six sigma & 7 qc tools

Welcome to the program on

Enhance Product quality thru’

Six Sigma & 7 QC tools

H K Varma Varmahk@Gmail.com98202 6298622 426 62986

Our Mission

Knowledge + Training =

Prosperity

Program schedule

• 10.00 – 11.15 Session I• 11.30 – 1.00 Session IILunch break 1.00 to 2.00

• 2.00 – 3.30 Session III• 3.30 – 4.50 Session IV• 4.50 – 5.00 Q / A• 5.00 ----------- Close

Globalization and Liberalization .....

• The challenge is even higher with continued reduction in tariffs and lifting of quantitative restrictions on imports .

• Import liberalization has led to free availability of global products at cheaper rates across the developing world.

• In fact those unable to face the growing challenges are forced to put down the shutters.

• The survival mantra has become

• “Survival of the fittest”

Mfg Cost Var Output at TP Stores cr. 4000241 3972 +/- in WIP 178

PBIT Misc Output -2061191 Input Cost

3731 Dir Malt 3000NOPAT Dir Lab 86

810 Mktg PBIT Sales/Serv 6000 Malt OH 47929 Cost of Sales 3972 Shop OH 261

ED on Sales 794 PGOH 36TAX OD Adj Pers Rel Exp 89 Comm Exp 163

EVA 381 -65 T&C 54 Alloc Exp 189361 Sales Pr Exp 8

Corp alloc NDC 1986 ODE 63

WACC Estb 3112% Other Exp 41

Cap Chg MMI 1034449 Cap Emp WIP 370

3738 Net F Assets FG 53601 Curr Assets Cust OS 3073

4597 Oth contl A 67Net WC

3137Curr Liabilities Vendor Cr 1273

1460 Cust Adv 33OCL 154

Areas of focus

1. Reduction in Material & labor costs2. Reduction in Cycle time and Lead time3. Reduction in Rejections , Wastage4. Increase in Productivity

How Six Sigmacan help

improve EVA

Six Sigma• Every mistake an organization or person makes ultimately has

a cost, – the need to do a certain task over again, – the part that has to be replaced, – time or material wasted

• Six Sigma is a scientific problem solving tool for– meeting your customer's needs (Time , speed , Quality )– minimizing wasted resources (Errors , rework , Hidden

factory , variations +/-)– maximizing profit in the process ,thru’ disciplined data

collection and analysis to determine best solutions

Six Sigma - approach

Six Sigma is a scientific tool for Process Improvement

Six Sigma helps to improve the quality of process outputs by identifying and removing the causes of defects (errors), and

Minimizing variability in manufacturing and business processes

Six Sigma - objective• Man-kind accepts all creations of God , Black –White ,

Short-tall , fat-slim with all distortions / discrepancies ,but ....

• When it comes to creations of another man-kind thesame men don’t accept any variation be it color ,aesthetics , size , weight etc

• Primary objective of Six Sigma is therefore to– “do it right the first time” FPY (FTR) , and– “do the right things right” SOP

• Hence a need to minimize the process outputvariations

Performance Scale & CTXs1. A performance scale represents

units, such as time, length, size, and so on, indicates the measured value of your CTX

2. The goal of Six Sigma is to come as close to your performance target as often as possible (Hitting the dart)

3. You can get close, but you will always have some variation

Say 12.5mm

> 12.5mm< 12.5mm

Why Six Sigma1. The sigma scale is a universal

measure of how well a critical characteristic performs

2. The higher the sigma score, the more capable the process.

3. Products with more characteristics (CTQs),need Six sigma quality standards to ensure final product performance

4. Even if the milestone of Six Sigma may take time to reach, the act of working toward that goal drives breakthrough changes.

Percent defective

Defects permillion

1 69% 691,462

2 31% 308,538

3 6.7% 66,807

4 0.62% 6,210

5 0.023% 233

6 0.00034% 3.4

7 0.0000019% 0.019

Note the difference1. Conventional quality 3 % d ,2. Under Six Sigma it is 3 out of a

million

Conventional quality 3 % d

3.4 3.0% d 30,000

Higher Sigma >>> Lower defects

Top Commitment and accountability

• A Six Sigma initiative begins at the top.

• The top management of an organization must actively commit to the Six Sigma initiative,

• Six Sigma, through its voice of the customer (VOC) tools, drives business processes to meet customer requirements

• The objective of Six Sigma is to ensure high quality and reliability of products, services, and transactions

• Six Sigma must include performance measures that are readily accessible & visible (Output , FTR , m/c breakdown etc)

Principles of Six Sigma

Six Sigma begins with one general-purpose equation

• Y = f(X) + E , where

• Y- is the outcome, the result you desire or need.

• X- represents the inputs, factors, or pieces that are needed to create the outcome. You can have several Xs.

• f- is the function, the method or process by which the inputs are transformed into the outcome.

• E- is the presence of error or variation in the process

• Common cause variation is : operating within +/- 3σCommon cause

1. Every outcome is the result of the inputs and the process that acts on it, plus the error that creates variation.

2. If good things happen, you want to know how to make them happen again. and

3. If bad things happen, you surely want to know how to prevent them next time.

4. Regardless of complexity, every result has one or more causes

5. The more you can single out these causes and understand them, the better your opportunity to change it for the better.

Determine the cause

Cause-Effect Diagramsub-causes

High MMI+

Shortages

External

Internal

SupplierLT high

RM n/awith Supplier

MatlRej

Rate settldelay

K Card Trigdelay /not trgr

Delayby buyer

Excess supplyfrom Supplier

K Qty large

Dispatchdisciplinemissing

Materialremains un-used

Extra matlbrought - buyer

K Card triggeredin spite of Matl availability

SAP stk highphy not avail

BOM error

Back-flashnot taking place Process Rej

un-accounted

K Card Triggeringdiscipline

Matl recdin last 3-4 daysof month

Cat.no. changed/clubbed under Kitting

Matl keptat diff loc

Effect

……… Xs ………

Importance of measurement

1. Until you include measurement and numbers in your knowledge, you're bound to the world of gut-feel, guessing, and marginal improvement.

2. You may work very hard, and even bring significant resources to improve goal, but without measuring your Ys and Xs, your ability to improve will be incomplete

3. Measurement begins with the Ys, and then extends to the Xs to understand the causes.

4. Data and Measurements are the foundation of Six Sigma

Vital few vs Trivial many1. Typically, only a few select variables (Xs) determine the

quality of a given outcome! 2. Basically It amounts finding those critical few(Xs) that give

you the leverage ie 80-20 rule , where 20 percent of the inputs account for 80 percent of the influence on the output.

3. After you determine that a factor is insignificant, don't waste time and energy putting attention on it. ie ,weed out the many trivial variables that take your time but offer no real advantage

4. DMAIC in Six Sigma helps you find the critical few(Xs) to follow a structured process for defining, measuring, and analyzing all the cause-and-effect relationships

The basics of a Six Sigma project

1. When a particular problem isselected to become a potential SixSigma project, it goes through acritical transformation :

2. By stating the problem in statisticallanguage, you ensure that you willuse data, and only data, to solve it.

3. This forces you to abandon gutfeelings, intuition, and best guessesto address your problems

Practical Problem

Statistical Problem

Statistical Solution

Practical Solution

Results

Determining Ys needing improvement

1. Identify which process output variables (Ys) need improvement to solve the business problem .

2. The Ys in need of improvement must be easily identifiable and quantifiable.

3. If there are more than two Ys, there's a good chance that your project is too large in scope.

4. You may have to break the project into two or more projects to be successful.

5. You must be able to express the magnitude of the problem (defect level) in some unit of measure (for example, hours, inches, percent late, and so on).

Y – Output needing ImprovementInputs

Xs Process

Collecting data

1. Don't be discouraged if your data is not perfect at this time.2. You can improve the integrity of your data when you are in

the Measure phase, plan to update the quality of your data at that time.

3. Verify that your data is long-term, not short-term, when estimating the baseline performance.

4. Short-term data is a snapshot of what's happening and could mislead you.

5. It also doesn't represent all the potential sources of variation that are contributing to your problem over the long-term, such as seasonal effects etc

Identifying & Tracking ImprovementPe

-Y Improving “Y”

Knowing the baseline level of performance allows you to calculate the potential financial benefits when you target a level of improvement

Improvements put in place

Base line

Objective

Developing Objective and Process Entitlement• Setting the objective for the project's level of improvement

is a triangle activity. The key inputs are : 1. Your own opinion of what success is. 2. Another input comes from a concept called entitlement.3. Benchmarking is another input.

• Finally, listen to VOC• Entitlement is the best performance a process, as currently

designed, has demonstrated in actual operation (Associated with St Variation)

• Entitlement is an extremely powerful Six Sigma concept, used to determine the potential level of improvement

Yield =(352 – 103)/

352= 70.7%= FTY

& The Hidden Factory

Hidden factory is due to

The inability to correctly comply

with required specifications the

first time

Hidden Factory103

The extra efforts put to get these 98nos.

accepted is HIDDEN FACTORY

352 347

Group 1 2 3 4Items In (Nos) 1200 1200 1200 1200

Accepted after change note 133 89 64 9

Reworked 121 70 43 6

Scrapped 53 23 13 3

Calculate Hidden factory

First Time Yield (%) 75% 85% 90% 99%

Ultimate yield (%) 96% 98% 99% 100%

Hidden factory (%) 21% 13% 9% 1%

ExerciseHidden Factory - Answers

Focus should be at improving the FTY

& reducing the Hidden factory

The Hidden factoryThe hidden factory is work that is done above and beyond what isrequired to produce a product or a service.....Work that gets ingrained into the organization when you don’t ask"Why are we doing this, since this is not adding any value?“"That's the way we have always done it." If you have heard this, you probably have a hidden operation.

Opr i Verification Opr i+1

AnalysisOff-linerepair Scrap

Fix ?Yes No

If problem

OEE = Availability * Performance * Quality Yield

Time available for production - downtime Time available for production

Performance :: Speed Loss Performance = Actual output rate

Std Output rate

Quality Yield :: Quality Loss

Total no. of parts produced – Defects Total No.of parts produced

Availability :: Downtime loss

Support Variable Calculation Calculated data Result

Planned Produ time Shift Length-Breaks 480 - 60 Min 420 Min

Operating Time Planned Prod Time-Down Time 420 - 47 Min 373 Min

Good Pieces Total Pieces-Rejects 19271 - 423 pcs 18848 PcsOEE Factor Calculation Calculated data OEE %

Availability Operating Time / Planned Prod time 88.81%

Performance Actual output rate / Ideal Run rate 86.11%

Quality Good Pcs / Total Pcs 97.80%Overall OEE Avail * Perf * Quality 74.79%

Production DataShift Length 8 Hrs=480 MinShort Breaks & Lunch 60 MinDown Time 47 MinIdeal Run rate 60 pcs per MinTotal pcs produced 19271 pcsReject pieces 423 pcs

Measure1. Measure : Is collecting useful data

1. Establishing relationship 2. Measure Variation , and also 3. Measuring gap

2. Variation is everywhere, and it diminishes your ability to consistently produce quality results, meet schedules, and stay under budget leading to performance problems

3. Until you include measurement, and numbers in your improvement efforts, you're bound to remain in the world of gut feel, educated guessing, and marginal improvement power

Significance of data

• To determine how well we fulfill customer requirements

• To determine how close are we wrt target

• To track accomplishments

• To determine when improvement is needed

• To track use of resources and how efficiently they are used

eg OEE ( A , P , Q )

• To provide information that supports improvements

• The data may be variable(measurable) or attribute(Go – NoGo ,

Good-Bad etc)

Type of data

• Subjective– Data is difficult to quantify – Could be 7% , 9% etc !– Very often decisions based on subjective data turn out to

be wrong and may cost organization money and time.• Objective

– Data is more reliable as it is countable / measurable– Accordingly they are classified as :– Variable (Time , length size etc) , measured and expressed

on continuous scale– Attribute ( Go-No-go , good taste , bad taste , No of

occurrences etc) or

Measures of Distribution1. Mode is the value observed most frequently and is

associated with the highest peak of a distribution. 2. Mean: The most common measure of central tendency is the

mean - widely called the average . It's important to understand that the mean is theoretical rather than real.

3. Median : The median is the point along the scale of measure where half the data are below and half are above

4. The mode, mean, and median all fail to communicate the critical information of how spread out or narrowly dispersed the data is around its central location point.

5. Hence a need to find out two more measures ie6. Range (R = Xmax-Xmin) and Standard deviationσ = ( )

Standard Deviation• The standard deviation-(σ) is by far the most commonly used

measure of dispersionThe long and short of variation• In fact, for any selected short period of time, the process

generally varies within the same rough limits – This natural level of variation is called the short-term (St)variation

• This short-term variation is purely random• It is caused by the combined effect of all the little things that

are too hard to include in your understanding of the process and is therefore also called Common cause or random variation, short-term variation.

Process Entitlement

1. This hard wall in the improvement path is called Entitlement (variation you can expect from a process under the best conditions ) of the process or

2. Random variation or ST variation3. Short-term, or entitlement, variation is used to compare

the capability of different processes to meet a specified goal

Histogram or Probability curve

1. Pictures of data helps you understand the process2. These pictures - called graphs or plots - are definitely better

than numbers at communicating your data to others.3. Plotting and charting data help you project

i. the central tendency and ii. the spread of variation (uniform or skewed)

4. One of the best tool used to project both these characteristics is called Histogram .

5. Bucket or Bin size selected should provide for 10 to 20 equal divisions between the largest and the smallest observed values.

A Picture’s worth a thousand words

Process capability of Tube filling plant

Sample Qty filled Sample Qty filled

1 19.50 14 20.702 19.30 15 20.403 20.20 16 20.204 20.30 17 20.175 19.80 18 19.606 20.80 19 19.407 20.50 20 19.318 19.90 21 20.259 20.00 22 20.34

10 20.40 23 19.9511 20.60 24 20.1712 19.70 25 20.4013 19.85

Plot Histogram , calculate Mean , Std Deviation

Mean 20.07Std Dev 0.43

Run chart(Control chart) & Histogram

1 3 5 7 9 11 13 15 17 19 21 23 25

DOE – Design of Experiments

• In the equation Y = f(x) , • ‘Y’ is called the response derived from the state at which ‘X’

is operating• X is called Cause -Input and Y is called Effect or Output• X1,X2,X3.. Input or Control factor , Y – Output or Response• Measure phase will help u establish this relationship• DOE helps to establish this relationship called • Y = f (X1,X2,X3..) + Variation

Specifications setting

• Understandable: Is the specification clearly stated anddefined so that there can be no argument about itsinterpretation?

• Measurable: Can you measure the characteristic'sperformance against the specification

• Believable: Can you and your coworker peers strive tomeet the specification?

• Attainable or achievable: Can the level and range of thespecification be reached?

The traditional and the Six Sigma views on specifications and the costs caused by poor quality

Characteristic scale of measure

LSL USLTarget

Task of Six Sigma is to understand how well the VOP meets the VOC

Meeting Six Sigma standards

• The basic aim of Six Sigma is to ensure processes give first time right output leading to consistent performance with variations between +/- 3σ

• Most of the output of a process generally meets the specifications(CTQ-X) , except few , who deviate to varying extent , measured by standard deviation (σ)

• So some units may have – X +/- 1σ , some – X +/- 2σ ,and some – X +/-3σ specifications

2 approaches to Improvement DMAIC DFSS

• Six Sigma offers two approaches for improvement

1. Improve the process so that chances of defects are reduced ,ie reduce the standard deviation DMAIC

2. Change the design (DFSS) so that product can accommodate process variations

Additional Information

Process Performance

• 2σ = 30.8% Rej

• 3σ = 6.68% Rej

• 3.4σ = 3% Rej

• 4σ = 0.62% Rej

• 5σ = 0.0223% Rej

• 6σ = 0.0003% Rej

Gr 3 Run chart sd 0.3 , Performance 2σ , Rej 30.8%

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

XiX barUSLLSL

Target 10.0 +/- 0.30

+1σ = 0.176-1σ

USL10.30

LSL9.70

3.4σPerformance

=3%Rej

StdDeviation

Perf=0.6/0.176

= 3.4σ

Specs width1. 2σ = 30.8% Rej2. 3σ = 6.68% Rej3. 3.4σ = 3% Rej4. 4σ = 0.62% Rej5. 5σ = 0.0223% Rej6. 6σ = 0.0003% Rej

Bell curve - Probability curve

Higher Process Sigma – lower Rejection

• A low process sigma means that a significant part of the tail of the distribution is extending past the specification limit. More defects.

• So the higher the process sigma , the fewer the defects

1. 2σ = 30.8% Rej2. 3σ = 6.68% Rej3. 3.4σ = 3% Rej4. 4σ = 0.62% Rej5. 5σ = 0.0223% Rej6. 6σ = 0.0003% Rej

} Most of Indian Industries are here

This is the journey we have to undertake

Process capability of a process or characteristic to meet its specifications (VOC/VOP)

1. Capability : Ability to match the voice of your process-VOP to the voice of your customer-VOC

2. The simplest capability index is called Cp. 3. It compares the width of a two-sided specification to the

effective short term width of the process.

USL - LSL representsthe VOC-voice of thecustomer'srequirements and

Cp =( USL-LSL )

6σstEffective process width under Six Sigma = 99.7%

In this example , Process capability = 1

LSLUSL

Sigma (Z) Score

• Six Sigma level of quality is defined as 3.4 defects per million opportunities.

•The central tendency of the performance distribution is defined by its mean 푋•The amount of variation in the performance, or the width of the distribution, is defined by its standard deviation σ .

Process Sigma Score Z = 2*Sigma Value

Simulation model

Statistically it is proven that shifting the process's St distributioncloser to its SL by a distance of 1.5 times its ST std. dev. wouldalmost cover the defects occurring in the long term.

The sigma (Z ) score of the shifted distribution isZshifted = Zst - 1.5 = Expected ZLT

1.5σST

Process Capability Index C non-centered distribution - (Contd)

LSL USL

1. The measure of Cp shift is called Process capacity Index2. ie, Distance from the revised X to each of the specification

limits divided by half-width of the short-term variation (3σ)

퐂퐩퐋 = 퐗 퐋퐒퐋ퟑ훔퐬퐭

Process Capability Index 퐶

Specifications 9.70 / 10.30 9.60 / 10.40

σ 0.10 0.10

Revised 푿 10 > 10.10 10 > 10.10푪풑풖푪풑푳푪풑풌

퐶 = min (퐔퐒퐋 퐗ퟑ훔퐒퐓

, 퐗 퐋퐒퐋ퟑ훔퐒퐓

)퐶 = min(퐶 , 퐶 )

퐂퐏퐔 =퐔퐒퐋 − 퐗ퟑ훔퐒퐓

퐂퐏퐋 =퐗 − 퐋퐒퐋ퟑ훔퐒퐓

1 3 5 7 9 11 13 15 17 19 21 23 25

흈 = ퟎ.ퟏퟔ

Sigma Value 3.1 Sigma

score Z 6.2

Cp 1.03Cpk 1.04 1.03

Run chart VOC USL/LSL , VOP ie UCL / LCL

Capability Improvement PlanSymptom Diagnosis Prescription

푪풑 = 푪풑풌 풂풏풅

푷풑 = 푷풑풌

Overall , your process or characteristic is centered within its specifications

Focus on reducing the long-term variation in your process or characteristic while maintaining on-center performance

푪풑 = 푷풑풌 Your process is operating at its entitlement level of variation

Continue to monitor the capability of your process. Redesign its entitlement level of performance.

The Seven QC tools

1. Check Sheets

2. Pareto charts

3. Histograms

4. Cause and effect diagrams

5. Scatter diagrams

6. Control Charts

7. Graphs

Identifying

Analyzing

Communicating

These tools are divided in to 4 broad categories

Scatter diagram1. Histogram plots only one distribution (characteristic) at a

time . Often one needs to explore the relationship between two characteristics .

2. Scatter plot helps to understand the relationship between two characteristics

3. The two characteristics can be an input and the other can be an output (X , Y) or can be two inputs (X , X ..)

4. The relationship could be :– Positive Correlation– Negative correlation– Positive or negative correlation possibility– No Correlation

Make Curb Wt. (Kg)

Fuel Economy (Km/liter)

Toyota Camry 1580 8.9

Toyota Sequoia 2400 10

Honda Civic 1200 13.9

Land rover 2300 8.9

Mercedes S500 2100 9.7

VW Jetta 1500 9.9

Chyyster 1800 10.4

Chevrolet 2030 11

Hyundai Tiburon 1450 8.2

Dodge Ram 2670 4.2

Fuel Efficiency vs Curb Weight

Y = Km/liter

X1 : Curb weightX2 : Fuel injection systemX3 : Tyre pressureX4 : ……………….

Establish the correlation thru scatter diagram.

Is the correlation ::1. Positive2. Negative3. No correlation4. Positive possibility exists5. Negative possibility exists

Steps to create B & W plot

1. Rank the captured data of a characteristic (X ) from least to the greatest value

2. Determine the Median3. Find the first quartile Q4. Find the third quartile Q5. Create a horizontal line

joining X to X6. Repeat steps 1 to 7 for each

additional characteristic to be compared against the same output

Amblagms Ph Value

100 3.30101 3.35103 3.55102 3.60104 3.66105 3.70106 3.80107 3.85109 3.90108 4.05110 4.10

Ambla ( bet 100-110gm)

ph value

110 4.10102 3.60101 3.35105 3.79103 3.55100 3.30108 4.05106 3.80107 3.85109 3.90104 3.66

Correlation between variables

1. Coefficient of Correlation between two variables : (r)

2. r = ퟏ풏 ퟏ

∑ (풙풊 풙흈풙

풏풊 ퟏ )(풚풊 풚

흈풚)

3. The calculated correlation coefficient will always be between -1 and 1

4. ‘r’ closer to zero indicates absence of linear fit (No correlation)

r = + 0.99

r = - 0.61

r = - 0.03

No correlation

Chyavanaprash

98 100 102 104 106 108 110 112

ph. Value (Y) vs Ambla - gms (X1)

β : Line slope = ∑ ∑( ).

β : Value at which fitted line crosses X axis = -16

Pareto ChartStratification of “Quality” category

290210

Stale Burned Undercooked Slicing Other

Stratification of the Quality category shows “Stale” and “ Burned” as the major causes of poor quality

The team decided to use Cause and effect tool for further analysis of the problem

Process Optimization toolsProcess tool RoleSIPOC Suppliers-Inputs-

Process-Outputs-Customers

Fundamental to application of Six Sigma strategy

CT (critical to) tree Areas of importance

Critical to quality , Delivery , cost ….

Cause & Effect diagram Fish bone diagram Method to capture potential causes and inputs effecting the output

ANOVA Analysis of variance Helps to analyze reasons for process variation

Tolerance analysis Helps to optimize product designs

POKAYOKE Error proofing Zero output defect

RPN ( Risk Priority Number)

• RPN is calculated as under– Severity * Occurrence * Detection level

• The RPN will range from 1 to 1000, with higher RPN indicating higher risks.

• Some organizations use threshold values , above which preventive action must be taken. Eg > 120 , > 200 etc

• Reducing RPN requires change in design or process• It is desired that a defective should not reach the customer 1st step is to prevent defectives reaching the customer• ie, Improving the ability to detect defects at the specific

process step ( not at subsequent step)

Control • A solution that isn’t sustained over the long term has little

value• They are basically a type of Run chart with control limitsWhy Control chart

– It shows nature of variation in the process over time– Helps in detecting changes in the process– Helps in controlling the process

• Specs : USL/LSL vs UCL/LCL– CONTROL is also capability , 푪풑 - Process Capability

Why Controls

1. Process behavior is complex and fragile and that hard-earned gains slip away if the process is left to itself.

2. The Control phase helps you make sure the problem stays fixed, and, if done properly, provides you with additional data to make further improvements to the process.

3. A well designed process exhibits inherent self control, but..

4. A poorly designed process requires frequent external control and adjustment to meet requirements.

5. A process with well built-in control acts like the heating and cooling system in a house: The system automatically maintains a comfortable temperature at all times.

Control Charts Background• Dr Shewhart in1920 observed that every process exhibits

some degree of variation• Since no two things can be produced exactly alike ,

variation is natural and should be expected • He defined that if a measurement falls within plus or

minus three standard deviations of its average, it is considered “expected” behavior for the process.

• This is known as common cause variation• He observed two types of variations in any process

Control Chart ( contd)

• If the process is operating within chance causes of variation( ie within Control limits ) , the process is said to be understatistical control

• Control charts can be used for• variable data ( Kgs , Cms etc )

– X chart, R chart or sd (휎) chartor

• discrete or attribute data ( No of defects in a product )– p chart , np chart , c chart and u chart

Variable Control Charts

• Variable Control charts are used to monitor measurablequality characteristics of a process eg Temperature ,dimension , weight , viscosity etc

• Variable charts can monitor only one quality characteristic ata time .

• Variable Control charts help to monitor both process meanand process variability

• Hence it becomes necessary to use minimum 2 control chartsto study the process. Ie– Range or Std Deviation– Process mean , with UCL & LCL

Control Limit factorsdev. by Statistical Quality Control and Management Institute

SampSize Factors for X charts Factors for R Charts Factors for S charts Samp

n A A2 A3 D1 D2 D3 D4 d3 B3 B4 B5 B6 n

2 2.121 1.880 2.659 0.000 3.686 0.000 3.267 0.853 0.000 3.267 0.000 2.606 2

3 1.732 1.023 1.954 0.000 4.358 0.000 2.574 0.880 0.000 2.568 0.000 2.276 3

4 1.500 0.729 1.628 0.000 4.698 0.000 2.282 0.880 0.000 2.266 0.000 2.088 4

5 1.342 0.577 1.427 0.000 4.918 0.000 2.114 0.864 0.000 2.089 0.000 1.964 5

6 1.225 0.483 1.287 0.000 5.078 0.000 2.004 0.848 0.030 1.970 0.029 1.874 6

7 1.134 0.419 1.182 0.204 5.204 0.076 1.924 0.833 0.118 1.882 0.113 1.806 7

8 1.061 0.373 1.099 0.388 5.306 0.136 1.864 0.820 0.185 1.815 0.179 1.751 8

Sample Sample observations X Range Std Dev1 9.26 10.44 10.39 9.87 10.26 10.04 1.18 0.492 10.92 10.08 9.97 10.16 9.30 10.09 1.62 0.583 10.10 10.61 8.62 10.24 10.17 9.95 1.99 0.774 10.17 9.24 10.60 10.08 10.51 10.12 1.35 0.545 10.29 10.36 10.39 10.58 9.96 10.32 0.63 0.236 9.84 9.52 10.11 9.65 10.18 9.86 0.66 0.297 9.84 9.77 10.47 10.25 10.28 10.12 0.70 0.3

…25 10.17 1.09 .48

UCL = 퐃ퟒ 퐑= 2.114*1.11= 2.35

SPC for Shaft lengths

D4 & D3 from control limit chart

Always start with R chart to ensure variability within samples (R- lowest to the highest)

R Chart out of limits

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

A process is not in statistical control if any point falls outside the control limits.

First , control the process before going for 푋 or S chart

Observations

VOC = 10” +/- 0.60C = VOC/VOP

= ( . . )∗ .

퐶 = 0.44

USL = 10.60

LSL = 9.40

ConclusionThough the process is under control (All points within UCL & LCL), the process capability C = 0.44If , however the σ is reduced to ∶ 0.20 , 퐂퐩 = ퟏ.ퟎퟎ andIf , the σ is further improved to ∶ 0.15 , 퐂퐩 = ퟏ.ퟑퟑHence it important that SPC is under control and 퐶 푖푠 > 1

100%Within+/- 3 std Dev

95%Within+/- 2 std Dev

Apprx. 69%Within+/- 1 std Dev

Interpreting Control Charts :: Test Zones :: Each control limit represents

1 std deviation

Centerline

Rarely a pointwould falloutside thecontrol limits

The formulae

MR Chart UCL = D ∗ MRLCL = D ∗ MR

Sigma Score Z = 2* C =(USL − LSL)

C = min ( , )

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

Qty filledX bar

UCLLCL

Sigma value

1.24 Process Sigma - Z

Cp 0.47Cpk 0.41 0.52

X Chart Gr 1퐗 σ20.07 0.43

Z = (ퟐퟎ.ퟔ ퟐퟎ.ퟎퟕ) ퟎ.ퟒퟑ

퐶 = (20.6− 19.4)

6 ∗ 0.43= 0.47

퐶 = (20.60− 20.07)

3 ∗ 0.43= 0.41

퐶 = (20.07− 19.40)

3 ∗ 0.43= 0.52

18.8019.0019.2019.4019.6019.8020.0020.2020.4020.6020.8021.0021.20

1 3 5 7 9 11 13 15 17 19 21 23 25

Sigma value

1.24 Process Sigma Z

Cp 0.47Cpk 0.41 0.52

푋 σ20.07 0.43

1 2 3 4 5 6 7 8 9 10111213141516171819202122232425

1 3 5 7 9 11 13 15 17 19 21 23 25

Sigma value

Cp 0.79Cpk 0.74 0.77

푋 σ20.07 0.18

푋 σ20.00 0.15

Sigma value

Cp 1.36Cpk 1.36 1.36

Control Charts for Attributes

• Whenever it is difficult to take numerical measurement thequality is judged either conforming / non-conforming -Defectives based on attributes( Np and p charts) :– Leaks / does not leak , No. of counts scratches , holes ,

dents etc .• It can also be no. of non-conformities (defects) that appear

on a unit ( No of dents , a/c opening form , scratches , holesetc) : C & U charts :

• The inspection doesn’t require spl trained people as nomeasurements are involved .

P Chart ( Control chart for fraction non-conforming)

• ‘P’ stands for proportion• Measures the proportion of non-conforming units in a group of

units being inspected.• P chart is the most versatile and widely used attribute chart• It can be used for following purposes.

– To determine the avg. proportion (or fraction) of non-conforming units over a given time

– To signal a change in the avg. fraction non-conforming– To identify out-of-control points that call for immediate action– To suggest places to implement X and R charts

• Np chart is used when analyzing only one type of defect

np Chart

• If the sample size is constant ( eg 100 in this example )and there is only one reason for non-conformance(Defective) , the chart for attribute data is called npcontrol chart

• If for any chart the LCL works out less than zero , theLCL is set to Zero.

np Chart

Batch NoNo of non-conforming

1 142 183 134 255 196 189 18

10 1211 17

…26 13Total 417

No. of non-conforming sheet metal components - Batch size 100

퐔퐂퐋 = 퐧 풑 + 3 퐧 풑 (ퟏ − 풑 ) = ퟐퟕ.ퟎퟓ

퐋퐂퐋 = 퐧 풑 - 3 퐧 풑 (ퟏ − 풑 ) = ퟓ.ퟎퟑ

풑 = ∑ 푫풊풎풊 ퟏ

∑ 풏풊풎풊 ퟏ

= ퟒퟏퟕퟐퟔ = ퟏퟔ.ퟎퟒ

np Chart

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 26

For fixed batch size

• The chart seems to be in control as no point falls beyond the control limits

• Avg. being high , further

investigation (푿 , R ) may be

carried-out to arrive at the root

cause for defectives

퐔퐂퐋 = 퐧 풑 + 3 퐧 풑 (ퟏ − 풑 ) = ퟐퟕ.ퟎퟓ

퐋퐂퐋 = 퐧 풑 - 3 퐧 풑 (ퟏ − 풑 ) = ퟓ.ퟎퟑ

풑 = 16.04

Defective units of 5gm pouch Gr 1

Day Smudged Printing

Improper sealing

Uneven margins

Total defective

Total (n)Inspected

Fraction(p) Non-confo

1 19 27 322 21 26 213 21 17 444 12 24 365 11 22 236 11 32 327 11 19 268 8 25 239 13 25 28

10 30 29 2611 26 34 2212 17 19 2213 31 35 3214 11 30 3115 28 34 3816 23 29 1817 16 31 2318 28 27 2319 24 23 1620 22 20 31

UCL = p + 3 ̅( ̅) LCL = p - 3 ̅( ̅)

c Chart

• Used for monitoring the non-conformities(defects) perinspection unit or in constant area of opportunity ( egFixed length of a unit , area :: Road length , Car bonnet ,PCB )

• Control limits are :

UCL = C + 3 C

LCL = C − 3 C

Control charts for attributes

• P or C chart give the average proportion of non-conforming units over a given time span

• To identify out-of-control points that call forimmediate action

• To suggest places to implement 푋 and R charts

• When the no. of units are not constant , u chart is usedinstead of c chart

The u Chart for complaints received

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21

LCL= 풖 - 3 풖풏풊

UCL= 풖 + 3 풖풏풊

풖 = ∑ 푪풊풌풊 ퟏ

∑ 풏풊풌풊 ퟏ

Process characteristic or measurement

What type of data ?

What type of attribute data

P chart C , U chart

What subgroup size

MR 퐜퐡퐚퐫퐭퐗 −퐑 퐜퐡퐚퐫퐭

퐗 − 퐒 퐜퐡퐚퐫퐭

Defectives defects 2 - 101 > 10

1. Not every performance indicator can be a KPI !

2. Just because some particular indicator is easy to measure it

should not become a KPI .Doing so dilutes your focus on what's

truly important , wastes time

3. KPIs should reflect what your CEO expects from you

4. KPIs should contribute towards meeting his goals

5. "K" in KPI stands for "key," meaning "important" – not just to

you, but to your CEO. So, report true KPI's, not mere PI's!

He wants to know :

Six Sigma Project stepsProcess out line

Calculate RPN no of each project using FMEA take projects with high RPN to start with

• Six Sigma : A powerful tool to control process variability to reduce rejections & defects

• Through a structured DMAIC process– Define : Breakthrough

results– Measure : Hidden

factory , Sd Deviation 흈푺푻 ,흈푳푻 , Mean , Bell curve

– Analyze : FMEA , SIPOC– Parreto , Cause Effect– Improve : VOP vs

VOC/VOB– Control : Variable and

Attribute• Process Capability : Z

score , Cp• Cpk - Capability Index• 7 QC tools / Control

Charts

Summarize

Our other Training ProgramsIn-company as well as Open prog.

• Enhance Productivity & Inventory turns thru Principles and Applications of Lean Manufacturing – 2days

• Vendor Management & Development - 1day

• Un-lock Working capital thru Effective Inventory Management -1day

• World class Mfg - 3 days

• SCM – 1day

• 5S & Visual Control Management - 1day

• Material & Inventory Management - 1day

• Materials – A profit centre - 2days

Our other Training ProgramsIn-company as well as Open program

• World class Mfg - 3 days– Enhance Productivity & Inventory turns thru Principles and

Applications of Lean Manufacturing – 2days– Lean Manufacturing – Basic Principles and applications - 1day

• Lean Six Sigma - 2days– Performance Excellence and 5S - 1day– Six Sigma – 2day

• Materials – A profit centre - 2days– Un-lock Working capital thru Effective Inventory Management -

1day– SCM - 1day– Vendor Management & Development - 1day

Lean Manufacturing Principles and Applications - 2days

1. What is World class organization2. Lean business model to enhance

EVA (Economic Value Addition)3. Toyota Production House4. Takt Time , VSM and Line

balancing5. Operational Wastes :: Muda Mura

Muri6. Work excellence thru’ 5S7. Total Productive Maintenance &

8. Product Lead time9. Tool Change over time &

SMED10. Autonomation & Pokayoke11. Effective Gemba meetings12. Kaizen – Continuous

Improvement , Bench marking

13. Lean Inventory – Kanban14. Lean vendor base

Six-Sigma

1. Coverage of Six Sigma across industry .

2. Transformation of abstract Market need into customer specific need /VOC .

3. Approach towards Business Excellence (DMAIC , DMADOV) .

4. QPPO identification, Development of PPMs

5. Short term & long term Variations6. FTY & hidden factory7. Taguchi loss curve8. Cp / Cpk

9. Type of data10. The seven QC tools

Check sheetsGraphsHistograms Control charts

R chartX chart S chartMR chartp chartnp chartc chart

Pareto ChartsCause-and-effect diagramsScatter diagrams

• Materials – A profit centre - 2days

1. Break-even analysis , Volume Discounts

2. Business model to make Materials dept a profit center

3. Action plan to achieve Supplier competitiveness

4. Supplier Relationship Mgt.(SRM)5. Vendor Assessment , Rating &

Ranking6. Vendor Development7. Healthy Vendor Base8. Supplier Negotiation9. Product Costing

1. Working capital cycle2. Optimum service levels3. EOQ , ROL , Safety stock4. Inventory plans Push vs Pull5. Kanban6. Third party logistics7. Measures of Inventory

• Inventory Ratio • Doc

8. Inventory Record Accuracy9. How to arrest stock discrepancy

• Bar code• RFID

Vendor Management & DevelopmentUn-lock the Working capital thru Effective Inventory Management

Thank you

H K Varma

9820262986

Varmahk@Gmail.com

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