minitab & six sigma - · pdf file1 © minitab inc., 2000 minitab & six sigma hong...

1 © Minitab Inc., 2000

MINITAB & Six Sigma

Hong Kong Society for Quality

March 1, 2004


Presented ByKristina T. Konrath

Minitab Inc.

Customer Services Manager

[email protected]


Local RepresentativeBuxway Consultants Ltd.

Iza Ng

Business Development Manager

(852) 2783 9299

[email protected]


Agenda• Introduction to Six Sigma

• Minitab History and Products

• DMAIC Methodology

• MINITAB and MQC Tools

• Tutorials (time permitting)

• Questions


Statistics & Six Sigma Six Sigma is a methodology that aims to remove

variation from any process. It is a data driven program that is focused on financial return.

Successful Six Sigma practitioners must have strong communication and quantitative skills. They must have excellent process knowledge and need to apply to appropriate tools. Statistics is one of the key tools used in Six Sigma.


Statistics & Six Sigma Good statistical software is essential tool for a

successful Six Sigma initiative

• Takes away “hand” calculations - reduces the chances for error

• Must be intuitive – practitioners are not usually statisticians

• Allow for exploration – must offer a well-rounded suite of tools

• Clear and consistent presentation of results


Why MINITAB? MINITAB has been the standard for global Six

Sigma operations since the mid 1990’s

• Developed in 1972 to teach introductory statistics, designed for non-statisticians

• Began developing for quality in the late 80’s

• Strong customer focus and support

• Developing translated product

• Developing companion products


Minitab Products MINITAB Release 14

• Statistical software

Minitab Quality Companion

• Process Improved Soft Tools

Minitab Quality Trainer

• Multimedia training tool available in 2005


DMAIC Model Define

• Where are your current problems and opportunities?• What do your customers require & want?

Measure• Where is your process currently?

Analyze• What are the sources or variation?

Improve• What can make the process better?

Control• How do you ensure your improvements last?


DefineDefine•• Determine the process to be improvedDetermine the process to be improved

•• Identify your customersIdentify your customers

•• Identify your problems and scopeIdentify your problems and scope

MeasureMeasure•• Determine the extent of problemDetermine the extent of problem

•• Identify your inputs & outputs (X’s & Y’s)Identify your inputs & outputs (X’s & Y’s)

•• Measure itMeasure it

MQCMQC•Project Charter•C&E Matrix•Critical To Matrix•FMEA•Brainstorming•Process Mapping•Data Collection Plan

MINITABMINITAB•Pareto•Gage R&R•Control Charts•Capability Analysis•Graphics


• Screen potential causes

• Identify sources or root causes of problem

• Draw Conclusions

AnalyzeAnalyze

MINITABMINITAB•Gage R&R•Hypothesis Tests•ANOVA•Correlation

•Regression•Capability Analysis•Graphics•DOE


• Identify what improvements to implement

• Determine optimal settings

• Confirm results

ImproveImprove

MINITABMINITAB

•Gage R&R•Hypothesis Tests•ANOVA•Regression

•Graphics•Capability Analysis•Response Optimizer•DOE


• Sustain the gains

• Permanent change

ControlControl

MINITABMINITAB

•Control Charts•Capability Analysis

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TutorialsTutorials Download Meet MINITAB for free from

www.minitab.com/downloads/

• Data is included in MINITAB – SHIPPINGDATA.MTW

• Emphasis on Analyze, Improve, Control phases of Six Sigma


Questions?Questions? Our technical support staff is also available to

help you whether you have purchased or are considering buying MINITAB. Please contact them at http://customer.minitab.com.


Thank you!Thank you!


Linked PagesLinked Pages


Identify Potential Root Causes MINITAB Release 14 – Pareto Chart

Coun

t

Perc

ent

Defects

Count13.9 10.2 4.5 2.4 4.3

Cum % 64.8 78.7 88.9 93.4

274

95.7 100.0

59 43 19 10 18Percent 64.8

Othe

r

Incom

plete

Part

Defec

tive H

ousi

Leak

y Gas

ket

Missing

Clips

Missing

Scre

ws

400

300

200

100

0

100

80

60

40

20

0

Pareto Chart of Defects


Measurement Systems AnalysisMINITAB Release 14 – Gage R&R

Per

cent

Part-to-PartReprodRepeatGage R&R

100

50

0

% Contribution

% Study Var

Sam

ple

Ran

ge 0.10

0.05

0.00

_R=0.0383

UCL=0.1252

LCL=0

1 2 3

Sam

ple

Mea

n

1.00

0.75

0.50

__X=0.8075UCL=0.8796

LCL=0.7354

1 2 3

Part10987654321

1.00

0.75

0.50

Operator321

1.00

0.75

0.50

Part

Ave

rage

10 9 8 7 6 5 4 3 2 1

1.00

0.75

0.50

Operator

1

23

Gage name: Line #2Date of study : 10/20/2003

Reported by : Shift #2Tolerance:Misc:

Components of Variation

R Chart by Operator

Xbar Chart by Operator

Response by Part

Response by Operator

Operator * Part Interaction

Gage R&R (ANOVA) for Response


MINITAB Release 14 – Attribute Gage Study for Acceptances

Measurement Systems Analysis

Reference Value of Measured Part

Perc

ent o

f Acc

epta

nce

-0.01-0.02-0.03-0.04-0.05

99

95

80

50

20

5

1

Reference Value of Measured PartPr

obab

ility

of A

ccep

tanc

e

0.000-0.025-0.050

1.0

0.5

0.0

L Limit

Bias: 0.0097955Pre-adjusted Repeatability : 0.0494705Repeatability : 0.0458060

F itted Line: 3.10279 + 104.136 * ReferenceR - sq for F itted Line: 0.969376

A IA G Test of Bias = 0 v s not = 0T DF P-V alue

6.70123 19 0.0000021

Gage name:Date of study :

Reported by :Tolerance:Misc:

Attribute Gage Study (Analytic Method) for Acceptances


MINITAB Release 14 – Attribute Agreement AnalysisMeasurement Systems Analysis of Appraisers

Appraiser

Perc

ent

SimpsonMontgomeryHolmesHayesDuncan

100

80

60

40

20

0

95.0% C IPercent

Date of study: Reported by:Name of product:Misc:

Assessment Agreement

Appraiser vs Standard


MINITAB Release 14 – Graphing TechniquesDescriptive Statistics

1009080706050

Median

Mean

7674727068

A nderson-Darling Normality Test

V ariance 121.192Skewness 0.397389Kurtosis -0.442443N 92

Minimum 48.000

A -Squared

1st Q uartile 64.000Median 71.0003rd Q uartile 80.000Maximum 100.000

95% C onfidence Interv al for Mean

70.590

0.98

75.149

95% C onfidence Interv al for Median

68.000 74.000

95% C onfidence Interv al for StDev

9.615 12.878

P-V alue 0.013

Mean 72.870StDev 11.009

95% Confidence Intervals

Summary for Pulse1


MINITAB Release 14 – Control Charts

Sample

Sa

mp

le M

ea

n

2018161412108642

602

600

598

__X=600.23

UC L=602.474

LC L=597.986

Sample

Sa

mp

le R

an

ge

2018161412108642

8

6

4

2

0

_R=3.890

UC L=8.225

LC L=0

11

Xbar-R Chart of Supp2

Is your process in control?


How Capable is your process?MINITAB Release 14 – Capability Analysis (Sixpack)

Sam

ple

Mea

n

2018161412108642

600.0

599.5

599.0

__X=599.548

UCL=600.321

LCL=598.775

Sam

ple

Ran

ge

2018161412108642

3.0

1.5

0.0

_R=1.341

UCL=2.835

LCL=0

Sample

Valu

es

2015105

601.5

600.0

598.5

601.0600.5600.0599.5599.0598.5598.0

602600598

Within

Overall

Specs

WithinStDev 0.57643C p 1.16C pk 0.90C C pk 1.16

O v erallStDev 0.62086Pp 1.07Ppk 0.83C pm 0.87

Process Capability Sixpack of Supp1Xbar Chart

R Chart

Last 20 Subgroups

Capability Histogram

Normal Prob PlotA D: 0.844, P: 0.029

Capability P lot


Project Charter – (Form Tool)


Cause and Effect Diagram


FMEA – (Form Tool)


Process Mapping Tool


Measurement Systems AnalysisMINITAB Release 14 – Gage R&R

Per

cent

Part-to-PartReprodRepeatGage R&R

100

50

0

% Contribution

% Study Var

Sam

ple

Ran

ge 0.10

0.05

0.00

_R=0.0383

UCL=0.1252

LCL=0

1 2 3

Sam

ple

Mea

n

1.00

0.75

0.50

__X=0.8075UCL=0.8796

LCL=0.7354

1 2 3

Part10987654321

1.00

0.75

0.50

Operator321

1.00

0.75

0.50

Part

Ave

rage

10 9 8 7 6 5 4 3 2 1

1.00

0.75

0.50

Operator

1

23

Gage name: Line #2Date of study : 10/20/2003

Reported by : Shift #2Tolerance:Misc:

Components of Variation

R Chart by Operator

Xbar Chart by Operator

Response by Part

Response by Operator

Operator * Part Interaction

Gage R&R (ANOVA) for Response


Two-Sample T-Test and CI: BTU.In, Damper

Two-sample T for BTU.In

Damper N Mean StDev SE Mean1 40 9.91 3.02 0.482 50 10.14 2.77 0.39

Difference = mu (1) - mu (2)Estimate for difference: -0.23525095% CI for difference: (-1.450131, 0.979631)T-Test of difference = 0 (vs not =): T-Value = -0.38 P-Value = 0.701 DF = 88Both use Pooled StDev = 2.8818

Test and CI for Two Proportions

Sample X N Sample p1 537 1000 0.5370002 778 1000 0.778000

Difference = p (1) - p (2)Estimate for difference: -0.24195% CI for difference: (-0.281232, -0.200768)Test for difference = 0 (vs not = 0): Z = -11.74 P-Value = 0.000

MINITAB Release 14 – Hypothesis Testing & GraphicsGraphical and Statistical Analysis of Data

Damper

BTU.

In

21

20

15

10

5

Boxplot


One-way ANOVA: Durability versus Carpet

Source DF SS MS F PCarpet 3 146.4 48.8 3.58 0.047Error 12 163.5 13.6Total 15 309.9

S = 3.691 R-Sq = 47.24% R-Sq(adj) = 34.05%

Individual 95% CIs For Mean Based onPooled StDev

Level N Mean StDev ---------+---------+---------+---------+1 4 14.483 3.157 (-------*-------)2 4 9.735 3.566 (-------*--------)3 4 12.808 1.506 (-------*-------)4 4 18.115 5.435 (-------*-------)

---------+---------+---------+---------+10.0 15.0 20.0 25.0

Pooled StDev = 3.691

MINITAB Release 14 – ANOVA & GraphicsGraphical and Statistical Analysis of Data

CarpetD

urab

ility

4321

22.5

20.0

17.5

15.0

12.5

10.0

7.5

5.0

Boxplot of Durability by Carpet


Correlations: Verbal, Math, GPA

Verbal MathMath 0.275

0.000

GPA 0.322 0.1940.000 0.006

Cell Contents: Pearson correlation

P-Value

Regression Analysis: Score1 versus Score2

The regression equation isScore1 = - 4.667 + 4.397 Score2

S = 0.572711 R-Sq = 95.7% R-Sq(adj) = 95.1%

Analysis of Variance

Source DF SS MS F PRegression 1 51.3529 51.3529 156.56 0.000Error 7 2.2960 0.3280Total 8 53.6489

MINITAB Release 14 – Regression & CorrelationDetermining Significant Factors

Score2

Scor

e1

3.253.002.752.502.252.001.751.50

12

10

8

6

4

2

0

S 0.572711R-Sq 95.7%R-Sq(adj) 95.1%

Regression95% CI95% PI

Fitted Line PlotScore1 = - 4.667 + 4.397 Score2


Factorial Fit: Yield versus Block, Time, Temp, Catalyst

Estimated Effects and Coefficients for Yield (coded units)

Term Effect Coef SE Coef T PConstant 45.5592 0.09546 477.25 0.000Block -0.0484 0.09546 -0.51 0.628Time 2.9594 1.4797 0.09546 15.50 0.000Temp 2.7632 1.3816 0.09546 14.47 0.000Catalyst 0.1618 0.0809 0.09546 0.85 0.425Time*Temp 0.8624 0.4312 0.09546 4.52 0.003Time*Catalyst 0.0744 0.0372 0.09546 0.39 0.708Temp*Catalyst -0.0867 -0.0434 0.09546 -0.45 0.663Time*Temp*Catalyst 0.0230 0.0115 0.09546 0.12 0.907

S = 0.381847 R-Sq = 98.54% R-Sq(adj) = 96.87%

Analysis of Variance for Yield (coded units)

Source DF Seq SS Adj SS Adj MS F PBlocks 1 0.0374 0.0374 0.0374 0.26 0.628Main Effects 3 65.6780 65.6780 21.8927 150.15 0.0002-Way Interactions 3 3.0273 3.0273 1.0091 6.92 0.0173-Way Interactions 1 0.0021 0.0021 0.0021 0.01 0.907Residual Error 7 1.0206 1.0206 0.1458Total 15 69.7656

MINITAB Release 14 – Design of Experiments (DOE)Determining Significant Factors

Standardized Effect

Pe

rce

nt

151050-5

99

90

50

10

1

Factor NameA TimeB TempC Catalyst

Effect TypeNot SignificantSignificant

Te

rm

Standardized Effect

ABC

AC

BC

C

AB

B

A

1614121086420

2.36Factor NameA TimeB TempC Catalyst

ABB

A

Normal Probability Plot of the Standardized Effects(response is Yield, Alpha = .05)

Pareto Chart of the Standardized Effects(response is Yield, Alpha = .05)


MINITAB Release 14 – Hypothesis Testing & GraphicsConfirming Improvements

Two-Sample T-Test and CI: BTU.In, Damper

Two-sample T for BTU.In

Damper N Mean StDev SE Mean1 40 9.91 3.02 0.482 50 10.14 2.77 0.39

Difference = mu (1) - mu (2)Estimate for difference: -0.23525095% CI for difference: (-1.450131, 0.979631)T-Test of difference = 0 (vs not =): T-Value = -0.38 P-Value = 0.701 DF = 88Both use Pooled StDev = 2.8818

Test and CI for Two Proportions

Sample X N Sample p1 537 1000 0.5370002 778 1000 0.778000

Difference = p (1) - p (2)Estimate for difference: -0.24195% CI for difference: (-0.281232, -0.200768)Test for difference = 0 (vs not = 0): Z = -11.74 P-Value = 0.000

Damper

BTU.

In21

20

15

10

5

Boxplot


MINITAB Release 14 – ANOVA & GraphicsConfirming Improvements

One-way ANOVA: Durability versus Carpet

Source DF SS MS F PCarpet 3 146.4 48.8 3.58 0.047Error 12 163.5 13.6Total 15 309.9

S = 3.691 R-Sq = 47.24% R-Sq(adj) = 34.05%

Individual 95% CIs For Mean Based onPooled StDev

Level N Mean StDev ---------+---------+---------+---------+1 4 14.483 3.157 (-------*-------)2 4 9.735 3.566 (-------*--------)3 4 12.808 1.506 (-------*-------)4 4 18.115 5.435 (-------*-------)

---------+---------+---------+---------+10.0 15.0 20.0 25.0

Pooled StDev = 3.691Carpet

Dur

abili

ty4321

22.5

20.0

17.5

15.0

12.5

10.0

7.5

5.0

Boxplot of Durability by Carpet


Regression Analysis: Score1 versus Score2

The regression equation isScore1 = - 4.67 + 4.40 Score2

Predictor Coef SE Coef T PConstant -4.6674 0.8572 -5.44 0.001Score2 4.3975 0.3514 12.51 0.000

S = 0.572711 R-Sq = 95.7% R-Sq(adj) = 95.1%

Analysis of Variance

Source DF SS MS F PRegression 1 51.353 51.353 156.56 0.000Residual Error 7 2.296 0.328Total 8 53.649

Predicted Values for New Observations

NewObs Fit SE Fit 95% CI 95% PI1 4.567 0.214 (4.060, 5.074) (3.121, 6.013)2 1.929 0.363 (1.071, 2.787) (0.326, 3.532)3 2.808 0.305 (2.087, 3.530) (1.274, 4.343)4 6.326 0.196 (5.864, 6.789) (4.895, 7.757)5 8.525 0.290 (7.839, 9.212) (7.007, 10.043)6 4.567 0.214 (4.060, 5.074) (3.121, 6.013)7 9.405 0.346 (8.586, 10.224) (7.822, 10.987)8 7.646 0.242 (7.074, 8.217) (6.176, 9.116)9 6.326 0.196 (5.864, 6.789) (4.895, 7.757)

MINITAB Release 14 – Regression Prediction Methods

Score2

Scor

e1

3.253.002.752.502.252.001.751.50

12

10

8

6

4

2

0

S 0.572711R-Sq 95.7%R-Sq(adj) 95.1%

Regression95% CI95% PI

Fitted Line PlotScore1 = - 4.667 + 4.397 Score2


Response Surface Regression: BeanYield vs Nitrogen, PhosAcid, Potash

Estimated Regression Coefficients for BeanYield

Term Coef SE Coef T PConstant 10.4623 0.4062 25.756 0.000Nitrogen -0.5738 0.2695 -2.129 0.059PhosAcid 0.1834 0.2695 0.680 0.512Potash 0.4555 0.2695 1.690 0.122Nitrogen*Nitrogen -0.6764 0.2624 -2.578 0.027PhosAcid*PhosAcid 0.5628 0.2624 2.145 0.058Potash*Potash -0.2734 0.2624 -1.042 0.322Nitrogen*PhosAcid -0.6775 0.3521 -1.924 0.083Nitrogen*Potash 1.1825 0.3521 3.358 0.007PhosAcid*Potash 0.2325 0.3521 0.660 0.524

S = 0.9960 R-Sq = 78.6% R-Sq(adj) = 59.4%

Analysis of Variance for BeanYield

Source DF Seq SS Adj SS Adj MS F PRegression 9 36.465 36.465 4.0517 4.08 0.019Linear 3 7.789 7.789 2.5962 2.62 0.109Square 3 13.386 13.386 4.4619 4.50 0.030Interaction 3 15.291 15.291 5.0970 5.14 0.021

Residual Error 10 9.920 9.920 0.9920Lack-of-Fit 5 7.380 7.380 1.4760 2.91 0.133Pure Error 5 2.540 2.540 0.5079

Total 19 46.385

MINITAB Release 14 – DOE & Response Optimizer Determine Optimal Settings

Nitrogen

Phos

Acid

654321

2.5

2.0

1.5

1.0

Hold ValuesPotash 2.42

BeanYield

9 - 1010 - 1111 - 1212 - 13

> 13

< 88 - 9

14

12

3

BeanYield

10

8

2

PhosAcid

1Nitrogen

2

4

6

Hold ValuesPotash 2.42

Contour Plot of BeanYield vs PhosAcid, Nitrogen

Surface Plot of BeanYield vs PhosAcid, Nitrogen

minitab & six sigma - · pdf file1 © minitab inc., 2000 minitab & six sigma hong...

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