6sigma handbook

8/2/2019 6SIGMA Handbook

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Information & Graphics Source :- TRW / Rath & Strong

6 Sigma

Hand Book The Basics


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What is 6 Sigma ?

A structured and disciplined data-driven process for improvingbusiness performance in TRWs day-to-day activities

Focus on not making mistakes and reducing the variability inour processes

Six Sigma is all about improving the bottom line

*** It costs less to do it right the first time ***


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DEFINE

IMPROVE


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Green Belt Project Charter

Project Name Business / Location

Green Belt Telephone Number

Master Black Belt Telephone Number

Champion Telephone Number

Start Date: Target End Date:

Project Details

Project Description

Business Case

Problem Statement

Process & Owner

Scope Start:Stop:Excludes:

Project Goals Metric Baseline Current Goal Entitlement

Expected BusinessResults

Expected CustomerBenefits

Team members

Support Required

Risks/Constraints

Project CharterThis document is a Contract between the Project Team and the Project Champion.

Its purpose is :

1. To clarify what is expected of the team2. To keep the team focused

3. To keep the team aligned with organizational priorities

4. To transfer the project from the champion to the team

Main Elements of the Charter include :

Focussed Problem Statement $ Impact

Team Metrics

Scope > Start >Stop >Excludes Customer Benefits

Business Impact Risks & Constraints

DEFINE


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SIPOCA SIPOC is a high-level process map that includes Suppliers, Inputs, Process, Outputs, andCustomers.

Rolled Throughput Yield ( RTY )

The calculated value of all the Process Steps multiplied together. Ie Y1 x Y2 x ..Yn = RTY

The individual Yield Value can help you focus the project.

Significant differences in Yield suggest creating a new map for the sub-process with the lowestyield.

Inflator Assy

Customers

Ball weld

OutputsProcessInputsSuppliers

Design

EngineersComponent

manufacturer

Gas Fill

Heat

Pressure

Time

Operator

Inflator assembly

Heat

Good Part

Prod. operator

Heat age oven

Plant Quality

Start Stop

Load inflator

Press start to

perform weldRemove

welded inflatorPlace in tray

Ball

Load ball

Tip Design

Weld upset

Bad Part

Worn Tip

LaboratoryQualification

Inflator Assy

Customers

Ball weld

OutputsProcessInputsSuppliers

Design

EngineersComponent

manufacturer

Gas Fill

Heat

Pressure

Time

Operator

Inflator assembly

Heat

Good Part

Prod. operator

Heat age oven

Plant Quality

Start Stop

Load inflator

Press start to

perform weldRemove

welded inflatorPlace in tray

Ball

Load ball

Tip Design

Weld upset

Bad Part

Worn Tip

LaboratoryQualification

Y1

Y2

Y3

Y4

Y5

DEFINE


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Voice Of The CustomerVoice of the Customer (VOC) is used to describe customers needs and their perceptions of yourproduct or service.

The tree diagram format converts the Customers Need, from Broad to Specific requirements.

The Specific requirements are known as Critical To Quality (CTQs), which must be measurable andin the Customers language. Ie. What the Customer wants, not what you think the customer wants.

More available uptime

Tip Change Frequency Increase Tip Life from 300 to 1000 (1)

Reduce Tip Changeover time (2)

Less testing More time / parts for production

Reliable Weld QualityGuarantee in quality

Right first time

Reduction in approval time

Need Drivers CTQs

General Specific

Hard to measure Easy to measure

DEFINE


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DEFINE

Completion - Check ListBy the end of the DEFINE Phase, you should be able to answer the following :-

1. Why is the project important ?

2. What business goals the project must achieve to be considered successful ?3. Who are the key players in the project ( Champion, Team )

4. What limitations have been placed on the project ?

5. What is the process ( SIPOC ) ?

6. What is the current Yield ( RTY ) ?

7. What are the Key, Critical to Quality ( CTQs ) requirements ?

Only after answering the above questions, should you move onto the next Phase.


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DEFINE

Summary


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MEASURE

Data

Sampling

GageR&R

Patterns

Capability


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MEASURE

Data Collection PlanIt is extremely important to create a Data Collection Plan, so that every one involved in the project,knows :

What data you want collecting ?

What type of data is it ( Continuous or Discrete ) ?

How do you want the measurements to be taken ?

What sampling frequency to use ?

How you want the data recording ?

How you will ensure consistency ?

What is the plan for starting the data collection ?

Data Collection Plan. TitleUpdated by: Issue: 01 Last saved: 30-Oct-01

Project:What questions do you want to answer?

Data Operational DefinitionWhat Measure type / data type How measured 1 Related conditions to

record 2Sam pl ing notes How / w here rec orded

(attach form)

How wil l you ensure consistenc y & st abil ity? What is your pl an for starting data col lection? (Atta ch details if nec essary)

How will the data be displayed? (Sketch below)

1 Include the unit of measurement where appropriate. Be sure to test and monitor any measurement procedures / instruments.2 Related factors are stratificati on or potential causes you want to monitor as you collect data.


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MEASURE

Data TypesContinuous Data Discrete Data

Often obtained by use of a measuringsystem.

The usefulness of the data depends onthe quality of the measurement system.

Counts of non-rare occurrences are besttreated as continuous data.

Includes proportions, counts, attribute

Proportions = the proportion of itemswith a given characteristic; need to beable to count both occurrences andand non-occurrences.

For count data, it is impossible orimpractical to count a non-occurrence;the event must be rare.

Occurrences must be independent.

Continuous Data Discrete Data

Often obtained by use of a measuringsystem.

The usefulness of the data depends onthe quality of the measurement system.

Counts of non-rare occurrences are besttreated as continuous data.

Includes proportions, counts, attribute

Proportions = the proportion of itemswith a given characteristic; need to beable to count both occurrences andand non-occurrences.

For count data, it is impossible orimpractical to count a non-occurrence;the event must be rare.

Occurrences must be independent.


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MEASURE

Basic Statistical Concept

Mean / Average

Median :- Middle Value

Mode :- Most frequent value value with the highest number of occurrences.

Range :-

Variance:- Std Dev :-12 =i

i

Mean

ModeMedian

==

n

i i

xn

x1

1

minmax xx

1

)( 2

=

n

xx

s

n

1

)(1

2

=

=

n

xx

s

n

i

i


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MEASURE

The Normal CurveA probability distribution where the most frequently occurring value is

in the middle and other probabilities tail off symmetrically in both

directions. This shape is sometimes called a bell-shaped curve.

95.46%

99.73%

3S 0 +3S+2S+1S2S 1S

34.13% 34.13%

13.60% 13.60%2.14% 2.14%0.13% 0.13%

3S 0 +3S+2S+1S2S 1S

34.13% 34.13%

13.60% 13.60%2.14% 2.14%0.13% 0.13%

68.26%


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MEASURE

SamplingThis is collecting a portion of all the data, and using that portion to draw conclusions.

We sample because looking at all the data may be too expensive, too time-consuming, ordestructive.

Sampling Approaches Sample Size Calculations

Random

Sampling

Stratified

Random

Sampling

SamplePopulation

Each unit has

the same

chance of being

selected

Randomly

sample a

proportionate

number from

each group

AABBBB CDDD

Population Sample

C

AB

D

AA

A

C

D D

D

D D

BB

B

BB

BB

SamplePopulationor Process

Preserve time order

SamplePopulationor Process

Preserve time order

SampleProcess

9:00 9:30 10:3010:00

Preserve time order

SampleProcess

9:00 9:30 10:3010:00

Preserve time order

Systematic

Sampling

SubgroupSampling

Sample every nth one

(e.g., every 3rd)

Sample n units every

tth time (e.g., 3 units

every hour); calculate

the mean (proportion )

for each subgroup

Purpose of Sample Formula*/ Minitab Commands

Estimate average

(e.g., determine baselinecycle time)

(Where d = precision: __ units)

Estimate proportion

(e.g., determine baseline %defective)

(Where d = precision: proportion (fraction, not percent))

2

d

2sn

=

( )( )p1pd

2n

2

=

Must remain, and analysed in Time Order


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MEASURE

Gauge R&RA set of trials conducted to assess the Repeatability and Reproducibility of your measurementsystem.

Multiple operators measure multiple units a multiple number of times.

Repeatability:- is often substituted for precision.

Repeatability is the ability to repeat the same

measurement by the same operator at or near the

same time.

Reproducibility :- is customarily checked by

comparing the results of different operators taken

at different times.

%R&R

Describes the variation of the measurement system in comparison to the part variation

of the process

%P/T

Describes the variation of the measurement system in comparison to the part tolerances

total

systemtmeasuremen

S

SRR

_&% =

Tolerances

STP

systemtmeasuremen _*15.5/% =

Unacceptable

Desired Acceptable Borderline

0% 10% 20% 30% 100%

Unacceptable

Desired Acceptable Borderline

0% 10% 20% 30% 100%

General guidelines for interpreting Gage R&R results.


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0

1

2

3

4

5

6

7

8

9

10

4.004.054.104.154.204.254.304.354.404.454.504.554.604.65

Target

Weight

Fill weight for SKU 1234

1 July 7 July

Fill Weight

Numberofoccurren

ces

0

1

2

3

4

5

6

7

8

9

10

4.004.054.104.154.204.254.304.354.404.454.504.554.604.65

Target

Weight

Fill weight for SKU 1234

1 July 7 July

Fill Weight

Numberofoccurren

ces

MEASURE

Patterns in DataFrequency Plot :- shows the shape or distribution of thedata by showing how often different values occur.

Pareto Chart :- The Pareto principle is often described bythe 80/20 rule. This rule says that, in many situations,roughly 80% of the problems are caused by only 20% of thecontributors.

0

5000

10000

15000

20000

25000

AmountofSpoila

ge($$)

Produce

Meat

Dairy

Bakery

Other

Category

100%

80%

60%

40%

20%

Percentageoftotal

0

5000

10000

15000

20000

25000

AmountofSpoila

ge($$)

Produce

Meat

Dairy

Bakery

Other

Category

100%

80%

60%

40%

20%

Percentageoftotal


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Patterns in DataStratification :- Stratification means dividing datainto groups (strata) based on key characteristics.

A key characteristic is some aspect of the data

that you think could help explain when, where, andwhy a problem exists.

The purpose of dividing data into groups is to detecta pattern that localizes a problem or explains why

the frequency or impact varies between times,locations, or conditions.

Disaggregation :- Many figures we see are aggregated.

For example, if we look at total monthly production figures,each data value is really a combined figure representing allproducts, lines, shifts, weeks, etc.

If we take apartdisaggregatethese figures, we can

often see patterns that are masked in the roll up.

1

2

3

4

5

6

Count

8 9 10 11 1 2 1 3 14 15 16 1 7 18 19 20 21

Minutes

0

1

2

3

4

5

6

7 8 9 10 11 12 13 14 15 16 17 18 19 20 21

0

1

2

3

4

5

6

7 8 9 10 11 12 13 14 15 16 17 1 8 19 20 21

0

1

2

3

4

5

6

7 8 9 10 11 12 13 14 15 16 17 18 19 20 21

Location A

Location B

Location C

Time to Complete Lubes

(all locations)

MEASURE


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MEASURE

Patterns in Data

Time Series Plot :- A time plot is a graph of data in timeorder.

Individuals Control Chart :-

Time ordered plot of results.

Statistically determined control limits are drawn on the plot.

3020100

70

80

90

100

110

120

130

140

Cycle Time for T420 Orders

June 130

Numberofdays

3020100

70

80

90

100

110

120

130

140

Cycle Time for T420 Orders

June 130

Numberofdays

3130292827262524232221201918171615141312111098765432Subgroup 1

250000

200000

150000

100000

50000

0

IndividualValue

July

June

May

April

M

arch

February

January

December

November

October

September

August

July

June

M

ay

April

M

arch

February

January

December

November

October

September

August

July

June

M

ay

April

M

arch

February

JanuaryMonth

I Chart for Volume by Year

Mean=69481

UCL=117036

LCL=21926

2001 2002 2003


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MEASURE

Patterns in DataCommon Cause & Special Cause Variation

Common Cause :- always present to somedegree in the process.

Special Cause :- something different

happening at a certain time or place


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MEASURE

Signals in Data

7 or more points in a row on the same

side of the median indicates a process shift.

(If the data are symmetric, its OK to use theaverage as the centerline instead of the median.)

7 or more points in a row continuously

increasing or decreasing indicates a trend.(Start counting at the point where the directionchanges.)

Too few runs indicates a shift in the process

average, a cycle, or a trend.

Too many runs indicates sampling from twosources, overcompensation, or a bias.

MEASU

REMENT

Median

MEASUREMENT

Upward Trend Downward Trend

MEASUREMENT

Median


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MEASURE

Signals in Data

14 or more points in a row alternating up

and down indicates bias or sampling problems.

One or more points outside the control

limits indicates that something is different aboutthose points.

MEASUREMENT

MEASURE

MENT

MEASUREMENT

MEASURE

MENT


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Process CapabilityProcess capability measures are statistical measures that summarize how much variation there is ina process relative to customer specifications.

To increase the Process Capability, you have to decrease the process variability.

When continuous data are normally distributed, calculating a process capability index is reallyequivalent to finding the area under the normal (or bell-shaped) curve that is outside the spec limits,as depicted in the diagram below.

Defects

Defects

Too early Too late

Delivery Time

Reduce

variation

Delivery Time

Too early Too late

Lower specification Upper specification

LSL USLLSL USL

MEASURE


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MEASURE

Process CapabilityChecking for Normality ( Normal Distribution )

If the data is Normal, the points will fall on a straight line.

Straight means within the 95% confidence bands.

You can say the data is Normal if approximately 95% of the data points fall within the confidencebands.

25 35 45 55

1

5

10

2030

40

50

60

70

80

90

95

99

Data

Percent

ML Estimates

Mean:

StDev:

40.1271

4.86721

95% confidence ba nds

25 35 45 55

1

5

10

2030

40

50

60

70

80

90

95

99

Data

Percent

ML Estimates

Mean:

StDev:

40.1271

4.86721

95% confidence ba nds

Conclusion

Not a serious departure

from Normality

Conclusion

There is a serious

departure from Normality

25 35 45 55

1

5

10

20

30

40

50

60

70

80

90

95

99

Data

Percent

ML Estimates

Mean:

StDev:

40.1271

4.86721

-2 -1 0 1 2 3 4

1

5

10

20

30

40

50

60

70

80

90

95

99

Data

Percent

ML Estimates

Mean:

StDev:

1.13627

1.07363


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MEASURE

Process CapabilityBaseline Sigma ValueProcess Sigma builds on the basic foundation of process data and specification limits.

Increase in ProcessSigma requiresexponential defect

reduction

DPMO

Process

Sigma

308,537 266,807 3

6,210 4233 53.4 6

ProcessCapability

Defects perMillion

Opportunities

(distribution shifted 1.5s)

Process

Sigma Scale


reduction


reduction

DPMO

Process

Sigma

308,537 266,807 3

6,210 4233 53.4 6

ProcessCapability

Defects perMillion

Opportunities


Process

Sigma Scale

DPMO

Process

Sigma

308,537 266,807 3

6,210 4233 53.4 6

ProcessCapability

Defects perMillion

Opportunities


Process

Sigma ScaleLSL USLLSL USL


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MEASURE

Process CapabilityBaseline Sigma ValueThere are two methods commonly used to determine Process Sigma.

Method 1 :-Look-up Actual Yield in a process sigma conversionTable.

Method 2 :-Look up a Normal Approximation of yield in theprocess sigma table.

LSL USL

Actual Yield:

60% Yield = 1.8 Process Sigma

LSL USL

Actual Yield:


LSL USL

Area under Normal Curve


LSL USL

Area under Normal Curve



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MEASURE

Process CapabilityMethod 1 :-Look-up Actual Yield in a process sigma conversion table.

1. Determine number of defect opportunities O = ______ per unit

2. Determine number of units processed N = ______

3. Determine total number of defects D = ______ made (include defects made and later fixed)

4. Calculate Defects Per Opportunity DPO= = ______

5. Calculate Yield Yield = (1-DPO) x 100 = ______

6. Look up Process sigma in the Process Sigma TableProcess Sigma = ______

D

N x O

D

N x O

5

100

7

.014

98.6

3.7


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MEASURE

Process CapabilityMethod 2 :-

Look up a Normal Approximation of yield inthe process sigma table.

1. ENTER AVERAGE, STANDAR D DEVIATION, AND SPEC LIMITS

2. LABEL A NORMAL CU RVE

Average Standard dev iation USL (and s hade to LEFT for A rea 1) LSL (and shade to LEFT for Area 2)

3. DETERMINE AREA BELOW USL ( AREA 1)

5. CALCULATE YIELD

6. LOOK UP YIELD IN PROCESS SIGMA TA BLE

s

X + sX X + sX + sXX

Find Z1

Look up Z1 in Normal Table NormDist (Z1) = Value from Normal Tab le =

4. DETERMINE AREA BELOW LSL, IF ANY (AREA 2)

Find Z2

Look up Z2 in Normal Table

Z 2 = =( ) ( )

( )

( ) ( )

( )=

NormDist (Z2) = Value from Normal Tab le =

LSL - X

s

LSL - X

s

LSL - X

s

Yield = Area 1 Area 2= ______ ______ =

Yield (percentage)= Yield x 100 % =

Process S igma = Look-Up from Sigma Table =

Z1 = =( ) ( )

( )

( ) ( )

( )=

USL - X

s

USL - X

s

USL - X

s

X = ______ s = ______ USL = ______ LSL = _______X = ______ s = ______ USL = ______ LSL = _______17 3 N/A25

3

17 20

USL = 25

25 17

32.67

.996533

N/A

.996533

99.6%

4.2

.996533 0

X = 17 s = 3 USL = 25 LSL = none

0

2

4

6

8

10

12

8-1

0

10-1

2

12-1

4

14-1

6

16-1

8

18-2

0

20-2

2

22-2

4

24-2

6

26-28

USL

Frequency


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MEASURE

Process Capability IndicesCp & PpThis is the performance index which is defined as the tolerance width divided by the performance,irrespective of process centering.

s

LSLUSLp

p 6

=

Where: USL = upper specification limit

LSL = lower specification limit

6s = 6 times the sample standard deviation

LSL USL

CAPABILITY INDICESPp = (USL-LSL)/6s

cap2.mgf

(USL-LSL)

6s 6s

The Pp

is determined by the tolerance and spread of the

process, location is not considered. The red (left) and blue

(right) distributions have the same Pp. Virtually all of the

parts produced on the red (left) process will be in

specification, while virtually all of the parts from the blue

(right) process will be out of specification.

EASU E


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MEASURE

Process Capability IndicesCpk & PpkThe process performance index, Ppk,, which accounts for process centering and is defined as :

( ) ( )

=

s

LSLxor

s

xUSLMinp

pk 33

LSL USL

cap4.mgf

CAPABILITY INDICESPpk = min{(USL - Xbar)/3s or (Xbar - LSL)/3s}

(Xbar - LSL)

(Xbar - LSL) Red 3s = Blue 3s

To estimate the Ppk perform both calculation above andreport the smaller value. A quicker way is to determinewhich specification limit (USL or LSL) is closest to theaverage and only do that calculation, it will be the smallest.

Here we can see the impact of the specification in thedefinition of Ppk. Both processes above will have the samePp, same spread and tolerance. The Ppk for the blue (left)

process will be lower because (Xbar-LSL) is smaller.

MEASURE


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MEASURE

Completion ChecklistBy the end of the Measure Phase, you should be able to answer the following :-

1. What specifically is the main problem or problems.

2. What you have done to validate the measurement system.

3. What patterns are exhibited in the data.

4. What the current / baseline capability is.


MEASURE


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MEASURE

Summary


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ANALYSE

DoE

IMPROVE

ANALYSE


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ANALYSE

Process Door vs Data Door

Process

Door

Process

Door

Data DoorData Door

Detailed Process Map

Value Added Analysis

Cycle Time Analysis

Stratification

Scatter Diagrams

Multi-Vari Analysis

ANALYSE


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ANALYSE

Process DoorActivity Flow Chart :- Specific about what happens in aprocess.

Deployment Flow Chart :- These show detailed steps

in a process and which people or departments are involvedin each step.

Value Stream Map :- Value Stream Mapping is agraphic representation of the flow from the customer andsupplier through the plant. The map is a visualrepresentation of both the material and information flows.This is a key difference between process mapping and

value stream mapping.

Sales Technical Shipping Coordinator Sales Technical Shipping Coordinator

ANALYSE


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Data Door

Scatter Plot :- a graph that helps you visualise therelationship between two variables. It can be used to checkwhether one variable is related to another variable and is

an effective way to communicate the relationship you find.

T i m e(mi ns )

M on ths on job

c a e r o o

T i me N e e de d to A s s e m bl e the Produc t v s .

W ork e rs T i me on the J ob

Produc t B

Produc t A

1

2

3

4

5

6

7

8

9

1 0

1 2 3 4 5 6 7 8 9 10 1 1 1 2 >12

222

2

Possible Positive

Correlation

Possible Negative

Correlation

Strong PositiveCorrelation

Strong NegativeCorrelation

Other PatternNo Correlation

AD-079

ANALYSE

ANALYSE


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ANALYSE

Transforming to Normal DataTransforming non normal data into normal data is necessaryas incorrect inferences will be made with tests, requiringnormal data.

Non-Normal Data can be transformed using a (Lambda)value calculated through a Box-Cox transformation.

Method Consequence ofNon-Normality

Process Sigma calculation Incorrect Process Sigma value

Individuals contr ol chart False detection of some specialcauses, missed signals of others

Hypothesis testing Incorrect conclusions aboutdifferences between groups

Regression Misidentification of importantfactors; poor predictive abi lities

Design of experiments Incorrect conclusions aboutimportant factors; poor predictionabilities

5 7 9 11 13 15 17 19 21 23

0

10

20

CycleTime

Freque

ncy

-5 -4 -3 -2 -1 0 1 2 3 4 5

2.0

2.5

3.0

3.5

4.0

4.5

5.0

5.595% Confidence Interval

StDe

v

Lambda

Last Iteration Info

Lambda StDev

-0.393

-0.337

-0.281

2.285

2.285

2.284

Low

Est

Up

Box-Cox Plot for CycleTime

0.8 0.9 1.0 1.1 1.2 1.3 1.4

0

10

20

LogCycletime

Freque

ncy

ANALYSE


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ANALYSE

Hypothesis Testing

A hypothesis test is a procedure that summarizes data so you can detect differences amonggroups.

Tests the null hypothesis -H0: no difference between groups

Against the alternative hypothesis -Ha: groups are different

Obtain a P-value for the null hypothesis -Use the data and the appropriate hypothesis test statistic to obtain a P-value

If P < .05, reject the H0 and conclude the Ha

If P .05, cannot reject the H0

IF P IS LOW

REJECT Ho

ANALYSE


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ANALYSE

Hypothesis Testing

Compare two or moregroup averages.

Compare two or more

group proportions.

Chi-square test

Compare two or moregroup variances.

Test for equal variances(F-test, Bartletts test,

Levenes test)

ANOVA

(Analysis Of Variance)

Compare two groupaverages when data is

matched.

paired t-test

Compare two groupaverages.

t-test

PurposeHypothesis Test

Discrete

Data Type

Continuous

ANALYSE


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ANALYSE

Hypothesis Testing

F-Test Output

( Minitab ) Bartletts Test:assumes normal

distributed data.

Levenes Test:

No normalitynecessary.

Conclusion: BothP-values are < .05, soconclude the variances

in production volumesare significantlydifferent before andafter the improvement.

25001500500

95% Confidence Intervals for Sigmas

new

std

52000510005000049000480004700046000

Boxplots of Raw Data

Prod Vol

P-Value : 0.017

Test Statistic: 6.282

Levene's Test

P-Value : 0.029


F-Test

Factor Levels

std

new

Test for Equal Variances for Prod VolBartletts Test:

assumes normal

distributed data.

Levenes Test:

No normalitynecessary.

Conclusion: BothP-values are < .05, soconclude the variances

in production volumesare significantlydifferent before andafter the improvement.

25001500500


new

std

52000510005000049000480004700046000


Prod Vol

P-Value : 0.017


Levene's Test

P-Value : 0.029


F-Test

Factor Levels

std

new

Test for Equal Variances for Prod Vol

25001500500


new

std

52000510005000049000480004700046000


Prod Vol

P-Value : 0.017


Levene's Test

P-Value : 0.029


F-Test

Factor Levels

std

new

Test for Equal Variances for Prod Vol

ANALYSE


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ANALYSE

Hypothesis Testing

T-Test Output ( Minitab )

= n= n

Draw conclusions by

looking at theP-value. Is it < .05?

Standard error of the

mean = st. dev. of the

average

Session Window Output Confidence interval for the avg. dif f.Std - New

Interval does not contain zero, so asignificant difference does exist with

95% Confidence

The value of t

ANALYSE


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ANALYSE

Hypothesis Testing

ANOVA Test Output ( Minitab )

Sum of Squares

One-way Analysis of Variance

Analysis of Variance for FaceAmt

Source DF SS MS F P

Form 6 539413 89902 11.56 0.000

Error 98 762240 7778

Total 104 1301653Individual 95% CIs For Mean

Based on Pooled StDev

Level N Mean StDev -------+---------+---------+---------

A 15 446.00 100.56 (----*---)

B 15 277.33 105.46 (----*---)

C 15 376.67 102.72 (----*---)

D 15 384.00 82.27 (---*----)

E 15 476.00 65.01 (----*---)

F 15 514.67 71.70 (---*----)

G 15 414.00 80.78 (---*----)

-------+---------+---------+---------

Pooled StDev = 88.19 300 400 500

The variance between

groups is 11.5 timesbigger than thevariance within groups

The parenthesesrepresent confidenceintervals forgroup

averages (notindividual values)

Draw conclusion

from P-value

We assume the variancesfor all groups are the same

Mean Squaresanother name for

varianceBetween

Within

ANALYSE


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Hypothesis Testing

Chi-Squared Test Output ( Minitab )

P value of


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Regression AnalysisRegression analysis generates a line that quantifies the relationship between X and Y.

The line, or regression equation is represented as Y=b0+b1X

Where :-

b0 = intercept ( where the line crosses X=0 )

b1 = slope ( change in Y per unit increase in X )

The regression line / equation is determined by aprocedure that minimises the total squareddistance of all the points to the line.

This is known as The Least Squares Method

Height (m)

ShoeS

ize

(Eur)

1.951.901.851.801.751.70

49

48

47

46

45

44

43

42

41

S 0.485759

R-Sq 89.7%

R-Sq( ad j) 88. 9%

Regression

95% CI

95% PI

Fitted Line PlotShoe Size (Eur) = 3.445 + 22.83 Height (m)

Read Model / Equation

y = 3.445 + 22.83x

ANALYSE


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Regression Analysis

R-Squared = R-sqMeasures the percent of variation in the Y-values that is explained by the linear relationship with X.

Ranges from 0 to 1 (= 0% to 100%)

The correlation, r:Ranges from -1 to 1

r = -1= perfect negative or inverse relationship

r = 0 = no linear relationshipr = +1 = perfect positive relationship

Measures the strength of the relationship

R2 is equal to square of r

Known as Pearsons correlation coefficient

Explained%100xvariationTotal

variationExplainedsq-R ==

X

Y

X

Y

X

Y

X

Y

X

Y

X

Y

Strong Positive Correlation

r = .95

R2 = 90%

Moderate Positive Correlation

r = .70

R2 = 49%

No Correlation

r = .006

R2 = .0036%

Other Pattern -

No Linear Correlationr = -.29

R2 = 8%

Moderate Negative Correlation

r = -.73R2 = 53%

Strong Negative Correlation

r = -.90R2 = 81%

X

Y

X

Y

X

Y

X

Y

X

Y

X

Y

Strong Positive Correlation

r = .95

R2 = 90%

Moderate Positive Correlation

r = .70

R2 = 49%

No Correlation

r = .006

R2 = .0036%

Other Pattern -

No Linear Correlationr = -.29

R2 = 8%

Moderate Negative Correlation

r = -.73R2 = 53%

Strong Negative Correlation

r = -.90R2 = 81%

ANALYSE


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Regression AnalysisOther Types of Regression

Using indicator variables(for discrete Xs)

x

x

x

xx

x

x

x

x x

xx

x

xx

Xi

Y

Xa

Xb

Xc

Using indicator variables(for discrete Xs)

x

x

x

xx

x

x

x

x x

xx

x

xx

Xi

Y

Xa

Xb

Xc

Curvilinear (One X)

X

Y

Curvilinear (One X)

X

Y

X

Y

Simple linear (One X)

X

Y

Simple linear (One X)

X

Y

X

Y

Multiple (Two or more Xs)

Y

X2

X 1

Multiple (Two or more Xs)

Y

X2

X 1

Y

X2

X 1

Logistic (for discrete Ys)

1

0

%yes

X

Logistic (for discrete Ys)

1

0

%yes

X

Curvilinear (Two or more Xs)

Y

X1

X2

Curvilinear (Two or more Xs)

Y

X1

X2

ANALYSE


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Design of Experiments ( DOE )Design of Experiments is an approach for effectively and efficiently exploring the cause-and-effect

relationship between numerous process variables (Xs) and the output or process performancevariable (Y).

1. Identifies the vital few sources of variation (Xs)

2. Those that have the biggest impact on results

3. Quantifies the effects of the important Xs, including their interactions

4. Produces an equation that quantifies the relationship between the Xs and Y

5. You can predict how much gain or loss will result from changes in process conditions

Types of Experimental Design

Full Factorial ( 2 or more Levels ) Fractional Factorial

Screening Designs Plackett-Burman Design

Central Composite Response Surface Methodology

ANALYSE


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Design of Experiments ( DOE )The Approach :-

Experiment

Design

Experiment

Analysis

1. Identify responses

2. Identify factors

3. Select design

4. Choose factor levels

5. Randomize runs

6. Conduct experiment and collect data

7. Analyze data

8. Draw conclusions

9. Verify results

Experiment

Design

Experiment

Analysis

1. Identify responses

2. Identify factors

3. Select design

4. Choose factor levels

5. Randomize runs

6. Conduct experiment and collect data

7. Analyze data

8. Draw conclusions

9. Verify results

ANALYSE


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Design of Experiments ( DOE )2 Level Full Factorial ( Example ) :- Fractional Factorial Fit: Bends versus Vendor, Size, Heat

Estimated Effects and Coefficients for Bends (coded units)

Term Effect Coef SE Coef T P

Constant 15.688 0.9902 15.84 0.000

Vendor -0.875 -0.437 0.9902 -0.44 0.670

Size 1.125 0.562 0.9902 0.57 0.586

Heat 8.125 4.062 0.9902 4.10 0.003

Vendor*Size -5.125 -2.563 0.9902 -2.59 0.032

Vendor*Heat -1.625 -0.813 0.9902 -0.82 0.436

Size*Heat 1.375 0.688 0.9902 0.69 0.507

Vendor*Size*Heat 1.625 0.812 0.9902 0.82 0.436

Analysis of Variance for Bends (coded units)

Source DF Seq SS Adj SS Adj MS F P

Main Effects 3 272.188 272.188 90.73 5.78 0.021

2-Way Interactions 3 123.188 123.188 41.06 2.62 0.123

3-Way Interactions 1 10.562 10.562 10.56 0.67 0.436

Residual Error 8 125.500 125.500 15.69

Pure Error 8 125.500 125.500 15.69

Total 15 531.438

Estimated Coefficients for Bends using data in uncoded units

Recommendations

In general, request or buy heat-treated clips

If you want to use both sizes and can have two vendors:

Purchase heat-treated No. 1 clips from Abel

Purchase heat-treated Jumbo clips from Noesting

If you want both sizes but only one vendor, choose heat-

treated Noestings

StdOrder RunOrder CenterPt Blocks Vendor Size Heat Bends

16 1 1 1 Abel Jumbo Yes 18

12 2 1 1 Abel Jumbo No 5

1 3 1 1 Noesting No.1 No 9

14 4 1 1 Abel No.1 Yes 21

9 5 1 1 Noesting No.1 No 7

2 6 1 1 Abel No.1 No 21

8 7 1 1 Abel Jumbo Yes 18

15 8 1 1 Noesting Jumbo Yes 26

13 9 1 1 Noesting No.1 Yes 15

7 10 1 1 Noesting Jumbo Yes 22

6 11 1 1 Abel No.1 Yes 173 12 1 1 Noesting Jumbo No 16

10 13 1 1 Abel No.1 No 10

4 14 1 1 Abel Jumbo No 12

5 15 1 1 Noesting No.1 Yes 21

11 16 1 1 Noesting Jumbo No 13

43210

C

AB

AC

ABC

BC

B

A

Pareto Chart of the Standardized Effects

(response is Bends, Alpha = .05)

A: Vendo rB : S iz eC: Heat

Vendor Size Heat

Noestin

g

Abel

No.1

Jumb

oNo Ye

s

12

14

16

18

20

Bends

Main Effects Plot (data means) for Bends

ANALYSE


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Completion Checklist

By the end of the Analyse Phase, you should be able to answer the following :-

1. What potential causes you have identified.

2. Which potential causes you decided to investigate and why ?

3. What data you collected to verify those causes.

4. How you interpreted the data.


ANALYSE


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Summary


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IMPROVE

Solutions

FMEA

Pilot

Impl

emen

-

tatio

n

IMPROVE

Solutions

FMEA

Pilot

Impl

emen

-

tatio

n

IMPROVE

IMPROVE


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Generating, Evaluating and Selecting Solutions

Creativity Techniques :-

Quick and Dirty Short Time Investment More Involved

Think like a kid Candid Comments SCAMPER

Challenge the rules Musical Chairs Slice & Dice

Set a deadline Edison Ideas box

Get rid of excuses Brutethink

IMPROVE


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Generating, Evaluating and Selecting SolutionsCost Benefit Analysis

Express the financial benefits in terms that make sense for your business :-

Return on Capital Return on Equity Return on Investment

Economic Value Added Cash Flow Payback PeriodNet Present Value

Express non-financial improvements in terms that make both sense for the customer and your

business :-Reduced cycle time Improved on-time delivery Increased flexibility

Faster response Reduced effort Increased availability

Fewer defects

Selecting Solutions

If there is an obvious winner from the evaluation step, go with that choice.

If there is no clear choice, use decision making :- Consensus,

Majority vote, One person

IMPROVE


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Assessing Risks

FMEA :-

Is a structured approach to identify, estimate, prioritize and evaluate risk.

Aims at failure prevention.Is primarily used to limit the risk involved in changing the process.

FMEA AnalysisProject: _____________________ Team: _____________________

Date ___________ (original)___________ (revised)

Item orProcess

Step

PotentialFailure

Mode

PotentialEff ect (s)

of Failure

Potential

Cause(s)

Current

Controls RPN Recommended

Action

Responsibilityand

Tar get Date Ac tion Taken Severity

Oc

currence

De

tection

RP

N

After

Se

verity

Oc

currence

De

tection

Total Risk Priority Number = After Risk Priority Number =

IMPROVE


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Piloting Solutions

Pilot when :-

You need to confirm the expected results andpracticality of the solution.

You want to reduce the risk of failure.

The scope of the change is large, and reversing the

change would be difficult.Implementing the change will be costly.

Changes would have far-reaching, unforeseenconsequences.

Steps of a Pilot Program

1. Select pilot steering team

2. Brief participants

3. Plan pilot

4. Inform associates

5. Train employees6. Conduct pilot

7. Evaluate results

8. Increase scope

IMPROVE


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Implementing SolutionsPlanning :- Elements of a Plan

Understand the why.

Plan the work.

Plan the tasks and the subtasks.

Plan the time.

Plan the people and resources.

Understand if it worked. Potential Problems

Tasks & Timeline

Aug. Sept. Oct. Nov. Dec. Jan. Feb.Step

How to Check

PLAN ACTUALS

Change made

Stakeholders

PERSONor GROUP

Communication& Participation

Finance

Sales

IS

Step Pot.

Failure

Pot.

Cause

Counter-

measures

Budget & Resources

Expenses

Staff time

xxxxx 00.00xxxxx 00.00xxxxx 00.00

Ted 5 hrs

IMPROVE


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Completion Check ListBy the end of the Improve Phase, you should be able to answer the following :-

1. What factors you considered to decide about the strategy.

2. What solutions you identified.

3. What criteria you used to select a solution.

4. The results of any small scale tests of the solutions.

5. Plans for detailed implementation.

6. How the planned changes align with management systems, policies, and procedures.


IMPROVE


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Summary


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CONTROL

Control

Standardize

Document

Monito

r

Evaluate

Closure

IMPROVE

Control

Standardize

Document

Monito

r

Evaluate

Closure

IMPROVE

CONTROL


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Quality Control & Process Change ManagementReacting to Problems :-

Howto

Produc

eit

Process

Inputs

Measurements Machines

Methods People Environment

Produce it

Policies

FixProduct

StoreProduct

Customer

Output

LEVEL 1: FIX THE OUTPUT- Containment

LEVEL 2: FIX T HE PROCESS- Defect Root Cause

LEVEL 3: FIX THE SYSTEM-Systemic Root Cause

What toProduce

Fix or control?

Where we

sometimes

stop

Example: Toaster Manufacturing Corrosion Problem

Level 1

Containment

Level 2

Defect Root Cause

Level 3

Systemic Root Cause

Fix the process forhandling corrodiblematerial:

a) in house

b) at suppliers

How??

Use no touchhandling

Fix the system thatproduced changesin designs that haveproblems like these.

How??

Incorporate as apart of all designreviews a checkfor possiblecorrosionproblems.

Fix the toasters thathave corrosionproblems:

a) units in the field

b) units still in house

How??

Replacedamaged parts

CONTROL


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Quality Control & Process Change ManagementQC Process Chart :-

The plan is

typicallycaptured as a

flowchart.

The middle column

describes what you willcheck in the process tomonitor its quality.

The thirdcolumn

describes howthe processoperators

should reactdepending on

what they findin the

measures.

Flowchart IndicatorsCorrective

Actions

PLAN/DO CHECK ACT

Count errors If more than 1 per order,stop process, contactSam

Alert Sam immediately;organize investigation

Plot time on each order;should be < 2 hours;check for special causes

The plan is

typicallycaptured as a

flowchart.

The middle column

describes what you willcheck in the process tomonitor its quality.

The thirdcolumn

describes howthe processoperators

should reactdepending on

what they findin the

measures.

Flowchart IndicatorsCorrective

Actions

PLAN/DO CHECK ACT

Count errors If more than 1 per order,stop process, contactSam

Alert Sam immediately;organize investigation

Plot time on each order;should be < 2 hours;check for special causes

CONTROL


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StandardizationNothing happens on a reliable, sustained basis unless we build a system to cause it to happen ona reliable, sustained basis.

Standardization is what allows high quality to happen on a reliable, sustained basis.

Standardization helps us compete more successfully in the marketplace by providing :-

Increased reliability Reduced costs Improved employee performance

Increased safety Continuous improvement Flexible practices

Processes that remain in control

CONTROL


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MonitoringOn-going monitoring is typically managed with a control chart.

Start

Type

of data

?

Counting

items with an

attribute or counting

occurrences?

Equal

sample

sizes

?

Equal

opportunity?

p chartp chart

np chartnp chart

Individuals

chart

Individuals

chart

EWMA

chart

EWMA

chart

Continuous

Yes

No

Yes

Rational

Subgroups

Discrete

Yes

No

No

u chartu chart

c chartc chart

Do limits

look right?

Try individuals chartTry individuals chart

Need to

detect small shifts

quickly?

Individual

measurements

or subgroups

?

Try transformation to make data normalTry transformation to make data normal

Do limits

look right?

YesNo

Either/Or

No

Yes

Individual

measurements

Occurrences

X, R chartX, R chart

Items withattribute

StartStart

Type

of data

?

Type

of data

?

Counting

items with an


occurrences?

Counting

items with an


occurrences?

Equal

sample

sizes

?

Equal

sample

sizes

?

Equal

opportunity?

Equal

opportunity?

p chartp chart

np chartnp chart

Individuals

chart

Individuals

chart

EWMA

chart

EWMA

chart

Continuous

Yes

No

Yes

Rational

Subgroups

Discrete

Yes

No

No

u chartu chart

c chartc chart

Do limits

look right?

Try individuals chartTry individuals chart

Need to

detect small shifts

quickly?

Need to

detect small shifts

quickly?

Individual

measurements

or subgroups

?

Individual

measurements

or subgroups

?

Try transformation to make data normalTry transformation to make data normal

Do limits

look right?

Do limits

look right?

YesNo

Either/Or

No

Yes

Individual

measurements

Occurrences

X, R chartX, R chartX, R chartX, R chart

Items withattribute

X = averageR = Range

p = proportion

c = count

Control Chart Type Data Type

Individuals chart Continuous or Discrete

p chart ornp chart Discrete-attribute

cchart oru chart Discrete-count

R,X R,X Continuous

CONTROL


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Before After

}Improvement

Target}Remaining Gap

Good

Step 4 changesimplemented

} ImprovementBefore After

A1 A2 A3 A4 A2 A1 A3 A4

Before After

Before After

}Improvement

Target}Remaining Gap

Good

Step 4 changesimplemented

} ImprovementBefore After

A1 A2 A3 A4 A2 A1 A3 A4

Before After

Evaluating ResultsIn advance of improvement implementation, it is help toconsider how you will present before and afterevaluation -

1. Allocate some time in project plan to step back andbuild the before / after graphics

2. Maintain a set of good illustrations of before versusafter as the project progresses

3. Consider from the perspective of selling thebenefits of the project to your key customers withsimple, clear graphics

4. Where possible, declare $ value of savingsattributable to a given aspect of the improvementproject

CONTROL


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Evaluating ResultsRe-Calculate Process Sigma

Step BEFOREOpportunitiesUnits

1

2

3

4

5

6

7

8

9

10

11

12

4040

2 x 40 = 80 6137

113

34

142

38

69

143

37

64

72

35

1 x 40 = 40

3 x 40 = 120

1 x 40 = 40

4 x 40 = 160

1 x 40 = 40

2 x 40 = 80

4 x 40 = 160

1 x 40 = 40

2 x 40 = 80

2 x 40 = 80

1 x 40 = 40

40

40

40

40

40

40

40

40

40

40

960 846

AFTER

171

12

0

8

0

3

37

0

5

2

1

86

Yield = 1

= 1 .88

= 12%

Sigma = 0.3

960846960846

Yield = 1

= 1 .09

= 91%

Sigma = 2.8

960

86

960

86

BEFORE

AFTER

CONTROL


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Closure1. Improvement must be continuous, but individual initiatives and project teams come to an end.

2. Learn when its time to say goodbye.

3. Effective project closure weaves together the themes of: Project purpose.

Improvement methods.

Team skills and structures.

4. Develop managerial systems to capture learnings and enable the organization to addresssystem issues.

5. Documentation and recognition are two critical aspects of project team closure.

6. Celebrate!

CONTROL

Completion Check List


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Completion Check ListBy the end of the Control Phase, you should be able to answer the following :-

1. What the data showed about the effectiveness of the solution, and how the actual resultscompare to the plan.

2. Why you are now confident that the current solution should be standardise.

3. How the new methods have been documented and how this is used in the day-to-daybusiness.

4. What you do to monitor the process to sustain the gains.

5. What the key learnings are, and what recommendations the team developed for furtherimprovements.

Only after answering the above questions, you can bring your project to an end.

CONTROL

Summary


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Summary

6sigma handbook

Documents