Statistical Robust Design: An Industrial Perspective

A UNIQUELY PRACTICAL APPROACH TO ROBUST DESIGN FROM A STATISTICAL AND ENGINEERING PERSPECTIVE Variation in environment, usage conditions, and the manufacturing process has long presented a challenge in product engineering, and reducing variation is universally recognized as a key to improving reliability and productivity. One key and cost-effective way to achieve this is by robust design – making the product as insensitive as possible to variation. With Design for Six Sigma training programs primarily in mind, the author of this book offers practical examples that will help to guide product engineers through every stage of experimental design: formulating problems, planning experiments, and analysing data. He discusses both physical and virtual techniques, and includes numerous exercises and solutions that make the book an ideal resource for teaching or self-study. Presents a practical approach to robust design through design of experiments. Offers a balance between statistical and industrial aspects of robust design. Includes practical exercises, making the book useful for teaching. Covers both physical and virtual approaches to robust design. Supported by an accompanying website www.wiley/com/go/robust featuring MATLAB scripts and solutions to exercises. Written by an experienced industrial design practitioner. This book's state of the art perspective will be of benefit to practitioners of robust design in industry, consultants providing training in Design for Six Sigma, and quality engineers. It will also be a valuable resource for specialized university courses in statistics or quality engineering.

Table of Contents:
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

About the Author :
Magnus Arnér, Tetra Pak Packaging Solutions, Sweden.