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1 © Minitab Inc., 2000
MINITAB & Six Sigma
Hong Kong Society for Quality
March 1, 2004
2 © Minitab Inc., 2000
Presented ByKristina T. Konrath
Minitab Inc.
Customer Services Manager
3 © Minitab Inc., 2000
Local RepresentativeBuxway Consultants Ltd.
Iza Ng
Business Development Manager
(852) 2783 9299
4 © Minitab Inc., 2000
Agenda• Introduction to Six Sigma
• Minitab History and Products
• DMAIC Methodology
• MINITAB and MQC Tools
• Tutorials (time permitting)
• Questions
5 © Minitab Inc., 2000
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.
6 © Minitab Inc., 2000
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
7 © Minitab Inc., 2000
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
8 © Minitab Inc., 2000
Minitab Products MINITAB Release 14
• Statistical software
Minitab Quality Companion
• Process Improved Soft Tools
Minitab Quality Trainer
• Multimedia training tool available in 2005
9 © Minitab Inc., 2000
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?
10 © Minitab Inc., 2000
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
11 © Minitab Inc., 2000
• 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
12 © Minitab Inc., 2000
• 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
13 © Minitab Inc., 2000
• Sustain the gains
• Permanent change
ControlControl
MINITABMINITAB
•Control Charts•Capability Analysis
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P o te n tia l (W i th in ) C a p a b i li ty
P ro c e s s D a ta
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O v e ra ll
14 © Minitab Inc., 2000
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
15 © Minitab Inc., 2000
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.
16 © Minitab Inc., 2000
Thank you!Thank you!
17 © Minitab Inc., 2000
Linked PagesLinked Pages
18 © Minitab Inc., 2000
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
19 © Minitab Inc., 2000
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
20 © Minitab Inc., 2000
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
21 © Minitab Inc., 2000
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
22 © Minitab Inc., 2000
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
23 © Minitab Inc., 2000
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?
24 © Minitab Inc., 2000
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
25 © Minitab Inc., 2000
Project Charter – (Form Tool)
26 © Minitab Inc., 2000
Cause and Effect Diagram
27 © Minitab Inc., 2000
FMEA – (Form Tool)
28 © Minitab Inc., 2000
Process Mapping Tool
29 © Minitab Inc., 2000
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
30 © Minitab Inc., 2000
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
31 © Minitab Inc., 2000
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
32 © Minitab Inc., 2000
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
33 © Minitab Inc., 2000
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)
34 © Minitab Inc., 2000
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
35 © Minitab Inc., 2000
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
36 © Minitab Inc., 2000
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
37 © Minitab Inc., 2000
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