Response Surfaces, Mixtures, and Ridge Analyses / Edition 2

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Overview

The authority on building empirical models and the fitting of such surfaces to data—completely updated and revised

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.

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Editorial Reviews

From the Publisher
“The book can be used as a primary text for graduate courses in response surface methodology, as a supplementary text for advanced undergraduate and beginning graduate courses in design of experiments, and as a reference for researchers.” (SciTech Book Reviews, June 2007)

"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)

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Product Details

Meet the Author

GEORGE E. P. BOX, PhD, DSc, FRS, is Ronald Aylmer Fisher Professor Emeritus of Statistics and Industrial Engineering at the University of Wisconsin–Madison. He is a Fellow of the Royal Society, an Honorary Fellow and Shewhart and Deming Medalist of the American Society for Quality, and was awarded the Guy Medal in Gold from the Royal Statistical Society. He is also the recipient of the Samuel S. Wilks Memorial Medal of the American Statistical Association.

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.

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Table of Contents

Preface to the Second Edition.

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.

Tables.

Bibliography.

Author Index.

Subject Index.

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