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Reviewer: Anthony Joseph Duben

Abrupt changes are a normal part of everyday life. In manufacturing, the sudden addition of a component to a mixture suddenly changes the composition of the system, and the control system needs to recognize the change and behave accordingly. Undetected changes in navigational systems can cause disasters. Vibrations in a mechanical device or structure can lead to sudden failures. The publisher states that this book is the first to address the topic of detecting abrupt changes in systems. The book is organized in three parts after a preface and introduction. The introduction states the book's goals and organization; techniques the authors will use in the remainder of the book; and five examples from different areas as motivation. The book emphasizes online detection. The authors use parametric statistical tools throughout. The first part of the book covers the theory behind detecting changes in a system that can be described by a single scalar parameter. Chapter 2 discusses the problem of designing online change detection algorithms, assuming that the parameter is known before the change occurs. The cumulative sum (CUSUM) and generalized likelihood ratio (GLR) algorithms are first presented in this chapter. These two algorithms are central to the discussion in the remainder of the book and appear in all the subsequent chapters. Chapter 3 is a summary of probability and system theory. More notation is presented, and definitions and theorems are presented without proof. The purpose of this chapter is not to teach probability theory, but to remind the reader of the important facts that he or she needs to know and apply in subsequent chapters, especially the concept of conditional probability. The fourth chapter gives statistical background. Like chapter 3, it restates important points without giving proof or extensive development. Statistical inference and hypothesis testing are emphasized. Since parametric statistical techniques constitute the approach used in the book, criteria for detecting changes are developed. The average run length (ARL) function is presented. It is applied throughout the rest of the book. Chapter 5 discusses the properties of online algorithms for single-parameter systems. This chapter depends heavily on the two preceding ones. The ARL function is developed more fully. Part 2 broadens the perspective to complex changes in which processes are characterized by multidimensional parameters. For complex systems, there are two kinds of problems—additive changes (such as changes in mean) and nonadditive changes (such as changes in variance). The distinct characters of the two kinds of problems are established in chapter 6 by using models and techniques developed in Part 1. Chapter 7 discusses additive changes by studying four models. Both the CUSUM and GLR algorithms are applied extensively. Nonadditive changes in scalar signals are discussed in chapter 8. Again, the authors select four models for study, and the CUSUM and GLR algorithms are the tools of choice. A new statistic—efficient score—is created for nonadditive signals based on the statistical notes in chapter 4. Chapter 9 extends the analysis of nonadditive changes to multidimensional systems. Again, the CUSUM and GLR algorithms are prominent. Questions of detectability are discussed. Part 3 is on tuning the algorithms and applications. Chapter 10 discusses implementation and tuning. A unified methodology based on the ARL function and the CUSUM and GLR algorithms is presented in order to achieve robustness. Chapter 11 revisits examples from the first chapter and conjectures on the applicability of the techniques in additional problem areas. The book is well organized. Although it may appear to be organized like a textbook, it is not a text. It is a resource book. Each of the three parts begins with an introductory chapter that is both an overview of the problems to be addressed and a preview of the remaining chapters in the part. Each chapter begins with a statement of its goals and the tools to be developed and applied, and ends with a list of notes and references and a summary of important mathematical formulas. The references also appear in a 20-page bibliography at the end of the book. Those who may be interested in this book should note that it is very formal and theoretical. Numerical examples and computer routines are absent. A researcher or engineer needing to detect abrupt changes would profit from studying this book, however.