Response Surfaces, Mixtures, and Ridge Analyses, 2nd Edition
Revising and updating a volume that represents the essential source on building empirical models, George Box and Norman Draper—renowned authorities in this field—continue to set the standard with the Second Edition of Response Surfaces, Mixtures, and Ridge Analyses, providing timely new techniques, new exercises, and expanded material.
A comprehensive introduction to building empirical models, this book presents the general philosophy and computational details of a number of important topics, including factorial designs at two levels; fitting first and second-order models; adequacy of estimation and the use of transformation; and occurrence and elucidation of ridge systems.
Substantially rewritten, the Second Edition reflects the emergence of ridge analysis of second-order response surfaces as a very practical tool that can be easily applied in a variety of circumstances. This unique, fully developed coverage of ridge analysis—a technique for exploring quadratic response surfaces including surfaces in the space of mixture ingredients and/or subject to linear restrictions—includes MINITAB® routines for performing the calculations for any number of dimensions.
Many additional figures are included in the new edition, and new exercises (many based on data from published papers) offer insight into the methods used. The exercises and their solutions provide a variety of supplementary examples of response surface use, forming an extremely important component of the text.
Response Surfaces, Mixtures, and Ridge Analyses, Second Edition presents material in a logical and understandable arrangement and includes six new chapters covering an up-to-date presentation of standard ridge analysis (without restrictions); design and analysis of mixtures experiments; ridge analysis methods when there are linear restrictions in the experimental space including the mixtures experiments case, with or without further linear restrictions; and canonical reduction of second-order response surfaces in the foregoing general case.
Additional features in the new edition include:
- New exercises with worked answers added throughout
- An extensive revision of Chapter 5: Blocking and Fractionating 2k Designs
- Additional discussion on the projection of two-level designs into lower dimensional spaces
This is an ideal reference for researchers as well as a primary text for Response Surface Methodology graduate-level courses and a supplementary text for Design of Experiments courses at the upper-undergraduate and beginning-graduate levels.
Chapter 1. Introduction to response Surface Methodology.
Chapter 2. The Use of Graduating Functions.
Chapter 3. Least Squares for Response Surface Work.
Chapter 4. Factorial Designs at Two Levels.
Chapter 5. Blocking and Fractionating 2k Factorial Designs.
Chapter 6. The Use of Steepest Ascent to Achieve Process Improvement.
Chapter 7. Fitting Second-Order Models.
Chapter 8. Adequacy of Estimation and the Use of Transformation.
Chapter 9. Exploration of Maxima and Ridge Systems with Second-Oder Response Surfaces.
Chapter 10. Occurrence and Elucidation of Ridge Systems, I.
Chapter 11. Occurrence and Elucidation of Ridge Systems, II.
Chapter 12. Ridge Analysis for Examining Second-Order Fitted Models, Unrestricted Case.
Chapter 13. Design Aspects of Variance, Bias, and Lack of Fit.
Chapter 14. Variance-Optimal Designs.
Chapter 15. Practical Choice of a Response Surface Design.
Chapter 16. Response Surfaces for Mixture Ingredients.
Chapter 17. Mixture Experiments in Restricted Regions.
Chapter 18. Other Mixture Methods and Topics.
Chapter 19. Ridge Analysis for Examining Second-Order Fitted Models when there Are Linear Restrictions on the Experimental region.
Chapter 20. Canonical Reduction of Second-Order Fitted Models Subject to Linear Restrictions.
Answers to Exercises.
NORMAN DRAPER is Professor Emeritus of Statistics in the Department of Statistics at the University of Wisconsin, Madison. He received his PhD from the University of North Carolina, Chapel Hill, and has published dozens of papers in professional journals. He is the coauthor (with Harry Smith) of Applied Regression Analysis, Third Edition, published by Wiley.
This volume represents the fundamental authority in the subject matter now that a few other competitors have appeared on the market. While the content may appear to be somewhat standard, the material is exceedingly well presented in a logical and understandable format.
Chapters 1-15 have all been updated and enchanced with new content and strategies.
New exercises have been added throughout the book, involving credible references and data sets; reanalyzing and recasting them in suitable form; and providing answers.
Further (and extensive) discussion on the projection of two-level designs into lower dimensional spaces is presented in Ch. 5.
Some new techniques are presented for the first time
Three new chapters on the design and analysis of mixture experiments have been added at the end of the book, along with yet one more chapter on the general ridge regression procedure.
Some additional topics that have been added include estimation of a few real effects among many possibilities and projection of response surface designs into mixture space.
A new Bibliography section has been written, updated and cross-referenced.
There is a need to keep this volume current given the authoritative nature of its content and its presentation.
The book is written by the major authorities in the field.
New methods are presented when and where necessary so that the book can maintain its high visibility.
It will soon become a classic in view of the fact that it was originally the first of its kind in response surface methodology.
"This book should be mandatory on the shelves of all statisticians. If you own the first edition, it is time to update it with this latest version." (Journal of the American Statistical Association, June 2008)
"…an important reference source." (International Statistical Review, 2007)