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Index
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Title
Copyright
PREFACE
1 INTRODUCTION
1.1 RESPONSE SURFACE METHODOLOGY
1.2 PRODUCT DESIGN AND FORMULATION (MIXTURE PROBLEMS)
1.3 ROBUST DESIGN AND PROCESS ROBUSTNESS STUDIES
1.4 USEFUL REFERENCES ON RSM
2 BUILDING EMPIRICAL MODELS
2.1 LINEAR REGRESSION MODELS
2.2 ESTIMATION OF THE PARAMETERS IN LINEAR REGRESSION MODELS
2.3 PROPERTIES OF THE LEAST SQUARES ESTIMATORS AND ESTIMATION OF σ2
2.4 HYPOTHESIS TESTING IN MULTIPLE REGRESSION
2.5 CONFIDENCE INTERVALS IN MULTIPLE REGRESSION
2.6 PREDICTION OF NEW RESPONSE OBSERVATIONS
2.7 MODEL ADEQUACY CHECKING
2.8 FITTING A SECOND-ORDER MODEL
2.9 QUALITATIVE REGRESSOR VARIABLES
2.10 TRANSFORMATION OF THE RESPONSE VARIABLE
EXERCISES
3 TWO-LEVEL FACTORIAL DESIGNS
3.1 INTRODUCTION
3.2 THE 22 DESIGN
3.3 THE 23 DESIGN
3.4 THE GENERAL 2k DESIGN
3.5 A SINGLE REPLICATE OF THE 2k DESIGN
3.6 THE ADDITION OF CENTER POINTS TO THE 2k DESIGN
3.7 BLOCKING IN THE 2k FACTORIAL DESIGN
3.8 SPLIT-PLOT DESIGNS
EXERCISES
4 TWO-LEVEL FRACTIONAL FACTORIAL DESIGNS
4.1 INTRODUCTION
4.2 THE ONE-HALF FRACTION OF THE 2k DESIGN
4.3 THE ONE-QUARTER FRACTION OF THE 2k DESIGN
4.4 THE GENERAL 2k–p FRACTIONAL FACTORIAL DESIGN
4.5 RESOLUTION III DESIGNS
4.6 RESOLUTION IV AND V DESIGNS
4.7 FRACTIONAL FACTORIAL SPLIT-PLOT DESIGNS
4.8 SUMMARY
EXERCISES
5 PROCESS IMPROVEMENT WITH STEEPEST ASCENT
5.1 DETERMINING THE PATH OF STEEPEST ASCENT
5.2 CONSIDERATION OF INTERACTION AND CURVATURE
5.3 EFFECT OF SCALE (CHOOSING RANGE OF FACTORS).
5.4 CONFIDENCE REGION FOR DIRECTION OF STEEPEST ASCENT
5.5 STEEPEST ASCENT SUBJECT TO A LINEAR CONSTRAINT
5.6 STEEPEST ASCENT IN A SPLIT-PLOT EXPERIMENT
EXERCISES
6 THE ANALYSIS OF SECOND-ORDER RESPONSE SURFACES
6.1 SECOND-ORDER RESPONSE SURFACE
6.2 SECOND-ORDER APPROXIMATING FUNCTION
6.3 A FORMAL ANALYTICAL APPROACH TO THE SECOND-ORDER MODEL
6.4 RIDGE ANALYSIS OF THE RESPONSE SURFACE
6.5 SAMPLING PROPERTIES OF RESPONSE SURFACE RESULTS
6.6 MULTIPLE RESPONSE OPTIMIZATION
6.7 FURTHER COMMENTS CONCERNING RESPONSE SURFACE ANALYSIS
EXERCISES
7 EXPERIMENTAL DESIGNS FOR FITTING RESPONSE SURFACES—I
7.1 DESIRABLE PROPERTIES OF RESPONSE SURFACE DESIGNS
7.2 OPERABILITY REGION, REGION OF INTEREST, AND MODEL INADEQUACY
7.3 DESIGN OF EXPERIMENTS FOR FIRST-ORDER MODELS
7.4 DESIGNS FOR FITTING SECOND-ORDER MODELS
EXERCISES
8 EXPERIMENTAL DESIGNS FOR FITTING RESPONSE SURFACES—II
8.1 DESIGNS THAT REQUIRE A RELATIVELY SMALL RUN SIZE
8.2 GENERAL CRITERIA FOR CONSTRUCTING, EVALUATING, AND COMPARING EXPERIMENTAL DESIGNS
8.3 COMPUTER-GENERATED DESIGNS IN RSM
8.4 SOME FINAL COMMENTS CONCERNING DESIGN OPTIMALITY AND COMPUTER-GENERATED DESIGN
EXERCISES
9 ADVANCED TOPICS IN RESPONSE SURFACE METHODOLOGY
9.1 EFFECTS OF MODEL BIAS ON THE FITTED MODEL AND DESIGN
9.2 A DESIGN CRITERION INVOLVING BIAS AND VARIANCE
9.3 ERRORS IN CONTROL OF DESIGN LEVELS
9.4 EXPERIMENTS WITH COMPUTER MODELS
9.5 MINIMUM BIAS ESTIMATION OF RESPONSE SURFACE MODELS
9.6 NEURAL NETWORKS
9.7 RSM FOR NON-NORMAL RESPONSES—GENERALIZED LINEAR MODELS
9.8 SPLIT-PLOT DESIGNS FOR SECOND-ORDER MODELS
EXERCISES
10 ROBUST PARAMETER DESIGN AND PROCESS ROBUSTNESS STUDIES
10.1 INTRODUCTION
10.2 WHAT IS PARAMETER DESIGN?
10.3 THE TAGUCHI APPROACH
10.4 THE RESPONSE SURFACE APPROACH
10.5 EXPERIMENTAL DESIGNS FOR RPD AND PROCESS ROBUSTNESS STUDIES
10.6 DISPERSION EFFECTS IN HIGHLY FRACTIONATED DESIGNS
EXERCISES
11 EXPERIMENTS WITH MIXTURES
11.1 INTRODUCTION
11.2 SIMPLEX DESIGNS AND CANONICAL MIXTURE POLYNOMIALS
11.3 RESPONSE TRACE PLOTS
11.4 REPARAMETERIZING CANONICAL MIXTURE MODELS TO CONTAIN A CONSTANT TERM (b0)
EXERCISES
12 OTHER MIXTURE DESIGN AND ANALYSIS TECHNIQUES
12.1 CONSTRAINTS ON THE COMPONENT PROPORTIONS
12.2 MIXTURE EXPERIMENTS USING RATIOS OF COMPONENTS
12.3 PROCESS VARIABLES IN MIXTURE EXPERIMENTS
12.4 SCREENING MIXTURE COMPONENTS
EXERCISES
APPENDIX 1 MOMENT MATRIX OF A ROTATABLE DESIGN
APPENDIX 2 ROTATABILITY OF A SECOND-ORDER EQUIRADIAL DESIGN
REFERENCES
INDEX
WILEY SERIES IN PROBABILITY AND STATISTICS
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