 5.5 31.69 2.9 3,731.76 5.5 0.0383.0 66,810.63 5.6 20.67 3.0 2,699.93 5.6 0.0213.1 54,801.40 5.7 13.35 3.1 1,935.34 5.7 0.0123.2 44,566.73 5.8 8.55 3.2 1,374.40 5.8 0.0073.3 35,931.06 5.9 5.42 3.3 966.97 5.9 0.0043.4 28,716.97 6.0 3.40 3.4 673.96 6.0 0.0023.5 22,750.35 6.1 2.11 3.5 465.35 6.1 0.001


XII. APPENDIX

XII-4 (1211)

Table III - Poisson DistributionProbability of r or fewer occurrences of an event that has an averagenumber of occurrences equal to np.

r

np0 1 2 3 4 5 6 7 8 9

0.020.040.060.080.10

0.150.200.250.30

0.350.400.450.50

0.550.600.650.700.75

0.800.850.900.951.00

1.1 1.2 1.3 1.4 1.5

1.6 1.7 1.8 1.9 2.0

0.9800.9610.9420.9230.905

0.8610.8190.7790.741

0.7050.6700.6380.607

0.5770.5490.5220.4970.472

0.4490.4270.4070.3870.368

0.3330.3010.2730.2470.223

0.2020.1830.1650.1500.135

1.0000.9990.9980.9970.995

0.9900.9820.9740.963

0.9510.9380.9250.910

0.8940.8780.8610.8440.827

0.8090.7910.7720.7540.736

0.6990.6630.6270.5920.558

0.5250.4930.4630.4340.406

1.0001.0001.0001.000

0.9990.9990.9980.996

0.9940.9920.9890.986

0.9820.9770.9720.9660.959

0.9530.9450.9370.9290.920

0.9000.8790.8570.8330.809

0.7830.7570.7310.7040.677

1.0001.0001.0001.000

1.0000.9990.9990.998

0.9980.9970.9960.9940.993

0.9910.9890.9870.9840.981

0.9740.9660.9570.9460.934

0.9210.9070.8910.8750.857

1.0001.0001.000

1.0001.0000.9990.9990.999

0.9990.9980.9980.9970.996

0.9950.9920.9890.9860.981

0.9760.9700.9640.9560.947

1.0001.0001.000

1.0001.0001.0001.0000.999

0.9990.9980.9980.9970.996

0.9940.9920.9900.9870.983

1.000

1.0001.0001.0000.9990.999

0.9990.9980.9970.9970.995

1.0001.000

1.0001.0000.9990.9990.999

1.0001.0001.000


XII. APPENDIX

XII-5 (1212)

Table III - Poisson Distribution (Cont.) r

np0 1 2 3 4 5 6 7 8 9

2.22.42.62.83.0

3.23.43.63.84.0

4.24.44.64.85.0

5.25.45.65.86.0

0.1110.0910.0740.0610.050

0.0410.0330.0270.0220.018

0.0150.0120.0100.0080.007

0.0060.0050.0040.0030.002

0.3550.3080.2670.2310.199

0.1710.1470.1260.1070.092

0.0780.0660.0560.0480.040

0.0340.0290.0240.0210.017

0.6230.5700.5180.4690.423

0.3800.3400.3030.2690.238

0.2100.1850.1630.1430.125

0.1090.0950.0820.0720.062

0.8190.7790.7360.6920.647

0.6030.5580.5150.4730.433

0.3950.3590.3260.2940.265

0.2380.2130.1910.1700.151

0.9280.9040.8770.8480.815

0.7810.7440.7060.6680.629

0.5900.5510.5130.4760.440

0.4060.3730.3420.3130.285

0.9750.9640.9510.9350.916

0.8950.8710.8440.8160.785

0.7530.7200.6860.6510.616

0.5810.5460.5120.4780.446

0.9930.9880.9830.9760.966

0.9550.9420.9270.9090.889

0.8670.8440.8180.7910.762

0.7320.7020.6700.6380.606

0.9980.9970.9950.9920.988

0.9830.9770.9690.9600.949

0.9360.9210.9050.8870.867

0.8450.8220.7970.7710.744

1.0000.9990.9990.9980.996

0.9940.9920.9880.9840.979

0.9720.9640.9550.9440.932

0.9180.9030.8860.8670.847

1.0001.0000.9990.999

0.9980.9970.9960.9940.992

0.9890.9850.9800.9750.968

0.9600.9510.9410.9290.916

10 11 12 13 14 15 162.83.03.23.43.63.84.0

4.24.44.64.85.0

5.25.45.65.86.0

1.0001.0001.0000.9990.9990.9980.997

0.9960.9940.9920.9900.986

0.9820.9770.9720.9650.957

1.0001.0000.9990.999

0.9990.9980.9970.9960.995

0.9930.9900.9880.9840.980

1.0001.000

1.0000.9990.9990.9990.998

0.9970.9960.9950.9930.991

1.0001.0001.0000.999

0.9990.9990.9980.9970.996

1.000

1.0001.0000.9990.9990.999

1.0001.0000.999 1.000


XII. APPENDIX

XII-6 (1213)

Table III - Poisson Distribution (Cont.) r

np0 1 2 3 4 5 6 7 8 9

6.2 6.4 6.6 6.8 7.0

7.2 7.4 7.6 7.8

8.0 8.5 9.0 9.510.0

0.0020.0020.0010.0010.001

0.0010.0010.0010.000

0.0000.0000.0000.0000.000

0.0150.0120.0100.0090.007

0.0060.0050.0040.004

0.0030.0020.0010.0010.000

0.0540.0460.0400.0340.030

0.0250.0220.0190.016

0.0140.0090.0060.0040.003

0.1340.1190.1050.0930.082

0.0720.0630.0550.048

0.0420.0300.0210.0150.010

0.2590.2350.2130.1920.173

0.1560.1400.1250.112

0.1000.0740.0550.0400.029

0.4140.3840.3550.3270.301

0.2760.2530.2310.210

0.1910.1500.1160.0890.067

0.5740.5420.5110.4800.450

0.4200.3920.3650.338

0.3130.2560.2070.1650.130

0.7160.6870.6580.6280.599

0.5690.5390.5100.481

0.4530.3860.3240.2690.220

0.8260.8030.7800.7550.729

0.7030.6760.6480.620

0.5930.5230.4560.3930.333

0.9020.8860.8690.8500.830

0.8100.7880.7650.741

0.7170.6530.5870.5220.458

10 11 12 13 14 15 16 17 18 19

6.2 6.4 6.6 6.8 7.0

7.2 7.4 7.6 7.8

8.0 8.5 9.0 9.510.0

0.9490.9390.9270.9150.901

0.8870.8710.8540.835

0.8160.7630.7060.6450.583

0.9750.9690.9630.9550.947

0.9370.9260.9150.902

0.8880.8490.8030.7520.697

0.9890.9860.9820.9780.973

0.9670.9610.9540.945

0.9360.9090.8760.8360.792

0.9950.9940.9920.9900.987

0.9840.9800.9760.971

0.9660.9490.9260.8980.864

0.9980.9970.9970.9960.994

0.9930.9910.9890.986

0.9830.9730.9590.9400.917

0.9990.9990.9990.9980.998

0.9970.9960.9950.993

0.9920.9860.9780.9670.951

1.0001.0000.9990.9990.999

0.9990.9980.9980.997

0.9960.9930.9890.9820.973

1.0001.0001.000

0.9990.9990.9990.999

0.9980.9970.9950.9910.986

1.0001.0001.0001.000

0.9990.9990.9980.9960.993

1.0000.9990.9990.9980.997

20 21 22

8.5 9.0 9.510.0

1.0001.0000.9990.998

1.0000.999 1.000


XII. APPENDIX

XII-7 (1214)

Table IV - Binomial DistributionProbability of r or fewer occurrences of an event in n trials

n r

p (the probability of occurrence on each trial)

0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50

2

3

4

5

6

7

8

9

10

01

012

0123

01234

012345

0123456

01234567

012345678

0123456789

0.90250.9975

0.85740.99280.9999

0.81450.98600.99951.0000

0.77380.97740.99881.00001.0000

0.73510.96720.99780.99991.00001.0000

0.69830.95560.99620.99981.00001.00001.0000

0.66340.94280.99420.99961.00001.00001.00001.0000

0.63020.92880.99160.99941.00001.00001.00001.00001.0000

0.59870.91390.98850.99900.99991.00001.00001.00001.00001.0000

0.81000.9900

0.72900.97200.9990

0.65610.94770.99630.9999

0.59050.91850.99140.99951.0000

0.53140.88570.98420.99870.99991.0000

0.47830.85030.97430.99730.99981.00001.0000

0.43050.81310.96190.99500.99961.00001.00001.0000

0.38740.77480.94700.99170.99910.99991.00001.00001.0000

0.34870.73610.92980.98720.99840.99991.00001.00001.00001.0000

0.72250.9775

0.61410.93920.9966

0.52200.89050.98800.9995

0.44370.83520.97340.99780.9999

0.37710.77650.95270.99410.99961.0000

0.32060.71660.92620.98790.99880.99991.0000

0.27250.65720.89480.97860.99710.99981.00001.0000

0.23160.59950.85910.96610.99440.99941.00001.00001.0000

0.19690.54430.82020.95000.99010.99860.99991.00001.00001.0000

0.64000.9600

0.51200.89600.9920

0.40960.81920.97280.9984

0.32770.73730.94210.99330.9997

0.26210.65540.90110.98300.99840.9999

0.20970.57670.85200.96670.99530.99961.0000

0.16780.50330.79690.94370.98960.99880.99991.0000

0.13420.43620.73820.91440.98040.99690.99971.00001.0000

0.10740.37580.67780.87910.96720.99360.99910.99991.00001.0000

0.56250.9375

0.42190.84380.9844

0.31640.73830.94920.9961

0.23730.63280.89650.98440.9990

0.17800.53390.83060.96240.99540.9998

0.13350.44490.75640.92940.98710.99870.9999

0.10010.36710.67850.88620.97270.99580.99961.0000

0.07510.30030.60070.83430.95110.99000.99870.99991.0000

0.05630.24400.52560.77590.92190.98030.99650.99961.00001.0000

0.49000.9100

0.34300.78400.9730

0.24010.65170.91630.9919

0.16810.52820.83690.96920.9976

0.11760.42020.74430.92950.98910.9993

0.08240.32940.64710.87400.97120.99620.9998

0.05760.25530.55180.80590.94200.98870.99870.9999

0.04040.19600.46280.72970.90120.97470.99570.99961.0000

0.02820.14930.38280.64960.84970.95270.98940.99840.99991.0000

0.42250.8775

0.27460.71820.9571

0.17850.56300.87350.9850

0.11600.42840.76480.94600.9947

0.07540.31910.64710.88260.97770.9982

0.04900.23380.53230.80020.94440.99100.9994

0.03190.16910.42780.70640.89390.97470.99640.9998

0.02070.12110.33730.60890.82830.94640.98880.99860.9999

0.01350.08600.26160.51380.75150.90510.97400.99520.99951.0000

0.36000.8400

0.21600.64800.9360

0.12960.47520.82080.9744

0.07780.33700.68260.91300.9898

0.04670.23330.54430.82080.95900.9959

0.02800.15860.41990.71020.90370.98120.9984

0.01680.10640.31540.59410.82630.95020.99150.9993

0.01010.07050.23180.48260.73340.90060.97500.99620.9997

0.00600.04640.16730.38230.63310.83380.94520.98770.99830.9999

0.30250.7975

0.16640.57480.9089

0.09150.39100.75850.9590

0.05030.25620.59310.86880.9815

0.02770.16360.44150.74470.93080.9917

0.01520.10240.31640.60830.84710.96430.9963

0.00840.06320.22010.47700.73960.91150.98190.9983

0.00460.03850.14950.36140.62140.83420.95020.99090.9992

0.00250.02320.09960.26600.50440.73840.89800.97260.99550.9997

0.25000.7500

0.12500.50000.8750

0.06250.31250.68750.9375

0.03120.18750.50000.81250.9688

0.01560.10940.34380.65620.89060.9844

0.00780.06250.22660.50000.77340.93750.9922

0.00390.03520.14450.36330.63670.85550.96480.9961

0.00200.01950.08980.25390.50000.74610.91020.98050.9980

0.00100.01070.05470.17190.37700.62300.82810.94530.98930.9990


XII. APPENDIX

XII-8 (1215)

Table V - t Distribution

tα

d.f. t.100 t.050* t.025** t.010 t.005 d.f.

123456789

1011121314151617181920212223242526272829inf.

3.0781.8861.6381.5331.4761.4401.4151.3971.3831.3721.3631.3561.3501.3451.3411.3371.3331.3301.3281.3251.3231.3211.3191.3181.3161.3151.3141.3131.3111.282

6.3142.9202.3532.1322.0151.9431.8951.8601.8331.8121.7961.7821.7711.7611.7531.7461.7401.7341.7291.7251.7211.7171.7141.7111.7081.7061.7031.7011.6991.645

12.7064.3033.1822.7762.5712.4472.3652.3062.2622.2282.2012.1792.1602.1452.1312.1202.1102.1012.0932.0862.0802.0742.0692.0642.0602.0562.0522.0482.0451.960

31.8216.9654.5413.7473.3653.1432.9982.8962.8212.7642.7182.6812.6502.6242.6022.5832.5672.5522.5392.5282.5182.5082.5002.4922.4852.4792.4732.4672.4622.326

63.6579.9255.8414.6044.0323.7073.4993.3553.2503.1693.1063.0553.0122.9772.9472.9212.8982.8782.8612.8452.8312.8192.8072.7972.7872.7792.7712.7632.7562.576

123456789

1011121314151617181920212223242526272829inf.

* one tail 5% α risk ** two tail 5% α risk


XII. APPENDIX

XII-9 (1216)

X 2 X 20.95 0.05

Table VI - Critical Values of theChi-Square (X2) Distribution

DF X20.99 X2

0.95 X20.90 X2

0.10 X20.05 X2

0.01

1 0.00016 0.0039 0.0158 2.71 3.84 6.632 0.0201 0.1026 0.2107 4.61 5.99 9.213 0.115 0.352 0.584 6.25 7.81 11.344 0.297 0.711 1.064 7.78 9.49 13.28

5 0.554 1.15 1.61 9.24 11.07 15.096 0.872 1.64 2.20 10.64 12.59 16.817 1.24 2.17 2.83 12.02 14.07 18.488 1.65 2.73 3.49 13.36 15.51 20.099 2.09 3.33 4.17 14.68 16.92 21.67

10 2.56 3.94 4.87 15.99 18.31 23.2111 3.05 4.57 5.58 17.28 19.68 24.7312 3.57 5.23 6.30 18.55 21.03 26.2213 4.11 5.89 7.04 19.81 22.36 27.6914 4.66 6.57 7.79 21.06 23.68 29.1415 5.23 7.26 8.55 22.31 25.00 30.5816 5.81 7.96 9.31 23.54 26.30 32.0018 7.01 9.39 10.86 25.99 28.87 34.8120 8.26 10.85 12.44 28.41 31.41 37.5724 10.86 13.85 15.66 33.20 36.42 42.9830 14.95 18.49 20.60 40.26 43.77 50.8940 22.16 26.51 29.05 51.81 55.76 63.6960 37.48 43.19 46.46 74.40 79.08 88.38120 86.92 95.70 100.62 140.23 146.57 158.95


XII. APPENDIX

XII-10 (1217)

f(F)

"

F "

Table VII - Distribution of FF Table α = 0.05

ν1(DF)

ν2(DF) 1 2 3 4 5 6 7 8 9 10 12 15

1 161.4 199.5 215.7 224.6 230.2 234.0 236.8 238.9 240.5 241.9 243.9 245.9

2 18.51 19.00 19.16 19.25 19.30 19.33 19.35 19.37 19.38 19.40 19.41 19.43

3 10.13 9.55 9.28 9.12 9.01 8.94 8.89 8.85 8.81 8.79 8.74 8.70

4 7.71 6.94 6.59 6.39 6.26 6.16 6.09 6.04 6.00 5.96 5.91 5.86

5 6.61 5.79 5.41 5.19 5.05 4.95 4.88 4.82 4.77 4.74 4.68 4.62

6 5.99 5.14 4.76 4.53 4.39 4.28 4.21 4.15 4.10 4.06 4.00 3.94

7 5.59 4.74 4.35 4.12 3.97 3.87 3.79 3.73 3.68 3.64 3.57 3.51

8 5.32 4.46 4.07 3.84 3.69 3.58 3.50 3.44 3.39 3.35 3.28 3.22

9 5.12 4.26 3.86 3.63 3.48 3.37 3.29 3.23 3.18 3.14 3.07 3.01

10 4.96 4.10 3.71 3.48 3.33 3.22 3.14 3.07 3.02 2.98 2.91 2.85

11 4.84 3.98 3.59 3.36 3.20 3.09 3.01 2.95 2.90 2.85 2.79 2.72

12 4.75 3.89 3.49 3.26 3.11 3.00 2.91 2.85 2.80 2.75 2.69 2.62

13 4.67 3.81 3.41 3.18 3.03 2.92 2.83 2.77 2.71 2.67 2.60 2.53

14 4.60 3.74 3.34 3.11 2.96 2.85 2.76 2.70 2.65 2.60 2.53 2.46

15 4.54 3.68 3.29 3.06 2.90 2.79 2.71 2.64 2.59 2.54 2.48 2.40

ν1(DF)

ν2(DF) 20 30 40 50 60 420 2.12 2.04 1.99 1.96 1.95 1.8430 1.93 1.84 1.79 1.76 1.74 1.6240 1.84 1.74 1.69 1.66 1.64 1.5150 1.78 1.69 1.63 1.60 1.58 1.4460 1.75 1.65 1.59 1.56 1.53 1.39

4 1.57 1.46 1.39 1.35 1.32 1.00


XII. APPENDIX

XII-11 (1218)

f(F)

"

F "

Table VIII - Distribution of FF Table α = 0.025

ν1(DF)

ν2(DF) 1 2 3 4 5 6 7 8 9 10 12 15

1 647.8 799.5 864.2 899.6 921.8 937.1 948.2 956.7 963.3 968.6 976.7 984.9

2 38.51 39.00 39.17 39.25 39.30 39.33 39.36 39.37 39.39 39.40 39.41 39.43

3 17.44 16.04 15.44 15.10 14.88 14.73 14.62 14.54 14.47 14.42 14.34 14.25

4 12.22 10.65 9.98 9.60 9.36 9.20 9.07 8.98 8.90 8.84 8.75 8.66

5 10.01 8.43 7.76 7.39 7.15 6.98 6.85 6.76 6.68 6.62 6.52 6.43

6 8.81 7.26 6.60 6.23 5.99 5.82 5.70 5.60 5.52 5.46 5.37 5.27

7 8.07 6.54 5.89 5.52 5.29 5.12 4.99 4.90 4.82 4.76 4.67 4.57

8 7.57 6.06 5.42 5.05 4.82 4.65 4.53 4.43 4.36 4.30 4.20 4.10

9 7.21 5.71 5.08 4.72 4.48 4.32 4.20 4.10 4.03 3.96 3.87 3.77

10 6.94 5.46 4.83 4.47 4.24 4.07 3.95 3.85 3.78 3.72 3.62 3.52

11 6.72 5.26 4.63 4.28 4.04 3.88 3.76 3.66 3.59 3.53 3.43 3.33

12 6.55 5.10 4.47 4.12 3.89 3.73 3.61 3.51 3.44 3.37 3.28 3.18

13 6.41 4.97 4.35 4.00 3.77 3.60 3.48 3.39 3.31 3.25 3.15 3.05

14 6.30 4.86 4.24 3.89 3.66 3.50 3.38 3.29 3.21 3.15 3.05 2.95

15 6.20 4.77 4.15 3.80 3.58 3.41 3.29 3.20 3.12 3.06 2.96 2.86

ν1(DF)

ν2(DF) 20 30 40 50 60 420 2.46 2.35 2.29 2.25 2.22 2.0930 2.20 2.07 2.01 1.97 1.94 1.7940 2.07 1.94 1.88 1.83 1.80 1.6450 1.99 1.87 1.80 1.76 1.72 1.5560 1.94 1.82 1.74 1.70 1.67 1.48

4 1.71 1.57 1.48 1.43 1.39 1.00


XII. APPENDIX

XII-12 (1219)

Table IX - Control Chart FactorsCHART FORAVERAGES

CHART FOR STANDARDDEVIATIONS CHART FOR RANGES

SampleObservations Control limit

Factors

CenterLine

Factors

Control LimitFactors

CenterLine

Factors

Control LimitFactors

n A2 A3 C4 B3 B4 d2 D3 D4

2 1.880 2.659 0.7979 0 3.267 1.128 0 3.267

3 1.023 1.954 0.8862 0 2.568 1.693 0 2.574

4 0.729 1.628 0.9213 0 2.266 2.059 0 2.282

5 0.577 1.427 0.9400 0 2.089 2.326 0 2.114

6 0.483 1.287 0.9515 0.030 1.970 2.534 0 2.004

7 0.419 1.182 0.9594 0.118 1.882 2.704 0.076 1.924

8 0.373 1.099 0.9650 0.185 1.815 2.847 0.136 1.864

9 0.337 1.032 0.9693 0.239 1.761 2.970 0.184 1.816

10 0.308 0.975 0.9727 0.284 1.716 3.078 0.223 1.777

15 0.223 0.789 0.9823 0.428 1.572 3.472 0.347 1.653

20 0.180 0.680 0.9869 0.510 1.490 3.735 0.415 1.585

25 0.153 0.606 0.9896 0.565 1.435 3.931 0.459 1.541

Approximate capability Approximate capability


XII. APPENDIXINDEX

XII-13 (1220)

IndexThe CQE Primer contains the following:

C Author/Name Index

C Subject Index

C Letter answers for questions given in the Primer