Experiments. Planning, analysis, and parameter design optimization.

*(English)*Zbl 0964.62065
Wiley Series in Probability and Mathematical Statistics. New York, NY: Wiley. xxviii, 630 p. (2000).

This book on experimental design is somewhat similar in flavor to the classic book by G.E.P. Box, W.G. Hunter and J.S. Hunter, Statistics for experimenters. An introduction to design, data analysis and model building. (1978, Zbl 0394.62003). However, it includes many of the recent developments in the field of experimental design, such as the concepts of minimum aberration designs, simultaneous location-dispersion modelling, Taguchi’s robust parameter design, and so on. The book appears to be suitable for readers with varying backgrounds – only an introductory course in statistical methods and experimental design is needed for the most part.

The book has thirteen chapters, eight appendices devoted to commonly used statistical tables, an author index and a subject index. Chapter 1 begins with a brief history of the subject of design and discusses some of the basic principles of experimental design – replication, randomization, and blocking. Experimental problems are classified into five broad categories: (1) treatment comparisons, (2) variable screening, (3) response surface exploration, (4) system optimization, and (5) system robustness. A useful systematic approach to planning and conducting experiments is outlined. Basic regression, ANOVA, linear models theory, and residual analysis are reviewed.

Chapter 2 is primarily an overview of experiments involving more than one treatment factor, block designs, Latin square designs, Greco-Latin square designs, two-way and multiway layouts, and balanced incomplete block designs. Analysis of covariance and data transformation techniques are also discussed. Chapter 3 is devoted to full \(2^k\)-factorial experiments. Factorial effects are defined and inference problems for estimating location as well as dispersion effects are discussed for both replicated and unreplicated experiments. Blocking and confounding in \(2^k\) factorial designs are discussed. The idea of “aberration” of a design is introduced and minimum aberration blocking schemes are discussed. Aside from the usual normal or half-normal plots for assessing the significance of factorial effects in unreplicated experiments, formal tests of effect significance are also discussed along with tests for variance homogeneity.

Two level fractional factorial designs are the topic of Chapter 4. The criteria of resolution and aberration are discussed as is the concept of aliasing and its implications. Methods for resolving ambiguities involving aliased effects are outlined. Blocking for fractional two-level factorial experiments is discussed. Chapter 5 contains a discussion of full and fractional 3-level factorial experiments along with blocking in such experiments. Chapter 6 considers mixed factorial experiments. In particular, designs and analyses for \(2^m 4^n\) and \(2^m 3^n\) experiments are included. Symmetrical and asymmetrical (mixed-levels) orthogonal arrays are introduced and their properties discussed.

Chapter 7 deals with non-regular designs, namely, designs that are not constructed through defining relations among factors. In particular, Plackett-Burman designs are introduced. Additionally, some methods of constructing mixed-level orthogonal arrays are discussed and a collection of commonly used mixed-level orthogonal arrays is provided. Chapter 8 contains a brief discussion of experimental designs involving complex aliasing patterns. Frequentist and Bayesian approaches for extracting useful information from such designs are considered. Supersaturated designs are introduced and methods of analysis are discussed.

Response surface methodology is the subject of Chapter 9. Standard topics such as the first-order and second-order response surface models, curvature checking, method of steepest ascent (descent) and ridge analysis, are included. Some strategies for the analysis of response surface problems involving multiple responses and constraints are presented. Central-composite designs, rotatable designs and Box-Behnken designs are described.

Chapter 10 introduces robust parameter designs, a statistical/engineering methodology for reducing the performance variation of a system (i.e., a product or a process) by choosing the settings of the factors controlling the properties of the system in order to make it less sensitive to uncontrollable variation. Factors are classified into control factors and noise factors, and various strategies are presented for designing experiments to identify the best parameter settings. Taguchi’s signal-to-noise ratio is introduced and its strengths and limitations are pointed out. Chapter 11 deals with parameter design for signal-response systems. Chapter 12 considers experiments for determining and improving the reliability of products. In particular, frequentist and Bayesian approaches for analyzing failure-time data and degradation data are discussed. Experiments with non-normal data are the topic of Chapter 13. Here the class of generalized linear models (GLMs) is introduced. This class includes discrete distributions such as the Poisson and the binomial, and also continuous distributions like the gamma and the inverse Gaussian. Likelihood as well as Bayesian methods of data analysis in such situations are discussed.

At the end of each chapter there is a section titled “Practical summary”, where the main points of the chapter are summarized. Each chapter concludes with an ample collection of problems and exercises. The book is filled with interesting applications and examples. Besides being suitable for use as a text book in a senior undergraduate or a first year graduate course on applied design, the book will also serve as an excellent reference for practicing statisticians, particularly those specializing in the area of quality and productivity.

The book has thirteen chapters, eight appendices devoted to commonly used statistical tables, an author index and a subject index. Chapter 1 begins with a brief history of the subject of design and discusses some of the basic principles of experimental design – replication, randomization, and blocking. Experimental problems are classified into five broad categories: (1) treatment comparisons, (2) variable screening, (3) response surface exploration, (4) system optimization, and (5) system robustness. A useful systematic approach to planning and conducting experiments is outlined. Basic regression, ANOVA, linear models theory, and residual analysis are reviewed.

Chapter 2 is primarily an overview of experiments involving more than one treatment factor, block designs, Latin square designs, Greco-Latin square designs, two-way and multiway layouts, and balanced incomplete block designs. Analysis of covariance and data transformation techniques are also discussed. Chapter 3 is devoted to full \(2^k\)-factorial experiments. Factorial effects are defined and inference problems for estimating location as well as dispersion effects are discussed for both replicated and unreplicated experiments. Blocking and confounding in \(2^k\) factorial designs are discussed. The idea of “aberration” of a design is introduced and minimum aberration blocking schemes are discussed. Aside from the usual normal or half-normal plots for assessing the significance of factorial effects in unreplicated experiments, formal tests of effect significance are also discussed along with tests for variance homogeneity.

Two level fractional factorial designs are the topic of Chapter 4. The criteria of resolution and aberration are discussed as is the concept of aliasing and its implications. Methods for resolving ambiguities involving aliased effects are outlined. Blocking for fractional two-level factorial experiments is discussed. Chapter 5 contains a discussion of full and fractional 3-level factorial experiments along with blocking in such experiments. Chapter 6 considers mixed factorial experiments. In particular, designs and analyses for \(2^m 4^n\) and \(2^m 3^n\) experiments are included. Symmetrical and asymmetrical (mixed-levels) orthogonal arrays are introduced and their properties discussed.

Chapter 7 deals with non-regular designs, namely, designs that are not constructed through defining relations among factors. In particular, Plackett-Burman designs are introduced. Additionally, some methods of constructing mixed-level orthogonal arrays are discussed and a collection of commonly used mixed-level orthogonal arrays is provided. Chapter 8 contains a brief discussion of experimental designs involving complex aliasing patterns. Frequentist and Bayesian approaches for extracting useful information from such designs are considered. Supersaturated designs are introduced and methods of analysis are discussed.

Response surface methodology is the subject of Chapter 9. Standard topics such as the first-order and second-order response surface models, curvature checking, method of steepest ascent (descent) and ridge analysis, are included. Some strategies for the analysis of response surface problems involving multiple responses and constraints are presented. Central-composite designs, rotatable designs and Box-Behnken designs are described.

Chapter 10 introduces robust parameter designs, a statistical/engineering methodology for reducing the performance variation of a system (i.e., a product or a process) by choosing the settings of the factors controlling the properties of the system in order to make it less sensitive to uncontrollable variation. Factors are classified into control factors and noise factors, and various strategies are presented for designing experiments to identify the best parameter settings. Taguchi’s signal-to-noise ratio is introduced and its strengths and limitations are pointed out. Chapter 11 deals with parameter design for signal-response systems. Chapter 12 considers experiments for determining and improving the reliability of products. In particular, frequentist and Bayesian approaches for analyzing failure-time data and degradation data are discussed. Experiments with non-normal data are the topic of Chapter 13. Here the class of generalized linear models (GLMs) is introduced. This class includes discrete distributions such as the Poisson and the binomial, and also continuous distributions like the gamma and the inverse Gaussian. Likelihood as well as Bayesian methods of data analysis in such situations are discussed.

At the end of each chapter there is a section titled “Practical summary”, where the main points of the chapter are summarized. Each chapter concludes with an ample collection of problems and exercises. The book is filled with interesting applications and examples. Besides being suitable for use as a text book in a senior undergraduate or a first year graduate course on applied design, the book will also serve as an excellent reference for practicing statisticians, particularly those specializing in the area of quality and productivity.

Reviewer: Hariharan Iyer (Fort Collins)

##### MSC:

62Kxx | Design of statistical experiments |

62-01 | Introductory exposition (textbooks, tutorial papers, etc.) pertaining to statistics |

62-02 | Research exposition (monographs, survey articles) pertaining to statistics |

62P30 | Applications of statistics in engineering and industry; control charts |