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 |  موضوع: كتاب Six Sigma - A Case Study Approach Using Minitab الأحد 24 مارس 2024, 1:47 am | |
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Six Sigma - A Case Study Approach Using Minitab
Timothy D. Blackburn
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Contentsx
4.3.3 Using Minitab to Calculate Ppk for Continuous Data:
Non-normal 69
4.3.4 Discrete Data Process Capability 71
4.3.5 Calculating Ppk for Discrete Data in Minitab 73
4.4 Measurement System Analysis (with Gage R&R, Attribute
Agreement Analysis): Minitab Methods and Analysis Detail 75
4.4.1 Introduction to Gage R&R and Attribute Agreement
Analysis . 75
4.4.2 GAGE R&R: Overview . 76
4.4.3 Designing and Analyzing the GAGE R&R
Study in Minitab 77
4.4.4 Attribute Agreement Analysis in Minitab . 86
4.5 Pareto Analysis: Minitab Methods and Analysis Detail 95
4.5.1 Creating a Pareto Chart . 95
4.5.2 Constructing a Pareto Chart in Minitab . 97
4.6 Test of Proportions: Minitab Methods and Analysis Detail 98
4.6.1 Introduction to Test of Proportions 98
4.6.2 Test of Two Proportions in Minitab 99
4.6.3 Chi-Square Test of Multiple Proportions in Minitab . 101
References 105
5 The Analyze Phase with Minitab Tools 107
5.1 The Analyze Phase: An Overview . 107
5.1.1 Introduction 107
5.1.2 Cause and Effect Analysis . 109
5.1.3 Verifying or Discarding Root Causes: Process Analysis 113
5.1.4 Verifying or Discarding Root Causes: Data Analysis 115
5.1.5 Piloting 116
5.1.6 Data Analysis Example: Regression . 116
5.1.7 Data Analysis Example: Two Sample T Test . 119
5.1.8 Data Analysis Example: Paired T Test 120
5.1.9 Data Analysis Example: ANOVA, ANOM 121
5.1.10 Data Analysis Example: Design of Experiment (DOE) . 123
5.1.11 Summary Root Cause Tables . 125
5.2 Regression Analysis: Minitab Methods and Analysis Detail . 127
5.2.1 Regression Overview . 127
5.2.2 Assumptions for Linear Regression and Key Data
Interpretations 128
5.2.3 Single Linear Regression 129
5.2.4 Multiple Linear Regression 134
5.2.5 Regression Issues 140
5.2.6 Correlation and Visualization in Minitab 141
5.2.7 Other Regression Tools (Introduction) 143
Contentsxi
5.3 Two Sample T Test, Mann-Whitney: Minitab Methods and
Analysis Detail 143
5.3.1 Two Sample T Test Overview 143
5.3.2 Two Sample T Test in Minitab 145
5.3.3 Mann-Whitney Test in Minitab . 149
5.3.4 Data Transformations in Minitab 154
5.3.5 Sample Size Determination in Minitab . 158
5.4 Paired T Test: Minitab Methods and Analysis Detail 160
5.4.1 Paired T Test Overview . 160
5.4.2 Paired T Test in Minitab . 161
5.4.3 One Sample Wilcoxon in Minitab (Nonparametric
Alternative to a Paired T Test) 165
5.5 ANOVA, ANOM: Minitab Methods and Analysis Detail . 167
5.5.1 ANOVA and ANOM Overview . 167
5.5.2 ANOVA in Minitab 168
5.5.3 ANOM in Minitab . 173
5.5.4 Kruskal-Wallis in Minitab (Nonparametric Alternative to
ANOVA) 176
5.6 Design of Experiment: Minitab Analysis and Methods Detail . 180
5.6.1 DOE Overview 180
5.6.2 Full Factorial DOE Example in Minitab (No Interactions
Between X’s) . 181
5.6.3 Full Factorial DOE Example in Minitab (with Interactions). 193
5.6.4 Introduction to Screening Designs and Reduced Factorials . 196
5.6.5 Other DOE Concepts and Methods 200
References 201
6 The Improve Phase 203
6.1 Introduction 203
6.2 Implementation Plans . 204
6.3 Arriving at Solutions . 206
6.4 Cost-Benefit Analysis . 208
6.5 Risk Analysis . 210
6.6 Piloting 213
References 213
7 The Control Phase . 215
7.1 Introduction 215
7.2 Confirming Objectives Were Achieved . 216
7.3 Monitoring and Control Strategy 220
7.4 Standardization . 222
7.5 Project Closure and Hand-off 223
References 224
Contentsxii
8 Storyboards 225
8.1 Define Phase Storyboard Recommended Contents 225
8.2 Measure Phase Storyboard Recommended Contents 226
8.3 Analyze Phase Storyboard Recommended Contents . 226
8.4 Improve Phase Storyboard Recommended Contents . 226
8.5 Control Phase Storyboard Recommended Contents . 226
Appendixes . 227
Epilogue . 251
References . 253
Index 255
ANOVA Analysis of Variance—hypothesis test for three or more sample means
CI Confidence Interval
Cpk Process capability (short term or within batch)
CTQ Critical to Quality
DMAIC Define, Measure, Analyze, Improve, and Control
DPMO Defects per Million Opportunities
FMEA Failure Mode and Effect Analysis
HVAC Heating, Ventilation, and Air Conditioning
Hurdle Rate Desired rate of return
IPO Initial Public Offering
IRR Internal Rate of Return
LCL Lower Control Limit
LSL Lower Specification Limit
MR Moving Range
MSA Measurement System Analysis
NPV Net Present Value
OpEx Operational Excellence—a common name for a function responsible
for continuous improvement and Six Sigma
Ppk Process performance, or long-term process capability
R&R Repeatability and Reproducibility
SIPOC Supplier, Inputs, Process, Outputs, and Customer
SME Subject Matter Expert
TPS Toyota Production System
UCL Upper Control Limit
USL Upper Specification Limit
VIF Variance Inflation Factor
VOC Voice of the Customer
Index
A
Abraizer machine, 139
Airbag, 126
Airbag seal failure, 23
Airbag seal images, 114
Airbag solutions, 206
Alternative (HA) states, 98
Analysis of means (ANOM), 121–123, 167
in Minitab, 173–175
Analysis of variance (ANOVA), 121–123, 167
dataset, 228–229
in Minitab, 168–173
Analyze phase, 107, 108
ANOM, 121–123
ANOVA, 121–123
cause and effect analysis, 109–113
design of experiment, 123–125
paired T test, 120, 121
piloting, 116, 117
regression, 116–119
root cause tables, 125, 126
two sample T test, 119, 120
verifying/discarding root causes, 113–116
Attribute agreement analysis
kappa value, 87
Minitab path, attribute study worksheet, 88
Minitab path to analyze, 89
sample selection, 88
subjective classifications, 86
Attribute agreement dataset, 229–238
B
Balance sheet, 5
Baseline, 14, 15, 18, 22
Binary logistic regression (BLR), 143
Box-Cox transformation, 155
Brake and airbag assembly process, 19
Brake caliper, 126
Brake caliper failure, 23
Brake caliper test, 76
Business case, 14
C
Caliper mold diameter, 117, 118
Capability analysis
binomial and Poisson process capability
tools, 75
capable process, 64
discrete data process capability, 71
airbag warranty claims, 72
defect rate example table, 73
defect rate Z value, 72
just capable process, 64
Minitab path for, 66
Ppk calculation
for continuous data, 67–69
for continuous data, non-normal, 69
for discrete data in Minitab, 73–75
process not capable, 65
upper CI for Ppk, 67
Causal Tree, 108, 112
Chi-square, 43, 44, 101–103, 105
Chi-square of multiple proportions, 98
Chi-square test of multiple proportions
dataset, 238
Common cause variation, 30, 46
Communication plan, 21
Control charts, 30, 33
common cause versus special cause
variation, 46
example, 47
I-MR in Minitab, 48, 50
LCL, 46
P-chart for proportional data in
Minitab, 49, 50
Run Chart, 60
special cause tests, 47
U-chart, 55, 56
UCL, 46
X-Bar R chart, 53
Control limits, 30, 33, 34, 46, 48, 50, 52, 55,
60, 63, 82
Control phase, 215
confirming objectives, 216–218
KIND Karz summary of objectives, 219
monitoring and control strategy, 220, 221
prior Ppk for KIND Karz, 219
project closure and hand-off, 223, 224
standardization, 222, 223
two sample T test outputs, 219
Cost-benefit analysis, 208–210
Critical to Quality (CTQ) hierarchy, 17
D
Data analysis, 115, 116
ANOM, 121–123
ANOVA, 121–123
design of experiment, 123–125
paired T test, 120, 121
regression, 116
two sample T test, 119, 120
Data collection, 26, 28–30
Data collection plan, 28
Datasets, 228–238
chi-square test of multiple proportions, 238
DOE, 243–244
Gage R&R, 244–246
I-MR, 238–239
multiple regression, 248–249
paired T test, 246–247
Pareto summarized data, 247
P-chart, 239–240
process capability, 247–248
run chart, 242–243
single regression, 248
test of two proportions, 249
two sample T test, 249–250
U-chart, 241–242
Xbar-R, 240–241
Data transformations in Minitab, 154–158
Defects, 8
types and counts, 3
Defects per million opportunities
(DPMO), 8, 71
Defects per opportunity (DPO), 73
Dependent variable, 127
Design of experiment (DOE), 29,
123–125, 180
concepts and methods, 200, 201
dataset, 243–244
full factorial DOE, 181–195
screening designs and reduced
factorials, 196–199
DMAIC phase, 9, 10, 12, 42, 44, 98, 225
F
Failure mode and effect analysis (FMEA),
210, 211
Full factorial DOE, 181–195
G
Gage R&R, 37, 39–41
analyzing, 78, 83
continuous data, 76
crossed vs. nested designs, 77
dataset, 244–246
designing, 77
Goals, 14, 15
I
Implementation plan, 204–206
Improve phase, 203, 204
arriving at solutions, 206, 207
cost-benefit analysis, 208–210
implementation plan, 204–206
piloting, 213
risk analysis, 210, 211, 213
root causes and improvements, 204
Independent variables, 127
Individual moving range control chart
(I-MR), 48
dataset, 238–239
Initial Public Offering (IPO), 7
Internal rate of return (IRR) method, 208, 209
J
Johnson’s transformation, 158
K
Kappa value, 87
KIND Karz, case study, 1, 3
Kruskal-Wallis in Minitab, 176–179
L
Leadership team, 20
Lean six sigma, 8, 9
Learnings from other events, 22
Index257
Linear regression
assumptions and key data interpretations,
128, 129
Lower control limit (LCL), 34, 46, 48, 63
M
Mann-Whitney test
in Minitab, 149–154
Mapping, 18
Measurement system analysis (MSA), 36
attribute agreement graph, 41
attribute agreement Minitab output, 40
Gage R&R Minitab output, 40
Gage R&R report graphs, 39
KIND Karz operational definitions, 38
sources of variation, 37
Measure phase
capability analysis (see Capability
analysis)
contents, 26
data collection, 26–28, 30
funneling and stratification
airbag vendor defect rates, 43
Chi-sq table for brake defect counts by
vehicle, 44
KIND Karz defect categories, 42
Minitab Chi-sq results, 44
Pareto chart, 42
test of two proportions Minitab
output, 43
measurement system analysis
attribute agreement graph, 41
attribute agreement Minitab output, 40
Gage R&R Minitab output, 40
Gage R&R report graphs, 37, 39
KIND Karz operational definitions, 38
operational definitions, 37
sources of variation, 37
Pareto chart (see Pareto chart)
process capability, 33–36
process stability, 30, 31, 33
Minitab
ANOM in, 173–175
ANOVA in, 168–173
correlation and visualization in, 141, 142
data transformations in, 154–158
DOE in, 181–195
Kruskal-Wallis in, 176–179
Mann-Whitney test in, 149–154
paired T test in, 161–164
one sample Wilcoxon, 165–167
sample size determination in, 158–160
20 layout, 228
Multiple linear regression, 134–139
Multiple regression datasets, 248–249
N
Nominal logistic regression, 143
Nonlinear regression, 143
Null hypothesis (Ho) states, 98
O
One sample Wilcoxon, 165–167
Ordinal logistic regression (OLR), 143
P
Paired T test, 120, 121, 160, 161
dataset, 246–247
in Minitab, 161–164
one sample Wilcoxon, 165–167
Pareto chart, 42
Minitab path, 97
no apparent Pareto effect, 96
with clear Pareto effect, 96
Pareto summarized data, 247
Partial least squares (PLS), 143
P-chart, 49, 51
dataset, 239–240
Piloting, 116, 117
improve phase, 213
Power and sample size tools, 29
Ppk
airbags, 35
brake caliper torsion rods, 35
for warrantees and recalls, 35
Priority matrix, 28
Process analysis, 113–115
Process capability, 33, 34, 36
datasets, 247–248
Process sigma, 73
Process stability, 30, 31, 33
Project charter, 13, 15, 16
Project plan, 16
Q
Questions to ask, 8
R
Regression, 116–119
Regression analysis, 127, 128
linear regression, assumptions and key data
interpretations, 128, 129
Index258
Minitab, correlation and visualization in,
141, 142
multiple linear regression, 134–139
regression issues, 140, 141
single linear regression, 129–134
tools, 143
Regression issues, 140, 141
Residual, 127
Responsibilities, 16
Risk analysis
improve phase, 210, 211, 213
Roles, 14, 16
Root cause tables, 125, 126
Run chart, 60
dataset, 242–243
S
Sample size determination
in Minitab, 158–160
Schedule, 14, 15
Scope, 14, 15, 17, 18, 22
Single linear regression, 129–134
Single regression datasets, 248
SIPOC, 18, 19
Sixpack, 66, 67, 69
Six Sigma, 3, 8, 9, 12, 37
Special cause, 30, 31, 45, 46, 48, 52, 61, 66
Specification limits, 34, 63
Stakeholder analysis, 19–21
Statement of operations, 5
Storyboards, 225
analysis phase storyboard recommended
contents, 226
control phase storyboard recommended
contents, 226
defining phase storyboard recommended
contents, 225
improve phase storyboard recommended
contents, 226
measuring phase storyboard recommended
contents, 226
phase storyboard recommended
contents, 225
Subject matter experts (SMEs), 37, 113
Sum of the least squares, 127
Supplier, Inputs, Process, Outputs, and
Customer, see SIPOC
Swim lane diagrams, 18
T
Team members, 14–16
Test of proportions
chi-square test, 101–103
test of two proportions in Minitab, 99
Test of two proportions, 43, 99
datasets, 249
Toyota Production System (TPS), 2, 3
Two sample T test, 119, 120, 143–149
datasets, 249–250
U
U-chart, 55
dataset, 241–242
Upper control limit (UCL), 34, 46, 48, 63
V
Voice of the Customer (VOC), 17
W
Warrantees claims and recalls, 4
X
X-Bar R Chart, 53
Xbar-R dataset, 240–2411
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