The Mahalanobis-Taguchi strategy: a pattern technology system
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York [u.a.]
Wiley
2002
|
| Schlagworte: | |
| Online-Zugang: | Publisher description Table of contents Inhaltsverzeichnis |
| Beschreibung: | XXII, 234 S. Ill. |
| ISBN: | 0471023337 |
Internformat
MARC
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| 245 | 1 | 0 | |a The Mahalanobis-Taguchi strategy |b a pattern technology system |c Genichi Taguchi ; Rajesh Jugulum |
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| 300 | |a XXII, 234 S. |b Ill. | ||
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| 650 | 4 | |a Taguchi methods (Quality control) | |
| 650 | 4 | |a Pattern recognition systems | |
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Datensatz im Suchindex
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| adam_text | CONTENTS
Preface xiii
Acknowledgments xvii
Terms and Symbols xix
Definitions of Mathematical and Statistical Terms xxi
1 Introduction 1
1.1 The Goal 3
1.2 The Nature of a Multidimensional System 5
1.2.1 Description of Multidimensional Systems 5
1.2.2 Correlations between the Variables 6
1.2.3 Mahalanobis Distance 6
1.2.4 Robust Engineering/Taguchi Methods 8
1.3 Multivariate Diagnosis—The State of the Art 10
1.3.1 Principal Component Analysis 10
1.3.2 Discrimination and Classification Method 11
1.3.3 Stepwise Regression 11
1.3.4 Test of Additional Information (Rao s Test) 12
1.3.5 Multiple Regression 12
1.3.6 Multivariate Process Control Charts 12
1.3.7 Artificial Neural Networks 13
1.4 Approach 14
1.4.1 Classification versus Measurement 14
1.4.2 Normals versus Abnormals 14
1.4.3 Probabilistic versus Data Analytic 15
1.4.4 Dimensionality Reduction 15
vii
viii CONTENTS
1.5 Refining the Solution Strategy 16
1.6 Guide to This Book 16
2 MTS and MTGS 19
2.1 A Discussion of Mahalanobis Distance 21
2.2 Objectives of MTS and MTGS 23
2.2.1 Mahalanobis Distance (Inverse Matrix
Method) 24
2.2.2 Gram-Schmidt Orthogonalization Process 25
2.2.3 Proof That Equations 2.2 and 2.3 Are the
Same 26
2.2.4 Calculation of the Mean of the Mahalanobis
Space 27
2.3 Steps in MTS 30
2.4 Steps in MTGS 31
2.5 Discussion of Medical Diagnosis Data: Use of MTGS and
MTS Methods 33
2.6 Conclusions 39
3 Advantages and Limitations of MTS and MTGS 41
3.1 Direction of Abnormalities 43
3.1.1 The Gram-Schmidt Process 44
3.1.2 Identification of the Direction of Abnormals 44
3.1.3 Decision Rule for Higher Dimensions 49
3.2 Example of a Graduate Admission System 50
3.3 Multicollinearity 52
3.4 A Discussion of Partial Correlations 55
3.5 Conclusions 57
4 Role of Orthogonal Arrays and Signal-to-Noise Ratios in
Multivariate Diagnosis 59
4.1 Role of Orthogonal Arrays 62
CONTENTS ix
4.2 Role of S/N Ratios 63
4.3 Advantages of S/N ratios 71
4.3.1 S/N Ratio as a Simple Measure to Identify Useful
Variables 71
4.3.2 S/N Ratio as a Measure of Functionality of the
System 79
4.3.3 S/N Ratio to Predict the Given Conditions 80
4.4 Conclusions 81
5 Treatment of Categorical Data in MTS/MTGS Methods 83
5.1 MTS/MTGS with Categorical Data 85
5.2 A Sales and Marketing Application 87
5.2.1 Selection of Suitable Variables 88
5.2.2 Description of the Variables 88
5.2.3 Construction of Mahalanobis Space 89
5.2.4 Validation of the Measurement Scale 89
5.2.5 Identification of Useful Variables (Developing
Stage) 92
5.2.6 S/N Ratio of the System (Before and After) 94
5.3 Conclusions 95
6 MTS/MTGS under a Noise Environment 97
6.1 MTS/MTGS with Noise Factors 99
6.1.1 Treat Each Level of the Noise Factor
Separately 101
6.1.2 Include the Noise Factor as One of the
Variables 101
6.1.3 Combine Variables of Different Levels of the
Noise Factor 102
6.1.4 Do Not Consider the Noise Factor If It Cannot Be
Measured 103
6.2 Conclusions 103
7 Determination of Thresholds—A Loss Function Approach 105
7.1 Why Threshold Is Required in MTS/MTGS 108
x CONTENTS
7.2 Quadratic Loss Function 109
7.2.1 QLF for the Nominal-the-Best Characteristic 109
7.2.2 QLF for the Larger-the-Better Characteristic 110
7.2.3 QLF for the Smaller-the-Better
Characteristic 111
7.3 QLF for MTS/MTGS 111
7.3.1 Determination of Threshold 112
7.3.2 When Only Good Abnormals Are Present 114
7.4 Examples 114
7.4.1 Medical Diagnosis Case 114
7.4.2 A Student Admission System 115
7.5 Conclusions 116
8 Standard Error of the Measurement Scale 117
8.1 Why Mahalanobis Distance Is Used for Constructing the
Measurement Scale 119
8.2 Standard Error of the Measurement Scale 120
8.3 Standard Error for the Medical Diagnosis Example 121
8.4 Conclusions 122
9 Advance Topics in Multivariate Diagnosis 123
9.1 Multivariate Diagnosis Using the Adjoint Matrix
Method 126
9.1.1 Related Topics of Matrix Theory 126
9.1.2 Adjoint Matrix Method for Handling
Multicollinearity 128
9.2 Examples for the Adjoint Matrix Method 130
9.2.1 Example 1 130
9.2.2 Example 2 136
9.3 j8-Adjustment Method for Small Correlations 139
9.4 Subset Selection Using the Multiple Mahalanobis
Distance Method 142
9.4.1 Steps in the MMD Method 145
9.4.2 Example 145
CONTENTS xi
9.5 Selection of Mahalanobis Space from Historical Data 147
9.6 Conclusions 149
10 MTS/MTGS versus Other Methods 151
10.1 Principal Component Analysis 155
10.2 Discrimination and Classification Method 157
10.2.1 Fisher s Discriminant Function 158
10.2.2 Use of Mahalanobis Distance 159
10.3 Stepwise Regression 161
10.4 Test of Additional Information (Rao s Test) 163
10.5 Multiple Regression Analysis 165
10.6 Multivariate Process Control 169
10.7 Artificial Neural Networks 169
10.7.1 Feed-Forward (Backpropagation) Method 170
10.7.2 Theoretical Comparison 171
10.7.3 Medical Diagnosis Data Analysis 171
10.8 Conclusions 174
11 Case Studies 175
11.1 American Case Studies 177
11.1.1 Auto Marketing Case Study 177
11.1.2 Gear-Motor Assembly Case Study 181
11.1.3 ASQ Research Fellowship Grant Case Study 188
11.1.4 Improving the Transmission Inspection System
Using MTS 189
11.2 Japanese Case Studies 191
11.2.1 Improvement of the Utility Rate of Nitrogen
While Brewing Soy Sauce 191
11.2.2 Application of MTS for Measuring Oil in Water
Emulsion 193
11.2.3 Prediction of Fasting Plasma Glucose (FPG) from
Repetitive Annual Health Checkup Data 195
11.3 Conclusions 197
xii CONTENTS
12 Concluding Remarks 199
12.1 Important Points of the Proposed Methods 201
12.2 Scientific Contributions from MTS/MTGS Methods 203
12.3 Limitations of the Proposed Methods 205
12.4 Recommendations for Future Research 205
Bibliography 207
Appendixes 213
A.I ASI Data Set 215
A.2 Principal Component Analysis
(MINITAB Output) 217
A.3 Discriminant and Classification Analysis
(MINITAB Output) 219
A.4 Results of Stepwise Regression
(MINITAB Output) 220
A.5 Multiple Regression Analysis
(MINITAB Output) 225
A.6 Neural Network Analysis
(MATLAB Output) 226
A.7 Variables for Auto Marketing Case Study 227
Index 229
|
| adam_txt |
CONTENTS
Preface xiii
Acknowledgments xvii
Terms and Symbols xix
Definitions of Mathematical and Statistical Terms xxi
1 Introduction 1
1.1 The Goal 3
1.2 The Nature of a Multidimensional System 5
1.2.1 Description of Multidimensional Systems 5
1.2.2 Correlations between the Variables 6
1.2.3 Mahalanobis Distance 6
1.2.4 Robust Engineering/Taguchi Methods 8
1.3 Multivariate Diagnosis—The State of the Art 10
1.3.1 Principal Component Analysis 10
1.3.2 Discrimination and Classification Method 11
1.3.3 Stepwise Regression 11
1.3.4 Test of Additional Information (Rao's Test) 12
1.3.5 Multiple Regression 12
1.3.6 Multivariate Process Control Charts 12
1.3.7 Artificial Neural Networks 13
1.4 Approach 14
1.4.1 Classification versus Measurement 14
1.4.2 Normals versus Abnormals 14
1.4.3 Probabilistic versus Data Analytic 15
1.4.4 Dimensionality Reduction 15
vii
viii CONTENTS
1.5 Refining the Solution Strategy 16
1.6 Guide to This Book 16
2 MTS and MTGS 19
2.1 A Discussion of Mahalanobis Distance 21
2.2 Objectives of MTS and MTGS 23
2.2.1 Mahalanobis Distance (Inverse Matrix
Method) 24
2.2.2 Gram-Schmidt Orthogonalization Process 25
2.2.3 Proof That Equations 2.2 and 2.3 Are the
Same 26
2.2.4 Calculation of the Mean of the Mahalanobis
Space 27
2.3 Steps in MTS 30
2.4 Steps in MTGS 31
2.5 Discussion of Medical Diagnosis Data: Use of MTGS and
MTS Methods 33
2.6 Conclusions 39
3 Advantages and Limitations of MTS and MTGS 41
3.1 Direction of Abnormalities 43
3.1.1 The Gram-Schmidt Process 44
3.1.2 Identification of the Direction of Abnormals 44
3.1.3 Decision Rule for Higher Dimensions 49
3.2 Example of a Graduate Admission System 50
3.3 Multicollinearity 52
3.4 A Discussion of Partial Correlations 55
3.5 Conclusions 57
4 Role of Orthogonal Arrays and Signal-to-Noise Ratios in
Multivariate Diagnosis 59
4.1 Role of Orthogonal Arrays 62
CONTENTS ix
4.2 Role of S/N Ratios 63
4.3 Advantages of S/N ratios 71
4.3.1 S/N Ratio as a Simple Measure to Identify Useful
Variables 71
4.3.2 S/N Ratio as a Measure of Functionality of the
System 79
4.3.3 S/N Ratio to Predict the Given Conditions 80
4.4 Conclusions 81
5 Treatment of Categorical Data in MTS/MTGS Methods 83
5.1 MTS/MTGS with Categorical Data 85
5.2 A Sales and Marketing Application 87
5.2.1 Selection of Suitable Variables 88
5.2.2 Description of the Variables 88
5.2.3 Construction of Mahalanobis Space 89
5.2.4 Validation of the Measurement Scale 89
5.2.5 Identification of Useful Variables (Developing
Stage) 92
5.2.6 S/N Ratio of the System (Before and After) 94
5.3 Conclusions 95
6 MTS/MTGS under a Noise Environment 97
6.1 MTS/MTGS with Noise Factors 99
6.1.1 Treat Each Level of the Noise Factor
Separately 101
6.1.2 Include the Noise Factor as One of the
Variables 101
6.1.3 Combine Variables of Different Levels of the
Noise Factor 102
6.1.4 Do Not Consider the Noise Factor If It Cannot Be
Measured 103
6.2 Conclusions 103
7 Determination of Thresholds—A Loss Function Approach 105
7.1 Why Threshold Is Required in MTS/MTGS 108
x CONTENTS
7.2 Quadratic Loss Function 109
7.2.1 QLF for the Nominal-the-Best Characteristic 109
7.2.2 QLF for the Larger-the-Better Characteristic 110
7.2.3 QLF for the Smaller-the-Better
Characteristic 111
7.3 QLF for MTS/MTGS 111
7.3.1 Determination of Threshold 112
7.3.2 When Only Good Abnormals Are Present 114
7.4 Examples 114
7.4.1 Medical Diagnosis Case 114
7.4.2 A Student Admission System 115
7.5 Conclusions 116
8 Standard Error of the Measurement Scale 117
8.1 Why Mahalanobis Distance Is Used for Constructing the
Measurement Scale 119
8.2 Standard Error of the Measurement Scale 120
8.3 Standard Error for the Medical Diagnosis Example 121
8.4 Conclusions 122
9 Advance Topics in Multivariate Diagnosis 123
9.1 Multivariate Diagnosis Using the Adjoint Matrix
Method 126
9.1.1 Related Topics of Matrix Theory 126
9.1.2 Adjoint Matrix Method for Handling
Multicollinearity 128
9.2 Examples for the Adjoint Matrix Method 130
9.2.1 Example 1 130
9.2.2 Example 2 136
9.3 j8-Adjustment Method for Small Correlations 139
9.4 Subset Selection Using the Multiple Mahalanobis
Distance Method 142
9.4.1 Steps in the MMD Method 145
9.4.2 Example 145
CONTENTS xi
9.5 Selection of Mahalanobis Space from Historical Data 147
9.6 Conclusions 149
10 MTS/MTGS versus Other Methods 151
10.1 Principal Component Analysis 155
10.2 Discrimination and Classification Method 157
10.2.1 Fisher's Discriminant Function 158
10.2.2 Use of Mahalanobis Distance 159
10.3 Stepwise Regression 161
10.4 Test of Additional Information (Rao's Test) 163
10.5 Multiple Regression Analysis 165
10.6 Multivariate Process Control 169
10.7 Artificial Neural Networks 169
10.7.1 Feed-Forward (Backpropagation) Method 170
10.7.2 Theoretical Comparison 171
10.7.3 Medical Diagnosis Data Analysis 171
10.8 Conclusions 174
11 Case Studies 175
11.1 American Case Studies 177
11.1.1 Auto Marketing Case Study 177
11.1.2 Gear-Motor Assembly Case Study 181
11.1.3 ASQ Research Fellowship Grant Case Study 188
11.1.4 Improving the Transmission Inspection System
Using MTS 189
11.2 Japanese Case Studies 191
11.2.1 Improvement of the Utility Rate of Nitrogen
While Brewing Soy Sauce 191
11.2.2 Application of MTS for Measuring Oil in Water
Emulsion 193
11.2.3 Prediction of Fasting Plasma Glucose (FPG) from
Repetitive Annual Health Checkup Data 195
11.3 Conclusions 197
xii CONTENTS
12 Concluding Remarks 199
12.1 Important Points of the Proposed Methods 201
12.2 Scientific Contributions from MTS/MTGS Methods 203
12.3 Limitations of the Proposed Methods 205
12.4 Recommendations for Future Research 205
Bibliography 207
Appendixes 213
A.I ASI Data Set 215
A.2 Principal Component Analysis
(MINITAB Output) 217
A.3 Discriminant and Classification Analysis
(MINITAB Output) 219
A.4 Results of Stepwise Regression
(MINITAB Output) 220
A.5 Multiple Regression Analysis
(MINITAB Output) 225
A.6 Neural Network Analysis
(MATLAB Output) 226
A.7 Variables for Auto Marketing Case Study 227
Index 229 |
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| id | DE-604.BV023525513 |
| illustrated | Illustrated |
| index_date | 2024-07-02T22:33:52Z |
| indexdate | 2024-07-09T21:23:54Z |
| institution | BVB |
| isbn | 0471023337 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-016845755 |
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| physical | XXII, 234 S. Ill. |
| publishDate | 2002 |
| publishDateSearch | 2002 |
| publishDateSort | 2002 |
| publisher | Wiley |
| record_format | marc |
| spelling | Taguchi, Genichi 1924- Verfasser (DE-588)118878085 aut The Mahalanobis-Taguchi strategy a pattern technology system Genichi Taguchi ; Rajesh Jugulum New York [u.a.] Wiley 2002 XXII, 234 S. Ill. txt rdacontent n rdamedia nc rdacarrier Taguchi methods (Quality control) Pattern recognition systems Multivariate Analyse (DE-588)4040708-1 gnd rswk-swf Mustererkennung (DE-588)4040936-3 gnd rswk-swf Multivariate Analyse (DE-588)4040708-1 s Mustererkennung (DE-588)4040936-3 s DE-604 Jugulum, Rajesh Verfasser (DE-588)129645567 aut http://www.loc.gov/catdir/description/wiley036/2002003927.html Publisher description http://www.loc.gov/catdir/toc/fy031/2002003927.html Table of contents HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016845755&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Taguchi, Genichi 1924- Jugulum, Rajesh The Mahalanobis-Taguchi strategy a pattern technology system Taguchi methods (Quality control) Pattern recognition systems Multivariate Analyse (DE-588)4040708-1 gnd Mustererkennung (DE-588)4040936-3 gnd |
| subject_GND | (DE-588)4040708-1 (DE-588)4040936-3 |
| title | The Mahalanobis-Taguchi strategy a pattern technology system |
| title_auth | The Mahalanobis-Taguchi strategy a pattern technology system |
| title_exact_search | The Mahalanobis-Taguchi strategy a pattern technology system |
| title_exact_search_txtP | The Mahalanobis-Taguchi strategy a pattern technology system |
| title_full | The Mahalanobis-Taguchi strategy a pattern technology system Genichi Taguchi ; Rajesh Jugulum |
| title_fullStr | The Mahalanobis-Taguchi strategy a pattern technology system Genichi Taguchi ; Rajesh Jugulum |
| title_full_unstemmed | The Mahalanobis-Taguchi strategy a pattern technology system Genichi Taguchi ; Rajesh Jugulum |
| title_short | The Mahalanobis-Taguchi strategy |
| title_sort | the mahalanobis taguchi strategy a pattern technology system |
| title_sub | a pattern technology system |
| topic | Taguchi methods (Quality control) Pattern recognition systems Multivariate Analyse (DE-588)4040708-1 gnd Mustererkennung (DE-588)4040936-3 gnd |
| topic_facet | Taguchi methods (Quality control) Pattern recognition systems Multivariate Analyse Mustererkennung |
| url | http://www.loc.gov/catdir/description/wiley036/2002003927.html http://www.loc.gov/catdir/toc/fy031/2002003927.html http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016845755&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT taguchigenichi themahalanobistaguchistrategyapatterntechnologysystem AT jugulumrajesh themahalanobistaguchistrategyapatterntechnologysystem |