Theory of Factorial Design - Single- And Multi-Stratum Experiments

This self-contained book provides a rigorous, systematic, and up-to-date treatment of the modem theory of factorial design. It includes lots of examples, predominantly from engineering and agriculture, to illustrate the methods. The book incorporates a few exercises in each chapter to enable the book to be used for self-study or for a special topics course. Topics covered include a general theory of multi-stratum factorial design, design key for constructing factorial designs, new construction methods of resolution IV designs, and some results on their structures taken from the literature of projective geometry.

List of contents

Introduction. Linear Model Basics. Randomization and Blocking. Factors. Analysis of Some Simple Orthogonal Designs. Factorial Treatment Structure and Complete Factorial Designs. Blocked, Split-Plot, and Strip-Plot Complete Factorial Designs. Fractional Factorial Designs and Orthogonal Arrays. Regular Fractional Factorial Designs. Minimum Aberration and Related Criteria. Structures and Construction of Two-Level Resolution IV Designs. Orthogonal Block Structures and Strata. Complete Factorial Designs with Orthogonal Block Structures. Multi-Stratum Fractional Factorial Designs. Non-Regular Designs. Appendix. References. Index.

About the author

Ching-Shui Cheng is currently a Distinguished Research Fellow and Director of the Institute of Statistical Science, Academia Sinica, in Taiwan, and a retired professor from the University of California, Berkeley. He received his B.S. in mathematics from National Tsing Hua University and both his MS in mathematics and Ph.D. in mathematics from Cornell University. After receiving his Ph.D., he became an assistant professor in the Department of Statistics at the University of California, Berkeley. He was later promoted to associate professor and then professor. He retired on July 1, 2013.
Dr. Cheng’s research interest is mainly in experimental design and related combinatorial problems. He is a fellow of the Institute of Mathematical Statistics and the American Statistical Association and an elected member of the International Statistical Institute. He was an associate editor of the Journal of Statistical Planning and Inference, Annals of Statistics, Statistica Sinica, Biometrika, and Technometrics. He also served as the chair-editor of Statistica Sinica from 1996 to 1999.

Summary

Bringing together both new and old results, Theory of Factorial Design: Single- and Multi-Stratum Experiments provides a rigorous, systematic, and up-to-date treatment of the theoretical aspects of factorial design. To prepare readers for a general theory, the author first presents a unified treatment of several simple designs, including completely randomized designs, block designs, and row-column designs. As such, the book is accessible to readers with minimal exposure to experimental design. With exercises and numerous examples, it is suitable as a reference for researchers and as a textbook for advanced graduate students.

In addition to traditional topics and a thorough discussion of the popular minimum aberration criterion, the book covers many topics and new results not found in existing books. These include results on the structures of two-level resolution IV designs, methods for constructing such designs beyond the familiar foldover method, the extension of minimum aberration to nonregular designs, the equivalence of generalized minimum aberration and minimum moment aberration, a Bayesian approach, and some results on nonregular designs. The book also presents a theory that provides a unifying framework for the design and analysis of factorial experiments with multiple strata (error terms) arising from complicated structures of the experimental units. This theory can be systematically applied to various structures of experimental units instead of treating each on a case-by-case basis.

Additional text

"The field of experimental design aims to help practitioners collect their data in a more efficient manner, or more specifically, run their experiments more effectively. There are many good textbooks in this area: the classical ones of the early 50’s (e.g.,Cochran and Cox 1957) focused more on agricultural experimentation; the later ones of the late 70’s (e.g., Box, Hunter, and Hunter 1978) focused more on industrial experimentation, and the recent ones (e.g., Santner, Williams, and Notz 2003; Fang, Li, and Sudjianto 2006) focused more on computer experiments. There are also some theoretical approaches, notably on optimal design (e.g., Pukelsheim 1993) and combinatorics (e.g., Street and Street 1987). This book is clearly one of the very first about design of experiment from a multi-stratum approach… Some topics have never appeared in any other book and the author has produced elegant mathematics accompanied with lucid explanations…I believe that this excellent book will soon become a must read for researchers and educators in experimental design. It could serve as a great reference or textbook for a high-level design course."—Dennis Lin, Penn State University, in Journal of the American Statistical Association, Volume 111, 2016
"… the book is extremely well written. It is a book on design theory authored by a well-known researcher in the field. As is pointed out by the author, the book provides an elegant and general theory, which once understood is simple to use and can be applied to various structures of experimental units in a unified and systematic way. The book is certainly a necessary reference for Technometrics readers who have an interest in the theory of factorial designs for single- and multi-stratum experiments."—Technometrics, May 2015
"This is a great book on factorial designs, both for academic statisticians and for practitioners. … The style of the presentation, based on the discussion of a large number of real-life examples, supports the overall clarity and readability of the text. … many chapters also contain some interesting topics usually not reported in books. In particular, I would like to mention the construction of two-level resolution IV designs in Chapter 11."—Zentralblatt MATH 1306

Product details

• Authors: Ching-Shui Cheng, Ching-Shui (University of California Cheng
• Publisher: Taylor & Francis Ltd.
• Languages: English
• Product format: Hardback
• Released: 21.12.2013
• EAN: 9781466505575
• ISBN: 978-1-4665-0557-5
• No. of pages: 409
• Series: Chapman & Hall/CRC Monographs on Statistics & Applied Probability; Chapman & Hall/CRC Monographs on Statistics & Applied Probability
• Subject: Natural sciences, medicine, IT, technology > Mathematics > Probability theory, stochastic theory, mathematical statistics