Six Sigma Training Posters

1

Welcome to

DMAIC

for BBs & MBBs

2

• I = Innovators• CA = Change Agents• P = Pragmatists• S = Skeptics• T = Traditionalists

It’s a Continual Wave, Skeptics and Traditionalists have to be convinced that they only have two choices:

• either get off the beach, or

• Get Wet!

10%

20%

40%

20%

10%I CA P S T

The Five Year Cultural Change Curve

Scale of Perceived RiskLittle Risk Perceived

Large Risk Perceived

• Innovators inspire Change Agents• Change Agents convince Pragmatists through clear

business case, with data• Skeptics have to see it in action • Traditionalists value the status quo above all else

3

The 12-Step Process

Process Capability Y, XCapability IndicesY, XDetermine Process Capability

11

Proposed SolutionFactorial DesignsXDiscover Variable Relationships

8List of Vital Few X’sDOE-ScreeningXScreen Potential Causes7

Control

Piloted Solution SimulationY, XEstablish Operating Tolerances

9

MSAContinuous Gage R&R, Test/Retest, Attribute R&R

Y, XDefine & Validate Measurement System on X’s in Actual Application

10

Sustained Solution Documentation

Control Charts, Mistake Proofing, FMEA

XImplement Process Control12

Improve

Prioritized List of all X’sProcess Analysis, Graphical Analysis, Hypothesis Tests

XIdentify Variation Sources6

Improvement Goal for Project Y

Team, BenchmarkingYDefine Performance Objectives

5

Process Capability for Project Y

Capability IndicesYEstablish Process Capabilities

4Analyze

Data Collection Plan & MSA Data for Project Y

Continuous Gage R&R, test/Retest, Attribute R&R

YMeasurement System Analysis

3

Performance Standard for Project Y

Customer, BlueprintsYDefine Performance Standards

2Project YCustomer, QFD, FMEAYSelect CTQ Characteristics1

MeasureHigh Level Process MapDefine Process MapCApproved CharterDevelop Team CharterBProject CTQ’sIdentify Project CTQ’sA

DefineDeliverablesToolsFocusDescriptionStep

4

Iterative Process

Steps A,B,C

Steps 1,2,3

Steps 4,5,6Steps 7,8,9

Steps 10,11,12

5

Problem statement

Project Y Magnitude Impact

Using Statistics to Solve Problems

Practical Problem

Statistical Problem

Statistical Solution

Practical Solution

D M A I C

Characterize the process Stability Shape Center Variation

Root cause analysis Critical X’s

Measure the influence of the critical X’s on the mean and variability Test Model Estimate

Verify critical X’s and ƒ(x)

Change process

Control the gains Risk

analysis Control

plans

Data Integrity MSA Brainstorm

potential X’s Sampling plan

Collect data

Capability ZBench ST & LT

6

Practical & Statistical Problem

• Look at Scale of Scrutiny and / or Measurement System Resolution

• Check Spread & Center Vs. Specifications & Target• Look at Histogram, Boxplot, Normality

Plot, and Basic Statistics with Specs superimposed

• Check Process Capability Relative to Specifications• Stat>Tables>Tally>Cumulative % to get

Yield on continuous data

• Stat>Table>Tally>Counts on discrete data for Yield

• State the Problem as one of Spread and/or Center

• State the Process Capability

7

The Goal of Six Sigma

To reduce the variation that the Customer feels from our process, centered around an appropriate

mean or target, and within specification limits as defined by

the Customer.

Process Capability = f(Spread, Center, Specifications)

8

Selecting ProjectsWhen selecting a project, consider these issues:• Process–select a low-performing process that has high

impact on CTQs. A significant gap exists between customer requirements and process performance.

• Feasibility• Don’t try to solve world hunger (too broad, too complex). • Is data available? • How will you close the project? Begin with the end in

mind. • Expect to conclude successfully within 4 to 6 months.

• Measurable Impact In dollars In ROI In defect/cycle time reduction In customer satisfaction

• Resource support within the organization Leadership support is critical for success How great is the support for the initiative? How much resistance is there to change? What is the sense of urgency? Resource and Team Members have the skills and

capabilities to support multiple teams and are dedicated.• Project interactions

Multiple teams affecting process Changes planned for the process (e.g., technology) MGPP

9

The Levels of a CTQ

• Level #1: Expressed Customer Need • High Level from VOC

• Level #2: CTQ Characteristic• WHAT you will measure• Effectiveness v. Efficiency• Goodness v. Timeliness

• Level #3: CTQ Metric or Project Y• HOW you will measure it.• A formula or the categories• e.g. Y = End Date - Start Date• e.g. Y = Dissatisfied, Satisfied,

No Opinion

10

Project Y / Defects

Project Y =

How we Measure the Type of Error

Unit (Loan, Day, App, Transaction)

Error Types:• Not Done (Percentage per period)• Done Wrong (How Wrong?)• Done Early and/or Late (How Late/Early?)

DPO = Defects / [Units x Opp/Unit]= D / [U x O] = D / Total

Opps

Defect = Units that fail to meet Customer Specifications

11

VOC Results and CTQ Drill down tree.

CTQ1:Y=Defect =

Business Y orLevel 1 CTQ: VOC

Level 2 CTQ:Responsiveness

Level 2 CTQ:Competitiveness

Level 2 CTQ:TechnicalPerformance

CTQ2:Y=Defect=

CTQ3:Y=Defect=

CTQ4:Y=Defect=

CTQ5:Y=Defect=

CTQ6:Y=Defect

Customer:

Level 2 CTQ:On timeDeliverables

Level 2 CTQ:Accurate &CompleteDeliverables

Important To Our Customer

Single CellProjects

Process-Based Projects

CTQ

Pro

ject

s

Con

trol

labl

e B

y U

sProcess 4

Process 1

Process 2

Process 3

Yellow indicates thisspecific project path

Determining the Project Y

Drill Down Tree

QFD or Detailed “AS IS” Process Map and/or FMEA on Current Process

C O P I S

12

Finding Potential X’s

C O P I S

Data Collection Plan

Detailed “AS IS” Process Map and

FMEA on Current Process

ProblemStatement

Measurements Materials Men & Women

MethodsEnvironment Machines

Process

InputVariables

(X’s)

n Key input andprocess measures(X) that trackvariablesidentified in yourproject as keydrivers of ProjectY variables

Output(Y’s)

n Key output measures(Y) from thecustomer’sperspectiveProcess Variables

(X’s)

X X X X

1313

Plan for Data Collection

Data Collection Is The First Step To Understanding The Variation The Customer Feels.

Clarify purpose of data collection

Identify what data to collect

Test and validate measurement systems

Write and pilot operational definitions

Develop and pilot data collection forms and procedures

Establish a sampling plan

Train data collectors

Pilot process and makeadjustments

Collect data

Monitor data accuracy and consistency

Ensure DataConsistencyAnd Stability

EstablishData CollectionGoals

Develop OperationalDefinitions AndProcedures

1 432 Collect DataAnd MonitorConsistency

14

CTQ’s Are The Bridge Between Our Process Output And Customer Satisfaction.

High Level Customer Need from VOC:

Quick Response

Timely ResponseProject Y(Characteristic)

Time from inquiry to resolution of inquiry(Project Y Metric)

5 minutes or less(Target)

Not greater than 60 minutes Specification/ Tolerance Limit)

Established inDefine Phase

Established inMeasure Phase



CTQ

Any response taking more than 60 minutes(Defect definition)


CTQ Elements (Performance Standards)

15

n = f( “delta”variation)

DESn

sp n

n

n

16

Measurement System Analysis (MSA)

Date Study Conducted: Type of Gage R&R conducted:_ Test-Retest (continuous data) Pass?

Standard Deviation < 1/10th of Tolerance _____ Y N

_ Short Form Reproducibility (continuous data) Pass?% Tolerance = 100x5.15xRbar / (d*xTolerance) [ 30%] _____ Y N

_ ANOVA Gage R&R (continuous data)1) Two-Way ANOVA Significant? Part p-value _____ Y N Oper p-value _____ Y N Oper & Part p-value _____ Y N

Pass?2) % Tolerance [ 30%] _____ Y N3) % Contribution [ 8%**] _____ Y N4) % Study Variation [ 30%**] _____ Y N 5) # Distinct Categories [ 4**] _____ Y N** Assumes Part-to-Part variation is large, these criteria reverse if each part submitted to the test were the same size.Graphical Diagnosis OK?1) Effective Resolution [Xbar, 50% outside Control Limits] Y N2) Stability [R Chart ”small” ranges, in Control ] Y N3) Consistency within [R Chart, similar patterns by Oper] Y N4) Consistency between [Oper/Part Inter. Plot, close intertwine] Y N 5) Systematic shift [Oper/Part Inter. Plot, consistent difference] Y N

_ Attribute Gage R&R (discrete data) Pass?1) % Repeatability [ 90%] _____ Y N2) % Reproducibility [ 90%] _____ Y N3) % Accuracy [ 90%] _____ Y N

Gage R&R pass? Y NIf no, describe plan for improvement: ______________________________________________________________________________________________________________________________________________________________________________________________

17

The Normal Curve

-3s -2s -1s X +1s +2s +3s

68.26%

95.46%

99.73%

68.26% Fall Within +\- 1 Standard Deviation95.46% Fall Within +\- 2 Standard Deviation99.73% Fall Within +\- 3 Standard Deviation

34.13% 34.13%

13.60% 13.60%2.14% 2.14%

0.13% 0.13%

18

Run Chart p-value Interpretation

Run begins each time the median is crossed

Run begins each time direction changes

P<.05 => Too Few Runs

P<.05 => Too Many Runs

Clusters

Mixtures Oscillations

Trends

19

Process Capability Decision Flow

Six Sigma>Product Report, DPMO, L1 (Input D, U and O)

•Sigma Conversion Table gives ZST

•Z LT = Z ST - Z Shift (1.5)

•Product Report and L1 give Z Bench

•Z Bench = Z ST

•Z LT = Z Bench - Z Shift (1.5)

Note:Z ST = Z LT + Zshift

Z ST = Z Bench-ST

Z LT = Z Bench-LT

Do you have

RationalSubgroups?

Is the Distribution

Normal?

No

Do you have

Continuous Data?

Yes

No

Yes

Use Z Bench-LT only and add 1.5 Shift to get Z Bench-ST

Use Six Sigma> Process Report (Input Data, Specification Limits

and Target as appropriate)

Yes

No Is the S-Chart in-control?

Z Bench-LT , Z Bench- ST

& Z Shift all valid on the Process

Report

Yes

Use Z Bench-LT only and add 1.5 Shift to get Z Bench-ST

No

20

SSBSST SSW

Total WithinBetween

2

11

2

1

2

11

jXijXXXnXijXn

i

g

jjj

g

j

n

i

g

j

ZBench Long-term The Shift Short-termVariation Type ALL Special Common Illustrated by

in time I or Run Chart Xbar Chart R or S Chart by Xs Histogram, Main Effects Plot, Box Plot

Normality Plot Interaction Plot Probability Plot Probability Plot Box Plots

Used to Measurea) Capability Accuracy Precisionb) Total R&R Reproducibility Repeatability

Improve Issue Performance Control TechnologyXs - Factors Vital Few Trivial Many

ANOVA Total X-Factor Levels Errordf nT - 1 g - 1 nT - gMS - Variance SST / (nT - 1) SSB / (g - 1) SSW / (nT - g)StDev Total = LT SE = LT / sqrt(n) sp = ST

Regression The Model The Residuals

DOE Main Effects & Experimental Interactions: Y-hat Error: s-hat

21

Testing Your Discrete X’s

Power >or= .90• X is Statistically Significant, i.e. A possible solution can be develop around this X.

• Cross Tab with other significant X’s to determine if they are correlated.

• Segment by level and remaining X’s to identify secondary effects on variation

• Main Effects / Box Plots indicate likely best settings.

• Fish Bone reasons

• Prioritize reasons according to impact and controllability

• Ask “Why?” till at Root Cause

P < .05 P >or= .05

Power < .90

• Not Statistically Significant and we are “sure” of it.

• i.e. Don’t use as a solution and do not include in any transfer function

• Not Statistically Significant, BUT

• Not enough data to be “sure”

• Get more data OR

• Rely on Subject Matter Experts to determine if this should be part of any solution, THEN

• Test it’s effect in a

• Pilot, or an• Experiment

Run Main Effects and Box Plots with Specifications to determine Practical Significance

22

Using the Six Sigma Process Report, Report 2 Control Chart

StabilityXbar R or S

? Not

Not Stable

Stable Stable

Column to Use

ST LT

NA OK

OK OK

OK OK

Capability Calculation

Xbar chart interpretation may not be reliable since the control limits on the Xbar chart are based on Rbar from the R chart or Sbar from the S chart.

Calculate ZST = ZLT + 1.5 or use the standard method

Shift = ZST - ZLT

Shift will be approximately zero for the data sample.

Unless the period over which the data is collected is a relatively long one, the convention is to assume it will eventually shift and toCalculate ZST = ZLT + 1.5 or use the standard method. This may be overly optimistic!

Check your subgroups to see if they are spaced far enough.

23

Is it Graphically Obvious?Histogram / Normality Plot / Run Chart on the Y

756555453525155

0.065

0.060

0.055

Observation

NC

_LA

TH

E

0.4632 0.5368 2.000049.666750.0000

0.7151 0.2849 8.000038.440036.0000

Approx P-Value for Oscillation:Approx P-Value for Trends:Longest run up or down:Expected number of runs:Number of runs up or down:

Approx P-Value for Mixtures:Approx P-Value for Clustering:Longest run about median:Expected number of runs:Number of runs about median:

Run Chart for NC_LATHE

54321

51.5

50.5

49.5

48.5

47.5

46.5

Oper 50

Dis

t 50

Others

No Beer in Park

Smoking in Q

Price Fast Food

Crowds

Wait Time

18 8 19 43 59274 4.3 1.9 4.510.214.065.1

100.0 95.7 93.8 89.3 79.1 65.1

400

300

200

100

0

100

80

60

40

20

0

Defect

CountPercentCum %

Per

cent

Cou

nt

Pareto Chart for Defects

50403020100

40

35

30

25

Amount ($K)

Cyc

le T

ime

P-Value: 0.713A-Squared: 0.257

Anderson-Darling Normality Test

N: 90StDev: 1.00430Average: -0.0018963

210-1-2

.999

.99

.95

.80

.50

.20

.05

.01

.001

Pro

babi

lity

SRES1

Normal Probability Plot

403530

2

1

0

-1

-2

-3

Fitted Value

Sta

ndar

dize

d R

esid

ual

Residuals Versus the Fitted Values(response is Cycle Ti)

Histograms or Normality Plot / Main Effects Plot / Box Plots on the Discrete Xs

Pareto on the Defect Categories

Scatter Plot X vs Y, Residual Plots for Continuous Xs

201482-4-10

95% Confidence Interval for Mu

8765

95% Confidence Interval for Median

Variable: Profits

4.9120

6.0819

4.5045

Maximum3rd QuartileMedian1st QuartileMinimum

NKurtosisSkewnessVarianceStDevMean

P-Value:A-Squared:

7.6595

7.8086

6.9253

23.5200 10.0950 6.3400 1.5300

-12.6800

1250.218488-3.3E-0146.74886.837315.71488

0.1280.582


95% Confidence Interval for Sigma



Descriptive StatisticsLSL Target

201482-4-10


8765


Variable: Profits

4.9120

6.0819

4.5045

Maximum3rd QuartileMedian1st QuartileMinimum

NKurtosisSkewnessVarianceStDevMean

P-Value:A-Squared:

7.6595

7.8086

6.9253

23.5200 10.0950 6.3400 1.5300

-12.6800

1250.218488-3.3E-0146.74886.837315.71488

0.1280.582


95% Confidence Interval for Sigma



Descriptive StatisticsLSL Target



N: 125StDev: 6.83731Average: 5.71488

20100-10

.999

.99

.95

.80

.50

.20

.05

.01

.001

Pro

babi

lity

Profits

Normal Probability PlotLSL Target



N: 125StDev: 6.83731Average: 5.71488

20100-10

.999

.99

.95

.80

.50

.20

.05

.01

.001

Pro

babi

lity

Profits

Normal Probability PlotLSL Target

SuperDeptGenderEducPrior Yr ExpYrs Em

454440 9 8 7 6 5 4 3 2 1 0Sales

Purchasin

g

Enginee

ring

Advertis

ingMale

Female1210 9 8 7 6 5 4 3 2 1 0191611 9 7 6 5 4 3 2 1 027252221201918151412 9 8 7 6 5 4 3 2 1 0

70

60

50

40

30

Sal

ary-

K

Main Effects Plot - Data Means for Salary-K

24

Variable Attribute

Is your “Y” variable data or attribute data?

Determine what should be tested for:1. a difference in the variation of the different subgroups OR2. a difference in the “centering” of the different subgroups

VariationNon-normalSubgroups

NormalSubgroups

Non-normalSubgroups

NormalSubgroups

“Centering”

Chi-

Square

Binomial

Regression

Correlation

HOV Levene’s

Mood’sMedian

1 Sample T-test

One-WayANOVA

HOV Levene’s

NOTE: Temperature, Cycle Time, and Length

are variables. Operators, Suppliers,

and Customers are not.

2 Sample T-test

Is the input being tested also a variable?

No Yes

Construct a Multi-Vari of the data.

Statistical Test Choices

25

Data Analysis

26

Statistical SolutionTests on Continuous Y & Discrete X’s for Differences

between SubgroupsSPREAD 1 X, 2+ SamplesHOV - LevenesNormal or Non-normal subgroups

Multiple X’s & InteractionsData NinjaUnbalanced or Not Full Rank

DOEBalanced & Full Rank

CENTER1 X, All Subgroups tested are Normal1 Sample t-test1 subgroup to a target

2 Sample t-test 2 subgroups, run Levenes first

One-Way ANOVA2+ subgroups, 1 X

1 X, At least 1 subgroup is Non-NormalMood’s Median2+ subgroup, 1 X

Prospectively Paired Data, testing 1 X while blocking another XPaired t-testMultiple X’s & InteractionsTwo-Way ANOVA2 Xs, Balanced & Full Rank

GLM, Data Ninja2+ Xs, Unbalanced or Not Full Rank

DOE3+ Xs, Balanced & Full Rank

27

Tools Categories

Continuous Y

Discrete Y

Continuous X Discrete XTime Series & Scatter Plots, Residual PlotsGage R&R ANOVA Linear RegressionMultiple RegressionGLMDOEData Ninja

Stratified Histograms & Normality PlotsMain Effects, Interactions & Box PlotsGage R&R ANOVACenter: t-tests, ANOVA, Mood’s Median, GLMSpread: HOV - LevenesDOEData NinjaParetoStratified Control ChartsAttribute R&RChi-Square (Test of Independence and Goodness of Fit) & Confidence IntervalLogistic Regression (Coded Y)DOE (Coded Y)GLM (Coded Y)Data Ninja (Coded Y)

Stratified HistogramsAttribute R&RLogistic Regression (Coded Y)DOE (coded Y)GLM (Coded Y)Data Ninja (coded Y)

28

Synonyms / Definitions

• Y = Response = Dependent Variable = Effect

• X = Factor = Independent Variable = Predictor = Model

• Aliasing = Confounding

• Type I Error = error = False Action = Tampering = Producer’s Risk

• Type II Error = error = No Action = Consumer’s Risk

• DOE Runs = # Experimental Conditions x # Replications

• Variance Inflation Factor (VIF) > 10 means that some X’s are intercorrelated, eliminate one of them.

29

Degrees of Freedom

When Subgroup Size Varies (n j)• dfSSB = g - 1,

• where g = # of subgroups

• dfSSW = nT - g = n1 + … + ng - g

• dfSST = dfSSB + dfSSW = nT - 1

When Subgroup Size is Constant (n)• dfSSB = g - 1,

• where g = # of subgroups

• dfSSW = g(n-1)

• dfSST = dfSSB + dfSSW = (gn) - 1

30

Select DOE design based on purpose (screening or optimization), considering # of factors, Resolution and DES, and create Minitab worksheet.

Sort the DOE, all columns, in Std Order Add a new column titled Exp Con for Experimental

Condition, number it 1 to n where n is the numbers of runs for one replication and repeat the sequence for each replication.

Re-Sort, All Columns - including the new Exp Con column, in Run Order and

Run Experiment in Run Order and do a Run Chart in that order. Do Descriptive Stats

Do Box Plots by each factor and by Exp Con Do Stat<DOE<Analyze Factorial Design on Response

column, Analyze Standardized Residual Plots, including Normality and the Pareto and Session Window.

Check for practical significance by running Stat<ANOVA<General Linear Model on the Response and the Statistically significant Factors and Interactions from the DOE. Repeat until the same set of factors/interactions are repeated as significant.

DOE for Mean Checklist

31

DOE for Variance Checklist Run One Way ANOVA by Exp Con, copy the Mean and

StDev for each Exp Con (place cursor in the Session Window at one corner of the two columns to copy, hold down Alt key, click and drag to highlight both columns, Copy)

Create a new Worksheet and paste the Mean and StDev from One Way ANOVA into the first two columns of the new worksheet, using spaces as delimiters.

Go back to the original worksheet Re-sort it again in Std Order and copy the titles and the first n rows, where n is the numbers of runs for one replication, from the Factor columns and paste into the new worksheet

While in the new Worksheet, Do Stat< DOE< Define Custom Factorial Design on the new factor columns. This will create Stdorder, Runorder, CenterPts, and Blocks columns in the new worksheet.

Do Stat<DOE<Analyze Factorial Design on StDev Do Stat<DOE<Factorial Plots, both Main Effects and

Interactions on both Mean and StDev to look for Trade-Offs and to determine optimal settings.

Document Transfer Functions, Run Confirmation Runs at Optimal Settings

32

Selecting the Appropriate Control Chart

Variable orAttribute Data?*

Defects or Defective

Constant Subgroup

Size?

u p

No Yes

Defects or Defective

c np

Rational Subgrouping

Possible?

I, MR X-Bar &R

Variable(Continuous)

Attribute(Discrete)

No Yes

Defects Defectives Defects Defectives

Defects per Unit

Percentage Defective

Defect Counts

Number of

Defective Units

Documents

Six Sigma Training Posters