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INSE 6220 -- Week 1

Advanced Stat is tical Approaches to Quality

Go over Course Outline

Overview of Quality Control

Introduction to Statistical Quality Control

Dr. A. Ben Hamza Concordia University

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Instructor: Dr. A. Ben Hamza

Office: EV 7.631

Lectures: Fri day 17:45 -20:15

Office Hours: Wednesday 14:00 - 16:00or by appointment

E-Mail: [email protected]

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What is INSE 6220?

INSE 6220 is a Quality Systems Engineering course

You will learn

To apply control charts to monitor the quality characteristics of a product orprocess

Learn techniques for multivariate process monitoring and diagnosis

Design and analyze experiments for improving a manufacturing process

Learn how to determine the reliability of engineering systems

You do not need prior knowledge of MATLAB programmingbut previous experience with programming is a must

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Roadmap of the Course?

ExperimentalDesign

Process QualityEngineering

Process ControlStatistical

Process Control

Modeling Inferences

Capability

An alys is

Statistical

MethodsControl Charts Multivariate

INSE 6220

AcceptanceSampling

Midterm Exam Final Exam

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Administration

Course web page: MyConcordia Portal (Moodle)

Its highly advised to checkMoodle regularly.

Syllabus, Slides, Assignments, Projects, etc Go to MyConcordia Portal (Moodle).

Preliminary exam dates and project due date: Midterm Exam

October 17, 2014 (Friday)

Project due

December 2, 2014

Final Exam

December ??, 2014 (TBA)

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Grading Policy

Important Dates:

Oct 10, 2014: Assignment #1 due Oct 17, 2013: Midterm Exam Nov 28, 2014: Assignment #2 due

Dec 2, 2014: Project Report due Dec ??, 2014: Final Exam

Final Project

Final reports due on December 2, 2014 A final project report, completedindividually or in teams of two, is required. The term project will have only one component:written report.

For more details:MyConcordiaPortal (Moodle)

Two Assignments 10%

Midterm Exam 30%

Project 15%Final Exam 45%

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What this course is about?

This course is about Advanced Statistical Techniques for QualityControl Engineering

Objectives:

To learn the fundamental concepts of Quality Control To learn how to apply control charts to monitor the quality

characteristics of a product or process

To learn techniques for multivariate monitoring and diagnosis To design and analyze experiments for improving a manufacturing

process

To learn how to determine the reliability of engineering systems

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What is this course really about?

We will cover...

Statistical Process Control (SPC)

Control Charts Process and Measurement System Capability Analysis Multivariate Process Monitoring and Control Engineering Process Monitoring and Control Process Design Acceptance Sampling And much more

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What is statistics?

The science of collecting, organizing, analyzing, and interpreting data inorder to make decisions.

Methods for processing and analyzing numbers Methods for helping reduce the uncertainty inherent in decision making

Why Learn Statistics?So you are able to make better sense of the ubiquitous use of numbers:

Business memos

Software defect data

Quality control

Data mining

Quality assurance

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Why?1. Collecting Data

e.g., Survey

2. Presenting Datae.g., Charts, Graphs & Tables

3. Characterizing Datae.g., Average

Data

Analysis

Decision-

Making

1984-1994 T/Maker Co.

What is Statistics?

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Quality

General Understanding:

Desirable characteristics that a productor service should possess.

The Eternal Battle:Quantityvs.Quality

Quantity goes directly to the bottomline:

more product out ==> more $$$

But what are the costs associatedwith Quality?

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What is Quality?

What makes a good quality car

computer

knife childrens toy

pizza delivery

Describe a recent time when youhave experienced bad quality?

So what are the common aspects ofquality?

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What is Quality?

Fitness for Use Conformance to Specifications Producing the Very Best Products

Excellence in Products and Services

Total Customer Satisfaction Exceeding Customer Expectations

Quality improvement starts with reducing Product VARIABILITY.

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Quality - Whats the Big Deal?

Direct Costs of Poor Quality: Lost Revenue: scrap, rework, repair

Lost Productivity: materials, machines, and personnel

Inspection Costs: inspectors, testing machines

External Costs: warranty claims, price adjustments, late charges

Indirect Costs of Poor Quality - Upset Customers: It is 5-7X harder to attract a new customer than to retain a current one

Dissatisfied customers tell 8-20 people about their dissatisfaction.

Satisfied customers only tell 3-5 people.

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Expressing Dissatisfaction

A d iss ati sfi ed

customer

Takes

action

Takes

no action

Public action

can be

Private action

Seeking redress directly from

the firm

Taking legal action

A comp lain t to bu sin ess, pri vate,

or governmental agencies

Stop buying the product or

boycott the seller

Warn friends about the product

and/or seller

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Eight Dimensions of Quality

1. Performance: Will the product do the intended job?2. Reliability: How often does the product fail?3. Durability: How long does the product last?4. Serviceability: How easy is it to repair the product?5.Aesthetics: What does the product look like?6. (Added) Features: What does the product do?7. Perceived Quality: What is the reputation of the company or its

product?

8. Conformance to Standards: Is the product made exactly as thedesigner intended?

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Quality Improvement

Improve quality

Quality is better if variability in the important quality characteristics of a productdecreases.

Quality improvement is the reduction of variability in processes and products.

Quality characteristics

Types Physical: Length, weight, volume, viscosity,

Sensory: taste, appearance, color,

Time orientation: reliability, durability, serviceability,

Data are needed to characterize quality characteristics Data can be classified

Attributes discrete

Variablescontinuous

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Quality Engineering The operational, managerial, and engineering activities that a company uses to ensure

that the quality characteristics of a product are at the nominal or required levels.

We dont want variability from the nominal levels. Statistical methods are used to deal with variability

Control Charts; Acceptance Sampling; Design of Experiments Quality Management System

Total Quality Management

Six Sigma: data-driven methodology for eliminating defects

Control Charts

DOE (Design of Experiments)

QFD (Quality Function Deployment)

Six Sigma processes are executed by Six Sigma Green Belts and SixSigma Black Belts, who are overseen by Six Sigma Master Black Belts.

To achieve Six Sigma, a process must not produce more than 3.4 defects p ermillion opportunities.

A Six Sigma defect is defined as anything outside of customer specifications.

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Key Definitions in Statistics

Apopulation (universe) is the collection of things underconsideration

Asample is a portion of the population selected for

analysis Aparameteris a summary measure computed to

describe a characteristic of the population

Astatistic is a summary measure computed to describe acharacteristic of the sample

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Population and Sample

Population Sample

Use parameters tosummarize features

Use statistics tosummarize features

Inference on the population from the sample

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Why a Manager Needs toKnow about Statistics

To know how to properly present information -KNOWLEDGE

To know how to draw conclusions about populationsbased on sample information

To know how to improve processes- IF YOU DONTKNOW WHATS GOING ON, YOU CAN NEVER

IMPROVE A PROCESS

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Statistical Process Control

new important tool: control chart measurements of production process

during production

prevention instead of detection afterwards

monitoring variance behaviour ofproduction

corresponding definition of quality: variation of process fits within

tolerances

How do we reduce Product Variability? We use Statistical Process Control ! (SPC) Statistical Process Control:

The application of statistical techniques tothe control and improvement of processes.

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SPC/Control Chart

Control charts Useful in monitoring processes,

On-line technique

Walter A. Shewart (1891-1967) Bell Labs, developed the first control chart about 1924

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Design of Experiments

Discovering the key factors that influence process performance Process optimization Off-line technique

A factorial experiment with three factors

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Six Sigma

Use of statistics & other analytical tools has grown steadily for over 93 years Statistical quality control (origins in 1920, explosive growth during WW II,

1950s)

Operations research (1940s)

TQM (Total Quality Management) movement in the 1980s

Reengineering of business processes (late 1980s)

Six-Sigma (origins atMotorola in 1987, expanded impact during 1990s topresent)

Six Sigma focus on Process Improvement with an Emphasis on AchievingSignificant Business Impact

A highly structured strategy for acquiring, assessing, and applying customer,competitor, and enterprise intelligence for the purposes of product, system orenterprise innovation and design.

To achieve Six Sigma, a process must not produce more than3.4 defects per 1million opportunities. A Six Sigma defect is defined as anything outsidecustomer specifications.

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Define

Improve Analyze

MeasureDefine the problem and customerrequirements.

Measure defect rates and documentthe process in its current incarnation.

Analyze process data and determinethe capability of the process.

Improve the process and removedefect causes.

Control process performance andensure that defects do not recur.

Six SigmaThe fundamental objective of the Six Sigma methodology is the implementationof a measurement based strategy that focuses on process improvement andvariation reduction. This is accomplished through the use of DMAIC

(Define, Measure, Analyze, Improve, Control)

Define

Control

Improve Analyze

Measure

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Companies implementing Six Sigma

Motorola Texas Instruments ABB AlliedSignal GE

Bombardier Nokia

DuPont American Express BBA Ford Dow Chemical Johnson Controls Noranda Toshiba

3.4 defects per million opportunities (DPMO)

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Six Sigma TrainingBlack Belt Program Session One Understanding Six Sigma Developing the Language of Six Sigma and Statistics How to Compute and Apply Basic Statistics How to Establish and Benchmark Process Capability Session Two

Understanding the Theory of Sampling and Hypothesis Testing How to Apply the Key Statistical Tools for Testing Hypotheses Understanding the Elements of Successful Applications Planning How to Apply and Manage the Breakthrough Strategy How to Identify and Leverage Dominant Sources of Variation How to Establish Realistic Performance Tolerances Session Three Understanding the Basic Principle of Experimentation How to Design and Execute Multivariable Experiments How to Interpret and Communicate the Results of an Experiment How to Plan and Execute a Variable Search Study Session Four Understanding the Basic Concepts of Process Control

How to Construct, Use, and Maintain Charts for Variables Data How to Construct, Use, and Maintain Charts for Attribute Data How to Implement and Maintain Pre-control and Post-control Plans How to Plan and Implement Process Control Systems

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How to start and quit MATLAB?

On both system leave a MATLAB session by typing :

>> quit

or by typing

>> exit

at the MATLAB prompt.

PC - a double click on the MATLAB icon on

your desktop

unix system - setup MATLAB (return)

MATLAB

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Getting started with MATLAB

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MATLAB Desktop

Command

Window

Launch Pad

History

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Algebraic operations inMATLAB:

Scalar Calculations:

+ addition

- subtraction

* multiplication

/ right division (a/b means a b)\ left division (a\b means b a)

^ exponentiation

For example >> 3*4 executed in 'MATLAB' gives ans=12

>> 4/5 gives ans=.8

>> 4\5 ans=1.25

>> x = pi/2; y = sin(x) y = 1

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Matrix, vector and scalar:

MATLAB uses variables that are defined to be matrices.

A matrix is a collection of numerical values that are organized into a specific

configuration of rows and columns. The number of rows and columns can be any

number.

A=[ 1 2 3 4

5 6 7 8];

A is for example, 2 rows and 4 columns define a 2 x 4 matrix which has 8 elements

in total.

A scalaris represented by a 1 x 1 matrix in MATLAB: a=1;

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A vectorof n elements can be represented by a n x 1 matrix, in which case it is

called a column vector, or a vector can be represented by a 1 x n matrix, in which

case it is called a row vector of n elements.

x = [ 3.5, 33.22, 24.5 ] ; x is a row vector or 1 x 3 matrix

x1 = [ 2 x1 is column vector or 4 x 1 matrix

5

3

-1];

The matrix name can be any group of letters and numbers up to 19, but always

beginning with a letter.

MATLAB is "case sensitive", that is, it treats the name 'C' and 'c' as two different

variables.

Similarly, 'MID' and 'Mid' are treated as two different variables.

Matrix, vector and scalar:

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Colon operator: The colon operator ' : ' is understood by Matlab to perform special

and useful operations.

For example, if two integer numbers are separated by a colon, Matlab will generate

all of the integers between these two integers.

a = 1:8

generates the row vector, a = [ 1 2 3 4 5 6 7 8 ].

If three numbers, integer or non-integer, are separated by two colons, the middle

number is interpreted to be a step" and the first and third are interpreted to be "limits:

b = 0.0 : .2 : 1.0

generates the row vector b = [ 0.0 .2 .4 .6 .8 1.0 ]

Syntax in MATLAB:

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The colon operator can be used to create a vector from a matrix.

Thus if

x = [ 2 6 8

0 1 7

-2 5 -6 ]

The command y = x(:,1) creates the column vector

y = [ 2

0

-2 ]

The command z = x(1,:) creates the row vector

z = [ 2 6 8 ]

Syntax in MATLAB:

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The colon operator is useful in extracting smaller matrices from larger matrices.

If the 4 x 3 matrix c is defined by

c = [ -1 0 0

1 1 0

1 -1 0

0 0 2 ]

Then

d1 = c(:,2:3)

creates a matrix for which all elements of the rows from the 2nd and third columns

are used. The result is a 4 x 2 matrix

d1 = [ 0 0

1 0

-1 0

0 2 ]

Syntax in MATLAB:

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Some basic commands you may need:

pwd prints working directory

>> pwd

ans =

C:\INSE6220>> load parts

whos: lists all of the variables in your MATLAB workspace

>> whosName Size Bytes Class

runout 36x4 1152 double array

Grand total is 144 elements using 1152 bytes

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figure creates an empty figure window

close by itself, closes the current figure window

hold on holds the current plot and all axis properties so that subsequent graphing

commands add to the existing graph

>> figure; x=0:.01:2*pi; Y=sin(x); plot(x,Y);hold on; Y=sin(2*x);plot(x,Y);

hold off sets the next plot property of the current axes to "replace

hold off is the default.

>> figure; x=0:.01:2*pi; Y=sin(x); plot(x,Y);hold off; Y=sin(2*x);plot(x,Y);

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find find indices of nonzero elements e.g.:

d = find(x>100) returns the indices of the vector x that are greater than 100

>> x = [120, 90, 100, 30, 220, 98, 12, 78, 900]; d = find(x>100)

d =

1 5 9

breakterminate execution of m-file or WHILE or FOR loop

for repeat statements a specific number of times, the general form of a FOR

statement is:

FOR variable = expr, statement, ..., statement END

a = zeros(k,k) % Preallocate matrix

for m = 1:k

for n = 1:k

a(m,n) = 1/(m+n -1);end

end

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Statistics with MATLAB

Online help for Statistics Toolbox is available from the Matlab prompt (>> a

double arrow), both generally (listing of all available commands):

>> help stats

[a long list of help topics follows]

and for specific commands:

>> help distool

[a help message on the disttool function follows].

>> help disttool

DISTTOOL Demonstration of many probability distributions.

DISTTOOL creates interactive plots of probability distributions.

This is a demo that displays a plot of the cumulative distribution

function (cdf) or probability distribution function (pdf) of the distributions

in the Statistics Toolbox.

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Plotting Probability Distributions

>> disttool

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Descriptive Statistics corrcoef - Linear correlation coefficient with confidence intervals. cov - Covariance. mean - Sample average (in MATLAB toolbox). median - 50th percentile of a sample. range - Range. std - Standard deviation (in MATLAB toolbox).

var - Variance (in MATLAB toolbox).

Example:

>> X = [ 1 2 3 5 6 7 23 45 33 46 22]X =

1 2 3 5 6 7 23 45 33 46 22

>> mean(X)ans =

17.5455

>> std(X)

ans =

17.2648

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Statistical Plotting

andrewsplot - Andrews plot for multivariate data. biplot - Biplot of variable/factor coefficients and scores. boxplot - Boxplots of a data matrix (one per column). cdfplot - Plot of empirical cumulative distribution function (cdf).

fsurfht - Interactive contour plot of a function. glyphplot - Plot stars or Chernoff faces for multivariate data. gplotmatrix- Matrix of scatter plots grouped by a common variable. gscatter - Scatter plot of two variables grouped by a third. hist - Histogram (in MATLAB toolbox). hist3 - Three-dimensional histogram of bivariate data. normplot - Normal probability plot. parallelcoords- Parallel coordinates plot for multivariate data. probplot - Probability plot.

surfht - Interactive contour plot of a data grid. wblplot - Weibull probability plot.

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Statistical Plotting using MATLAB

Create a Pareto chart from data measuring thenumber of manufactured parts rejected forvarious types of defects.

>> defects = {'pits';'cracks';'holes';'dents'};>> quantity = [5 3 19 25];>> pareto(quantity,defects);

Boxplot(X) produces a box and whisker plot foreach column of the matrix X. The box has linesat the lower quartile, median, and upper quartilevalues. The whiskers are lines extending fromeach end of the box to show the extent of therest of the data. Outliers are data with valuesbeyond the ends of the whiskers

>> load parts>> boxplot(runout);

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Statistical Process Control (SPC)

capable - Capability indices. capaplot - Capability plot. capability - Capability indices. ewmaplot - Exponentially weighted moving average plot.

histfit - Histogram with superimposed normal density. normspec - Plot normal density between specification limits. controlchart - Shewhart control chart. controlrules - Control rules (Western Electric or Nelson) for SPC.

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Control chart using MATLAB

Syntax: controlchart(data,chart,charttype)>> load parts

>> st = controlchart(runout,'chart',{'xbar' 'r'})

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Tips for success

Start every assignment early Dont fall behind Ask if you dont know Do your own work

Expect to spend enough time studying the material of the course

Reading: course notes

Assignment #1 To be posted soon on thecourse webpage

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