MINITAB & Six Sigma
Hong Kong Society for Quality
March 1, 2004
1
© Minitab Inc., 2000
Presented By
Kristina T. Konrath
Minitab Inc.
Customer Services Manager
tkonrath@minitab.com
2
© Minitab Inc., 2000
Local Representative
Buxway Consultants Ltd.
Iza Ng
Business Development Manager
(852) 2783 9299
iza@buxway.com
3
© Minitab Inc., 2000
Agenda
4
•
Introduction to Six Sigma
•
Minitab History and Products
•
DMAIC Methodology
•
MINITAB and MQC Tools
•
Tutorials (time permitting)
•
Questions
© 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.
5
© 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
6
© 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
7
© 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
8
© 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?
9
© Minitab Inc., 2000
Define
•
Determine the process to be improved
•
Identify your customers
•
Identify your problems and scope
Measure
•
Determine the extent of problem
•
Identify your inputs & outputs (X’s & Y’s)
•
Measure it
10
© Minitab Inc., 2000
MQC
•Project Charter
•C&E Matrix
•Critical To Matrix
•FMEA
•Brainstorming
•Process Mapping
•Data Collection Plan
MINITAB
•Pareto
•Gage R&R
•Control Charts
•Capability Analysis
•Graphics
Analyze
•
Screen potential causes
•
Identify sources or root causes of problem
•
Draw Conclusions
MINITAB
•Gage R&R
•Hypothesis Tests
•ANOVA
•Correlation
11
© Minitab Inc., 2000
•Regression
•Capability Analysis
•Graphics
•DOE
Improve
•
Identify what improvements to implement
•
Determine optimal settings
•
Confirm results
MINITAB
•Gage R&R
•Hypothesis Tests
•ANOVA
•Regression
12
© Minitab Inc., 2000
•Graphics
•Capability Analysis
•Response Optimizer
•DOE
Sustain the gains
•
Permanent change
Sample Mean
•
1
1
603
UC L = 6 0 2 .4
602
601
M e an=6 0 0 .2
600
599
L C L = 5 9 8 .1
598
S ub g ro up
Sample Range
Control
X bar/R C h art for T ech S u pport
0
10
20
9
8
7
6
5
4
3
2
1
0
UC L = 7 .8 6 6
R =3 .7 2
LC L=0
P r o c e s s C a p a b ilit y A n a ly s is fo r S a le s
MINITAB
•Control Charts
•Capability Analysis
US L
T a rg e t
LSL
M ean
P ro c e s s D a ta
6 0 5 .0 0 0
*
5 9 5 .0 0 0
5 9 9 .5 4 8
S a m p le N
S tD e v (W i th i n )
S tD e v (O v e ra ll)
© Minitab Inc., 2000
USL
W it h in
O v e r a ll
100
0 .5 7 6 4 2 9
0 .6 2 0 8 6 5
P o te n ti a l (W i th i n ) C a p a b i li ty
2 .8 9
Cp
3 .1 5
CPU
CPL
C pk
2 .6 3
2 .6 3
C pm
*
O v e ra ll C a p a b i li ty
13
LSL
Pp
PPU
PPL
2 .6 8
2 .9 3
2 .4 4
Ppk
2 .4 4
595
597
O b s e rv e d P e r fo rm a n c e
0 .0 0
PPM < LSL
0 .0 0
PPM > USL
0 .0 0
P P M T o ta l
599
601
E x p . " W i th i n " P e rfo r m a n c e
0 .0 0
PPM < LSL
0 .0 0
PPM > USL
0 .0 0
P P M T o ta l
603
605
E x p . " O v e ra ll" P e rfo r m a n c e
0 .0 0
PPM < LSL
0 .0 0
PPM > USL
0 .0 0
P P M T o ta l
Tutorials
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
14
© Minitab Inc., 2000
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.
15
© Minitab Inc., 2000
Thank you!
16
© Minitab Inc., 2000
Linked Pages
17
© Minitab Inc., 2000
MINITAB Release 14 – Pareto Chart
Identify Potential Root Causes
Pareto Chart of Defects
100
400
80
Count
60
200
40
100
Defects
0
g
in
si s
M
Count
Percent
Cum %
18
© Minitab Inc., 2000
20
re
Sc
w
s
274
64.8
64.8
g
in
si s
M
C
s
lip
y
ak
Le
59
13.9
78.7
et
sk
a
G
i
us
Ho
rt
Pa
e
e
et
pl
ti v
c
m
fe
co
De
In
43
19
10
10.2
4.5
2.4
88.9
93.4
95.7
r
he
t
O
18
4.3
100.0
0
Percent
300
MINITAB Release 14 – Gage R&R
Measurement Systems Analysis
Gage R&R (ANOVA) for Response
G age name:
Date of study :
Reported by : S hift #2
Tolerance:
M isc:
Line #2
10/20/2003
Response by Part
Components of Variation
100
% Contribution
1.00
Percent
% Study Var
0.75
50
0.50
0
Gage R&R
Repeat
Reprod
1
Part-to-Part
2
3
Sample Range
2
3
0.10
7
8
9
10
1.00
0.75
0.05
_
R=0.0383
0.00
LCL=0
1
0.50
1
2
2
Operator
0.75
0.50
_
UCL=0.8796
_
X=0.8075
LCL=0.7354
1.00
Operator
0.75
2
3
1
0.50
1
© Minitab Inc., 2000
3
Operator * Part Interaction
3
1.00
Average
Sample Mean
6
Response by Operator
UCL=0.1252
Xbar Chart by Operator
19
5
Part
R Chart by Operator
1
4
2
3
4
5
6
Part
7
8
9
10
MINITAB Release 14 – Attribute Gage Study for
Acceptances
Measurement Systems Analysis
Attribute Gage Study (Analytic Method) for Acceptances
Reported by :
Tolerance:
M isc:
G age name:
Date of study :
Bias:
P re-adjusted Repeatability :
Repeatability :
99
0.0097955
0.0494705
0.0458060
95
80
A IA G Test of Bias = 0 v s not = 0
T DF
P -V alue
6.70123 19 0.0000021
50
20
5
1
20
© Minitab Inc., 2000
-0.05
-0.04
-0.03
-0.02
Reference Value of Measured Part
-0.01
Probability of Acceptance
Percent of Acceptance
F itted Line: 3.10279 + 104.136 * Reference
R - sq for F itted Line:
0.969376
L Limit
1.0
0.5
0.0
-0.050
-0.025
0.000
Reference Value of Measured Part
MINITAB Release 14 – Attribute Agreement Analysis
Measurement Systems Analysis of Appraisers
Date of study :
Reported by :
Name of product:
Misc:
Assessment Agreement
Appraiser vs Standard
100
95.0% C I
P ercent
Percent
80
60
40
20
0
Duncan
21
© Minitab Inc., 2000
Hayes
Holmes
Appraiser
Montgomery
Simpson
MINITAB Release 14 – Graphing Techniques
Descriptive Statistics
Summary for Pulse1
A nderson-D arling N ormality Test
50
60
70
80
90
A -S quared
P -V alue
0.98
0.013
M ean
S tDev
V ariance
S kew ness
Kurtosis
N
72.870
11.009
121.192
0.397389
-0.442443
92
M inimum
1st Q uartile
M edian
3rd Q uartile
M aximum
100
48.000
64.000
71.000
80.000
100.000
95% C onfidence Interv al for M ean
70.590
75.149
95% C onfidence Interv al for M edian
68.000
95% Confidence Intervals
9.615
Mean
Median
68
22
© Minitab Inc., 2000
70
72
74.000
95% C onfidence Interv al for S tD ev
74
76
12.878
MINITAB Release 14 – Control Charts
Is your process in control?
Xbar-R Chart of Supp2
1
1
Sample M ean
U C L=602.474
602
_
_
X=600.23
600
598
LC L=597.986
2
4
6
8
10
Sample
12
14
16
18
20
U C L=8.225
Sample Range
8
6
_
R=3.890
4
2
0
LC L=0
2
23
© Minitab Inc., 2000
4
6
8
10
Sample
12
14
16
18
20
MINITAB Release 14 – Capability Analysis (Sixpack)
How Capable is your process?
Process Capability Sixpack of Supp1
C apability H istogr am
Xbar C har t
Sample Mean
UCL=600.321
600.0
_
_
X=599.548
599.5
599.0
LCL=598.775
2
4
6
8
10
12
14
16
18
20
598.0
598.5
Sample Range
R C har t
3.0
UCL=2.835
1.5
_
R=1.341
0.0
599.0
4
6
8
10
12
14
16
18
20
601.0
598
600
Within
S tDev 0.57643
Cp
1.16
C pk
0.90
C C pk
1.16
598.5
Within
Overall
Specs
5
10
Sample
602
C apability P lot
600.0
© Minitab Inc., 2000
600.5
Nor mal P r ob P lot
A D : 0.844, P : 0.029
Last 2 0 Subgr oups
601.5
24
600.0
LCL=0
2
Values
599.5
15
20
O v erall
S tD ev 0.62086
Pp
1.07
P pk
0.83
C pm
0.87
Project Charter – (Form Tool)
25
© Minitab Inc., 2000
Cause and Effect Diagram
26
© Minitab Inc., 2000
FMEA – (Form Tool)
27
© Minitab Inc., 2000
Process Mapping Tool
28
© Minitab Inc., 2000
MINITAB Release 14 – Gage R&R
Measurement Systems Analysis
Gage R&R (ANOVA) for Response
G age name:
Date of study :
Reported by : S hift #2
Tolerance:
M isc:
Line #2
10/20/2003
Response by Part
Components of Variation
100
% Contribution
1.00
Percent
% Study Var
0.75
50
0.50
0
Gage R&R
Repeat
Reprod
1
Part-to-Part
2
3
Sample Range
2
3
0.10
7
8
9
10
1.00
0.75
0.05
_
R=0.0383
0.00
LCL=0
1
0.50
1
2
2
Operator
0.75
0.50
_
UCL=0.8796
_
X=0.8075
LCL=0.7354
1.00
Operator
0.75
2
3
1
0.50
1
© Minitab Inc., 2000
3
Operator * Part Interaction
3
1.00
Average
Sample Mean
6
Response by Operator
UCL=0.1252
Xbar Chart by Operator
29
5
Part
R Chart by Operator
1
4
2
3
4
5
6
Part
7
8
9
10
MINITAB Release 14 – Hypothesis Testing & Graphics
Graphical and Statistical Analysis of Data
Two-Sample T-Test and CI: BTU.In, Damper
Boxplot
Two-sample T for BTU.In
N
40
50
Mean
9.91
10.14
StDev
3.02
2.77
SE Mean
0.48
0.39
Difference = mu (1) - mu (2)
Estimate for difference: -0.235250
95% CI for difference: (-1.450131, 0.979631)
T-Test of difference = 0 (vs not =): T-Value = -0.38
Value = 0.701 DF = 88
Both use Pooled StDev = 2.8818
15
P-
BTU.In
Damper
1
2
20
10
Test and CI for Two Proportions
Sample
1
2
X
537
778
N
1000
1000
Sample p
0.537000
0.778000
Difference = p (1) - p (2)
Estimate for difference: -0.241
95% CI for difference: (-0.281232, -0.200768)
Test for difference = 0 (vs not = 0): Z = -11.74
= 0.000
30
© Minitab Inc., 2000
5
1
P-Value
2
Damper
MINITAB Release 14 – ANOVA & Graphics
Graphical and Statistical Analysis of Data
Boxplotof DurabilitybyCarpet
One-way ANOVA: Durability versus Carpet
DF
3
12
15
S = 3.691
Level
1
2
3
4
N
4
4
4
4
SS
146.4
163.5
309.9
MS
48.8
13.6
F
3.58
20.0
17.5
R-Sq = 47.24%
Mean
14.483
9.735
12.808
18.115
P
0.047
StDev
3.157
3.566
1.506
5.435
R-Sq(adj) = 34.05%
Individual 95% CIs For Mean Based on
Pooled StDev
---------+---------+---------+---------+
(-------*-------)
(-------*--------)
(-------*-------)
(-------*-------)
---------+---------+---------+---------+
10.0
15.0
20.0
25.0
Pooled StDev = 3.691
Durability
Source
Carpet
Error
Total
22.5
15.0
12.5
10.0
7.5
5.0
1
2
3
Carpet
31
© Minitab Inc., 2000
4
MINITAB Release 14 – Regression & Correlation
Determining Significant Factors
Regression Analysis: Score1 versus Score2
FittedLine Plot
The regression equation is
Score1 = - 4.667 + 4.397 Score2
S = 0.572711
R-Sq = 95.7%
Score1 = - 4.667 +4.397 Score2
12
R-Sq(adj) = 95.1%
10
Analysis of Variance
DF
1
7
8
SS
51.3529
2.2960
53.6489
MS
51.3529
0.3280
Correlations: Verbal, Math, GPA
Math
Verbal
0.275
0.000
Math
0.322
0.000
0.194
0.006
F
156.56
P
0.000
S
R-Sq
R-Sq(adj)
8
Score1
Source
Regression
Error
Total
Regression
95%CI
95%PI
6
4
2
0
GPA
Cell Contents: Pearson
correlation
P-Value
32
© Minitab Inc., 2000
1.50
1.75
2.00
2.25 2.50
Score2
2.75
3.00
3.25
0.572711
95.7%
95.1%
MINITAB Release 14 – Design of Experiments (DOE)
Determining Significant Factors
Factorial Fit: Yield versus Block, Time, Temp, Catalyst
Normal Probability Plot of the StandardizedEffects
(response is Yield, Alpha = .05)
Estimated Effects and Coefficients for Yield (coded units)
S = 0.381847
2.9594
2.7632
0.1618
0.8624
0.0744
-0.0867
0.0230
Coef
45.5592
-0.0484
1.4797
1.3816
0.0809
0.4312
0.0372
-0.0434
0.0115
R-Sq = 98.54%
SE Coef
0.09546
0.09546
0.09546
0.09546
0.09546
0.09546
0.09546
0.09546
0.09546
T
477.25
-0.51
15.50
14.47
0.85
4.52
0.39
-0.45
0.12
P
0.000
0.628
0.000
0.000
0.425
0.003
0.708
0.663
0.907
33
DF
1
3
3
1
7
15
© Minitab Inc., 2000
Adj SS
0.0374
65.6780
3.0273
0.0021
1.0206
Adj MS
0.0374
21.8927
1.0091
0.0021
0.1458
B
Factor Name
A
Time
AB
50
B
C
Temp
Catalyst
10
1
-5
0
5
Standardized Effect
10
15
Pareto Chart of the StandardizedEffects
(response is Yield, Alpha = .05)
R-Sq(adj) = 96.87%
Seq SS
0.0374
65.6780
3.0273
0.0021
1.0206
69.7656
Effect Type
Not Significant
Significant
A
2.36
A
B
Analysis of Variance for Yield (coded units)
Source
Blocks
Main Effects
2-Way Interactions
3-Way Interactions
Residual Error
Total
P er cent
Effect
90
F
0.26
150.15
6.92
0.01
P
0.628
0.000
0.017
0.907
T er m
Term
Constant
Block
Time
Temp
Catalyst
Time*Temp
Time*Catalyst
Temp*Catalyst
Time*Temp*Catalyst
99
AB
C
BC
AC
ABC
0
2
4
6
8
10
Standardized Effect
12
14
16
Factor
Name
A
B
C
Time
Temp
Catalyst
MINITAB Release 14 – Hypothesis Testing & Graphics
Confirming Improvements
Two-Sample T-Test and CI: BTU.In, Damper
Boxplot
Two-sample T for BTU.In
N
40
50
Mean
9.91
10.14
StDev
3.02
2.77
SE Mean
0.48
0.39
Difference = mu (1) - mu (2)
Estimate for difference: -0.235250
95% CI for difference: (-1.450131, 0.979631)
T-Test of difference = 0 (vs not =): T-Value = -0.38
Value = 0.701 DF = 88
Both use Pooled StDev = 2.8818
15
P-
BTU.In
Damper
1
2
20
10
Test and CI for Two Proportions
Sample
1
2
X
537
778
N
1000
1000
Sample p
0.537000
0.778000
Difference = p (1) - p (2)
Estimate for difference: -0.241
95% CI for difference: (-0.281232, -0.200768)
Test for difference = 0 (vs not = 0): Z = -11.74
= 0.000
34
© Minitab Inc., 2000
5
1
P-Value
2
Damper
MINITAB Release 14 – ANOVA & Graphics
Confirming Improvements
Boxplotof DurabilitybyCarpet
One-way ANOVA: Durability versus Carpet
DF
3
12
15
S = 3.691
Level
1
2
3
4
N
4
4
4
4
SS
146.4
163.5
309.9
MS
48.8
13.6
F
3.58
20.0
17.5
R-Sq = 47.24%
Mean
14.483
9.735
12.808
18.115
P
0.047
StDev
3.157
3.566
1.506
5.435
R-Sq(adj) = 34.05%
Individual 95% CIs For Mean Based on
Pooled StDev
---------+---------+---------+---------+
(-------*-------)
(-------*--------)
(-------*-------)
(-------*-------)
---------+---------+---------+---------+
10.0
15.0
20.0
25.0
Pooled StDev = 3.691
Durability
Source
Carpet
Error
Total
22.5
15.0
12.5
10.0
7.5
5.0
1
2
3
Carpet
35
© Minitab Inc., 2000
4
MINITAB Release 14 – Regression
Prediction Methods
Regression Analysis: Score1 versus Score2
The regression equation is
Score1 = - 4.67 + 4.40 Score2
Predictor
Constant
Score2
Coef
-4.6674
4.3975
S = 0.572711
SE Coef
0.8572
0.3514
R-Sq = 95.7%
FittedLine Plot
Score1 = - 4.667 +4.397 Score2
T
-5.44
12.51
P
0.001
0.000
12
10
8
SS
51.353
2.296
53.649
MS
51.353
0.328
F
156.56
P
0.000
Score1
DF
1
7
8
S
R-Sq
R-Sq(adj)
R-Sq(adj) = 95.1%
Analysis of Variance
Source
Regression
Residual Error
Total
Regression
95%CI
95%PI
6
4
Predicted Values for New Observations
2
New
Obs
1
2
3
4
5
6
7
8
9
Fit
4.567
1.929
2.808
6.326
8.525
4.567
9.405
7.646
6.326
36
SE Fit
0.214
0.363
0.305
0.196
0.290
0.214
0.346
0.242
0.196
95% CI
(4.060, 5.074)
(1.071, 2.787)
(2.087, 3.530)
(5.864, 6.789)
(7.839, 9.212)
(4.060, 5.074)
(8.586, 10.224)
(7.074, 8.217)
(5.864, 6.789)
© Minitab Inc., 2000
95% PI
(3.121, 6.013)
(0.326, 3.532)
(1.274, 4.343)
(4.895, 7.757)
(7.007, 10.043)
(3.121, 6.013)
(7.822, 10.987)
(6.176, 9.116)
(4.895, 7.757)
0
1.50
1.75
2.00
2.25 2.50
Score2
2.75
3.00
3.25
0.572711
95.7%
95.1%
MINITAB Release 14 – DOE & Response Optimizer
Determine Optimal Settings
Response Surface Regression: BeanYield vs Nitrogen, PhosAcid, Potash
Estimated Regression Coefficients for BeanYield
S = 0.9960
Coef
10.4623
-0.5738
0.1834
0.4555
-0.6764
0.5628
-0.2734
-0.6775
1.1825
0.2325
R-Sq = 78.6%
SE Coef
0.4062
0.2695
0.2695
0.2695
0.2624
0.2624
0.2624
0.3521
0.3521
0.3521
T
25.756
-2.129
0.680
1.690
-2.578
2.145
-1.042
-1.924
3.358
0.660
P
0.000
0.059
0.512
0.122
0.027
0.058
0.322
0.083
0.007
0.524
BeanYield
< 8
8- 9
9 - 10
10 - 11
11 - 12
12 - 13
> 13
2.5
PhosAcid
Term
Constant
Nitrogen
PhosAcid
Potash
Nitrogen*Nitrogen
PhosAcid*PhosAcid
Potash*Potash
Nitrogen*PhosAcid
Nitrogen*Potash
PhosAcid*Potash
Contour Plot of BeanYieldvs PhosAcid, Nitrogen
2.0
1.5
Hold Values
Potash 2.42
1.0
1
2
3
4
Nitrogen
5
Surface Plot of BeanYieldvs PhosAcid, Nitrogen
R-Sq(adj) = 59.4%
Hold Values
Potash 2.42
Analysis of Variance for BeanYield
Source
Regression
Linear
Square
Interaction
Residual Error
Lack-of-Fit
Pure Error
Total
37
DF
9
3
3
3
10
5
5
19
Seq SS
36.465
7.789
13.386
15.291
9.920
7.380
2.540
46.385
© Minitab Inc., 2000
Adj SS
36.465
7.789
13.386
15.291
9.920
7.380
2.540
6
Adj MS
4.0517
2.5962
4.4619
5.0970
0.9920
1.4760
0.5079
F
4.08
2.62
4.50
5.14
P
0.019
0.109
0.030
0.021
8
10
BeanYield
12
2
14
2.91
0.133
4
3
2
1
6
PhosAcid
Nitrogen