Statistical robust design : an industrial perspective

Content: 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