Preface ix
1 What is robust design? 1
1.1 The importance of small variation 1
1.2 Variance reduction 2
1.3 Variation propagation 4
1.4 Discussion 5
1.4.1 Limitations 6
1.4.2 The outline of this book 7
Exercises 8
2 DOE for robust design, part 1 11
2.1 Introduction 11
2.1.1 Noise factors 11
2.1.2 Control factors 12
2.1.3 Control-by-noise interactions 12
2.2 Combined arrays: An example from the packaging industry 13
2.2.1 The experimental array 15
2.2.2 Factor effect plots 15
2.2.3 Analytical analysis and statistical significance 17
2.2.4 Some additional comments on the plotting 20
2.3 Dispersion effects 21
Exercises 23
Reference 25
3 Noise and control factors 27
3.1 Introduction to noise factors 27
3.1.1 Categories of noise 28
3.2 Finding the important noise factors 33
3.2.1 Relating noise to failure modes 33
3.2.2 Reducing the number of noise factors 34
3.3 How to include noise in a designed experiment 40
3.3.1 Compounding of noise factors 40
3.3.2 How to include noise in experimentation 45
3.3.3 Process parameters 48
3.4 Control factors 48
Exercises 49
References 51
4 Response, signal, and P diagrams 53
4.1 The idea of signal and response 53
4.1.1 Two situations 54
4.2 Ideal functions and P diagrams 55
4.2.1 Noise or signal factor 56
4.2.2 Control or signal factor 56
4.2.3 The scope 58
4.3 The signal 63
4.3.1 Including a signal in a designed experiment 64
Exercises 65
5 DOE for robust design, part 2 69
5.1 Combined and crossed arrays 69
5.1.1 Classical DOE versus DOE for robust design 69
5.1.2 The structure of inner and outer arrays 70
5.2 Including a signal in a designed experiment 74
5.2.1 Combined arrays with a signal 74
5.2.2 Inner and outer arrays with a signal 81
5.3 Crossed arrays versus combined arrays 89
5.3.1 Differences in factor aliasing 91
5.4 Crossed arrays and split-plot designs 94
5.4.1 Limits of randomization 94
5.4.2 Split-plot designs 95
Exercises 98
References 99
6 Smaller-the-better and larger-the-better 101
6.1 Different types of responses 101
6.2 Failure modes and smaller-the-better 102
6.2.1 Failure modes 102
6.2.2 STB with inner and outer arrays 103
6.2.3 STB with combined arrays 106
6.3 Larger-the-better 106
6.4 Operating window 108
6.4.1 The window width 110
Exercises 113
References 115
7 Regression for robust design 117
7.1 Graphical techniques 117
7.2 Analytical minimization of (g'(z))2 120
7.3 Regression and crossed arrays 121
7.3.1 Regression terms in the inner array 127
Exercises 128
8 Mathematics of robust design 131
8.1 Notational system 131
8.2 The objective function 132
8.2.1 Multidimensional problems 136
8.2.2 Optimization in the presence of a signal 138
8.2.3 Matrix formulation 139
8.2.4 Pareto optimality 141
8.3 ANOVA for robust design 144
8.3.1 Traditional ANOVA 144
8.3.2 Functional ANOVA 146
8.3.3 Sensitivity indices 149
Exercises 152
References 153
9 Design and analysis of computer experiments 155
9.1 Overview of computer experiments 156
9.1.1 Robust design 157
9.2 Experimental arrays for computer experiments 161
9.2.1 Screening designs 161
9.2.2 Space filling designs 163
9.2.3 Latin hypercubes 165
9.2.4 Latin hypercube designs and alphabetical optimality criteria 166
9.3 Response surfaces 167
9.3.1 Local least squares 168
9.3.2 Kriging 169
9.4 Optimization 171
9.4.1 The objective function 171
9.4.2 Analytical techniques or Monte Carlo 173
Exercises 175
References 176
10 Monte Carlo methods for robust design 177
10.1 Geometry variation 177
10.1.1 Electronic circuits 179
10.2 Geometry variation in two dimensions 179
10.3 Crossed arrays 192
11 Taguchi and his ideas on robust design 195
11.1 History and origin 195
11.2 The experimental arrays 197
11.2.1 The nature of inner arrays 197
11.2.2 Interactions and energy thinking 199
11.2.3 Crossing the arrays 200
11.3 Signal-to-noise ratios 200
11.4 Some other ideas 203
11.4.1 Randomization 203
11.4.2 Science versus engineering 204
11.4.3 Line fitting for dynamic models 204
11.4.4 An aspect on the noise 206
11.4.5 Dynamic models 207
Exercises 208
References 208
Appendix A Loss functions 209
A.1 Why Americans do not buy American television sets 209
A.2 Taguchi's view on loss function 211
A.3 The average loss and its elements 211
A.4 Loss functions in robust design 214
Exercises 215
References 217
Appendix B Data for chapter 2 219
Appendix C Data for chapter 5 223
Appendix D Data for chapter 6 231
Index 233
