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Response Surface Methodology: Process and Product Optimization Using Designed Experiments, 3rd Edition

Response Surface Methodology: Process and Product Optimization Using Designed Experiments, 3rd Edition

ISBN: 978-0-470-17446-3

Jan 2009

704 pages


Praise for the Second Edition:

"This book [is for] anyone who would like a good, solid understanding of response surface methodology. The book is easy to read, easy to understand, and very applicable. The examples are excellent and facilitate learning of the concepts and methods."
Journal of Quality Technology

Complete with updates that capture the important advances in the field of experimental design, Response Surface Methodology, Third Edition successfully provides a basic foundation for understanding and implementing response surface methodology (RSM) in modern applications. The book continues to outline the essential statistical experimental design fundamentals, regression modeling techniques, and elementary optimization methods that are needed to fit a response surface model from experimental data. With its wealth of new examples and use of the most up-to-date software packages, this book serves as a complete and modern introduction to RSM and its uses across scientific and industrial research.

This new edition maintains its accessible approach to RSM, with coverage of classical and modern response surface designs. Numerous new developments in RSM are also treated in full, including optimal designs for RSM, robust design, methods for design evaluation, and experiments with restrictions on randomization as well as the expanded integration of these concepts into computer software. Additional features of the Third Edition include:

  • Inclusion of split-plot designs in discussion of two-level factorial designs, two-level fractional factorial designs, steepest ascent, and second-order models

  • A new section on the Hoke design for second-order response surfaces

  • New material on experiments with computer models

  • Updated optimization techniques useful in RSM, including multiple responses

  • Thorough treatment of presented examples and experiments using JMP 7, Design-Expert Version 7, and SAS software packages

  • Revised and new exercises at the end of each chapter

  • An extensive references section, directing the reader to the most current RSM research

Assuming only a fundamental background in statistical models and matrix algebra, Response Surface Methodology, Third Edition is an ideal book for statistics, engineering, and physical sciences courses at the upper-undergraduate and graduate levels. It is also a valuable reference for applied statisticians and practicing engineers.

Preface xi

1 Introduction 1

1.1 Response Surface Methodology, 1

1.2 Product Design and Formulation (Mixture Problems), 10

1.3 Robust Design and Process Robustness Studies, 10

1.4 Useful References on RSM, 11

2 Building Empirical Models 13

2.1 Linear Regression Models, 13

2.2 Estimation of the Parameters in Linear Regression Models, 14

2.3 Properties of the Least Squares Estimators and Estimation of s2, 22

2.4 Hypothesis Testing in Multiple Regression, 24

2.5 Confidence Intervals in Multiple Regression, 31

2.6 Prediction of New Response Observations, 35

2.7 Model Adequacy Checking, 36

2.8 Fitting a Second-Order Model, 47

2.9 Qualitative Regressor Variables, 55

2.10 Transformation of the Response Variable, 58

3 Two-Level Factorial Designs 73

3.1 Introduction, 73

3.2 The 22 Design, 74

3.3 The 23 Design, 86

3.4 The General 2k Design, 96

3.5 A Single Replicate of the 2k Design, 96

3.6 The Addition of Center Points to the 2k Design, 109

3.7 Blocking in the 2k Factorial Design, 114

3.8 Split-Plot Designs, 121

4 Two-Level Fractional Factorial Designs 135

4.1 Introduction, 135

4.2 The One-Half Fraction of the 2k Design, 136

4.3 The One-Quarter Fraction of the 2k Design, 148

4.4 The General 2k2p Fractional Factorial Design, 154

4.5 Resolution III Designs, 158

4.6 Resolution IV and V Designs, 167

4.7 Fractional Factorial Split-Plot Designs, 168

4.8 Summary, 172

5 Process Improvement with Steepest Ascent 181

5.1 Determining the Path of Steepest Ascent, 182

5.2 Consideration of Interaction and Curvature, 189

5.3 Effect of Scale (Choosing Range of Factors), 193

5.4 Confidence Region for Direction of Steepest Ascent, 195

5.5 Steepest Ascent Subject to a Linear Constraint, 198

5.6 Steepest Ascent in a Split-Plot Experiment, 202

6 The Analysis of Second-Order Response Surfaces 219

6.1 Second-Order Response Surface, 219

6.2 Second-Order Approximating Function, 220

6.3 A Formal Analytical Approach to the Second-Order Model, 223

6.4 Ridge Analysis of the Response Surface, 235

6.5 Sampling Properties of Response Surface Results, 242

6.6 Multiple Response Optimization, 253

6.7 Further Comments Concerning Response Surface Analysis, 264

7 Experimental Designs for Fitting Response Surfaces—I 281

7.1 Desirable Properties of Response Surface Designs, 281

7.2 Operability Region, Region of Interest, and Model Inadequacy, 282

7.3 Design of Experiments for First-Order Models, 285

7.4 Designs for Fitting Second-Order Models, 296

8 Experimental Designs for Fitting Response Surfaces—II 349

8.1 Designs that Require a Relatively Small Run Size, 350

8.2 General Criteria for Constructing, Evaluating, and Comparing Experimental Designs, 362

8.3 Computer-Generated Designs in RSM, 386

8.4 Some Final Comments Concerning Design Optimality and Computer-Generated Design, 405

9 Advanced Topics in Response Surface Methodology 417

9.1 Effects of Model Bias on the Fitted Model and Design, 417

9.2 A Design Criterion Involving Bias and Variance, 420

9.3 Errors in Control of Design Levels, 432

9.4 Experiments with Computer Models, 435

9.5 Minimum Bias Estimation of Response Surface Models, 442

9.6 Neural Networks, 446

9.7 RSM for Non-Normal Responses—Generalized Linear Models, 449

9.8 Split-Plot Designs for Second-Order Models, 466

10 Robust Parameter Design and Process Robustness Studies 483

10.1 Introduction, 483

10.2 What is Parameter Design?, 483

10.3 The Taguchi Approach, 486

10.4 The Response Surface Approach, 495

10.5 Experimental Designs for RPD and Process Robustness Studies, 525

10.6 Dispersion Effects in Highly Fractionated Designs, 537

11 Experiments with Mixtures 557

11.1 Introduction, 557

11.2 Simplex Designs and Canonical Mixture Polynomials, 560

11.2.1 Simplex Lattice Designs, 560

11.3 Response Trace Plots, 576

11.4 Reparameterizing Canonical Mixture Models to Contain a Constant Term (b0), 577

12 Other Mixture Design and Analysis Techniques 589

12.1 Constraints on the Component Proportions, 589

12.2 Mixture Experiments Using Ratios of Components, 617

12.3 Process Variables in Mixture Experiments, 621

12.4 Screening Mixture Components, 641

Appendix 1 Moment Matrix of a Rotatable Design 655

Appendix 2 Rotatability of a Second-Order Equiradial Design 661

References 665

Index 677

  • Updated optimization techniques useful in RSM, including multiple responses
  • The most current RSM approach to robust parameter design and process robustness studies
  • Revised and updated end-of-chapter problems; large, easy-to-read book format and side-by-side art program; an extensive reference section; and valuable technical appendices on RSM

“This new third edition has been substantially rewritten and updated with new topics and material, new examples and exercises, and to more fully illustrate modern applications of RSM.Working with the most useful software packages, the authors bring an applied focus that emphasizes models useful in industry for product and process design and development.”  (Zentralblatt Math, 1 October 2013)

"The third edition of a well-regarded text on response surface methodology. Christine M. Anderson-Cook, has been added … [bringing] an applied perspective to the material." (Mathematical Reviews, December 2009)
  • Authoritative discussion on methods for design evaluation
  • Comprehensive treatment of mixture experiments
  • Coverage of two-level factorial and fractional factorial design, split-block design, and empirical modeling of response surface methodology (RSM)
  • Classical and modern response surface designs, including computer generated designs and graphical methods for design comparison
  • Support by Design-Expert, SAS®, JMP, and Minitab