Edited by Connie M. BorrorChance Encounters
Chance Encounters by Christopher J. Wilder and George A. F. Seber. John Wiley and Sons, Inc., New York, NY, 2000. xviii + 611 pp. $86.95.
Reviewer: Lloyd S. Nelson, Statistical Consultant, Londonderry, NH 03053-3647.
The wonderfully general title is cleared up by the following subtitle, "A First Course in Data Analysis and Inference." There are twelve chapters titled as follows:
There are 144 references. An appendix contains the following statistical tables: Random Numbers, Individual Terms of the Binomial Distribution, Sample Sizes for Confidence Intervals for a Proportion, the Standard Normal Distribution, Student´s t, and Chi Square. Instead of an F table the authors utilize computer programs to do analyses of variance.
The book uses many examples taken from a very wide variety of fields. They are so well chosen that the reader´s imagination will be immediately stimulated resulting in a sincere interest in the analyses being illustrated. This is a great feature and leads to a discussion of how this book could be used both in the classroom and for self study.
Instructors would soon see that their job is not to explain but to supplement what is in the book. Class time should be spent enlarging on some of the subjects, answering questions, doing demonstrations, and so forth. It must be made clear that it is the student´s job to learn what the book says about subject A before subject A is discussed in class.
This book is ideally suited for self study. Mastering its contents will provide a decent start in elementary statistics. This is a non-calculus approach, but that doesn't make the fundamental concepts easy. I found the book to be both technically sound and interestingand that's a combination which is hard to beat.
Linear Models: A Mean Model Approach by Barry Kurt Moser. Academic Press, San Diego, CA, 1996. 228 pp. $59.00.
Reviewer: Charles W. Champ, Mathematics and Computer Science, Georgia Southern University, Statesboro, GA 30460-8093.
This is an introductory linear models text intended for "graduate students interested in linear statistical modeling." The "objective of this book is to cover a series of introductory topics that give a student a solid foundation in the study of linear models." The author uses the students´ expected background in mathematical statistics, linear algebra, and normal distribution theory to develop their background in linear regression and design of experiments into a linear models framework.
The first three chapters give reviews of linear algebra, random vectors, multivariate normal theory, and quadratic forms. The material on linear models begins in Chapter 4 with a concentration on the familiar complete, balanced designs. The author believes that "students are generally more comfortable learning structured material." These designs are used to introduce this structure into the material. In later chapters, the author expands his discussion on complete, balanced designs to incomplete, unbalanced, and mixed models.
The chapter and appendix titles are (1) Linear Algebra and Related Introductory Topics; (2) Multivariate Normal Distribuiton; (3) Distributions of Quadratic Forms; (4) Complete, Balanced Factorial Experiments; (5) Least-Squares Regression; (6) Maximum Likelihood Estimation and Related Topics; (7) Unbalanced Designs and Missing Data; (8) Balanced Incomplete Block Designs; (9) Less Than Full Rank Models; (10) The General Mixed Model; (Appendix 1) Computer Output for Chapter 5; (Appendix 2) Computer Output for Chapter 7; (Appendix 3) Computer Output for Chapter 8; (Appendix 4) Computer Output for Chapter 9; (Appendix 5) Computer Output for Chapter 10.
Many of the results are presented as theorems or examples. A few illustrative data examples are given. Various examples are given in the appendices in the form of SAS (Statistical Analysis System) programs and output. Exercises are given at the end of each chapter ranging from six to seventeen with an average of twelve per chapter. The text is well organized and the material is clearly presented.
There appears to be an adequate amount of material for a one semester or one quarter course. No recommendation is given by the author as to how much of the text can be presented in a given semester or quarter. If one is looking for an introductory text that presents a solid introduction to the study of linear models, Moser´s book would be worth considering.
Multivariate Quality Control: Theory and Applications by Camil Fuchs and Ron S. Kenett. Marcel Dekker, New York, NY, 1998, 212 pp. $150.00.
Reviewer: Steven E. Rigdon, Department of Mathematics and Statistics, Southern Illinois University Edwardsville, Edwardsville, IL 62026-1653.
The back cover describes this book as a "solutions-oriented reference [that] provides a sound theoretical foundation as well as practical tools for the effective, efficient analysis of multivariate dataemploying case studies and MINITABTMcomputer macros throughout to illustrate basic and advanced quality control methods." (Emphasis in original.) In the Preface, the authors state "The main objective of the book is to provide a practical introduction to multivariate quality control by focusing on typical quality control problem formulations and by relying on case studies for illustrating the tools. The book is aimed at practitioners and students alike and can be used in regular university courses, in industrial workshops, and as a reference."
As these quotes (and the title) suggest, this is a book about multivariate quality control. Although not explicitly stated, it is assumed that the reader already knows about univariate control charts, such as the Shewhart chart.
The chapter titles are:
Chapter 1 discusses the presence of multivariate data in the control of quality. This first chapter would have been a good place to compare multivariate control charts with multiple univariate control charts, but this was not done; surprisingly, this comparison isn´t made until Chapter 6. Chapter 2 presents a number of properties of the multivariate normal distribution. These range from the basic (e.g., ) to several advanced properties that involve the Wishart distribution (e.g., (n 1)S, where S is the usual unbiased estimate of the covariance matrix, has a Wishart distribution). These properties are just stated; a reader interested in seeing the derivations is referred to a book on multivariate statistics. Chapter 3 deals with the Hotelling T 2 chart with externally assigned targets. Here, the objective of the control chart is to tell whether the process is operating with a given mean vector; the covariance matrix is estimated from the data. Chapters 4 and 5 assume that both the process mean vector and covariance matrix are unknown, and must be estimated from the data. Chapters 3 through 5 make use of the properties of the multivariate normal distribution presented in Chapter 2. Chapters 6 and 7 deal with plotting the T 2 chart and interpreting out-of-control signals that arise from the Hotelling T 2 chart. Chapter 8 presents some results on multivariate tolerance regions for means. These tolerance regions are used in the next chapter to assess the stability of batch processes. Chapter 10 gives a brief explanation of principal components and how they can be used to monitor a multivariate process. Chapter 11 shows some graphical methods to present multivariate data. These include the scatter plot matrix, star plots, and what the authors call MP-charts. The star plot is a plot of Hotelling´s T 2 but the symbol used is a star (actually, more like an asterisk) whose arms have varying lengths, which are proportional to the values of the quality characteristics. The MP chart is similar, but instead of plotting a star, the user plots a small bar chart for the p quality characteristics. I found that these MP charts were helpful in identifying the causes of an out-of-control signal. The last chapter gives some guidance on implementing multivariate control techniques.
Throughout the book, the authors present a number of case studies, including the raw data. Each chapter begins with a statement of objectives and a list of the key concepts. Graphics are usually well done. Macros for MINITAB are given in the appendix.
This is a fairly small book: 212 pages, including the appendices and the index. Of these 212 pages, 18 are blank and 33 contain the code for the MINITAB macros; many of the remaining pages contain data for the case studies. For such a small book the cost ($150) is somewhat high.
I found it somewhat annoying that multiline displayed equations are usually not aligned at the equal sign, but rather each line is centered. I caught eight citations that were not listed in the references section at the end of the book. The authors seem to make no distinction between Phase I (using the data to take a retrospective look at the data to see whether the process was in control during the time that the reference sample was taken) and Phase II (using estimates of the parameters to monitor the process after the reference sample was taken). The terminology (Phase I, Phase II) is unimportant, but the concept is because the control limits are different for the two cases. As Lowry and Montgomery (1995) suggest, we really need to look at four distinct cases:
Here n is the subgroup size. The cases n = 1 and n > 1 must be considered separately because the distributional results for the T 2 statistic are different. This failure to distinguish Phase I from Phase II uses of control charts is a serious omission. The chapter on principal components is only seven pages long, which is too short to adequately address the topic. For these reasons, I find it difficult to recommend this book for students or practitioners.
Given this recommendation, where should one turn to learn about multivariate control charts? Although this book is, as far as I can tell, the only book devoted to just multivariate control charts, many books on statistical quality control contain a section or chapter on multivariate control charts. For example, Montgomery (1997) and Alwan (2000) contain substantial sections and Ryan (1989) contains a full chapter on multivariate methods. The review paper by Lowry and Montgomery (1995) is concise, but thorough. Johnson and Wichern (1998) have a section on multivariate quality control charts in their chapter on inferences about a mean vector, and a section on using principal components to monitor quality in their chapter on principal components. The Johnson and Wichern (1998) book may be the most complete source for learning about multivariate control charts because all the distributional results are given and most are derived.
Alwan, L. C. (2000). Statistical Process Analysis. IrwinMcGraw-Hill, Boston, MA.
Johnson, R. A. and Wichern, D. W. (1998). Applied Multivariate Statistical Analysis, 4th ed. Prentice Hall, Upper Saddle River, NJ.
Lowry, C. L. and Montgomery, D. C. (1995). "A Review of Multivariate Control Charts". IIE Transactions 27, pp. 800810.
Montgomery, D. C. (1997). Introduction to Statistical Quality Control, 3rd ed. John Wiley & Sons, New York, NY.
Ryan, T. P. (1989). Statistical Methods for Quality Improvement. John Wiley & Sons, New York, NY.
Statistical Quality Assurance Methods for Engineers by S. B. Vardeman and J. M. Jobe. John Wiley & Sons, New York, 1999, 559 + xiv pp., $104.95.
Reviewer: Marvin M. Kilgo, III, Tamarack Scientific Company, Inc., Anaheim, CA 92806-2605
Ideally, an introductory text should provide a consistent motivation for pursuing the subject as well as presenting the details of its application. This is particularly true for technical material, where developing facility with new methods is often emphasized at the expense of understanding the framework within which the tools were developed and in which they are applied. Fortunately, the authors of this book have succeeded in addressing both the details and the "big picture" of application of statistical quality control (SQC) tools.
The book is primarily intended as a text for a project oriented course. As a result, it makes extensive use of worked examples and exercises; in fact, end-of-chapter exercises comprise approximately thirty percent of the book! The target audience is upper level undergraduate engineers, and an exposure to introductory statistics and reasonable mathematical maturity is assumed. Supplementary materials and errata are easily accessible on-line.
The tone of the book is reminiscent of Ott (1975), in its emphasis on pragmatic application of the tools being introduced.
The first two chapters provide an overview of the subject and introduce simple process analysis tools such as fishbone diagrams and process flow charting. Issues in data collection are discussed as well, including gauge studies and the use of simple graphics such as histograms and Pareto charts. The third and fourth chapters focus on "Process Monitoring" through the use of control charts. The design of standard Shewhart charts and their interpretation are introduced in Chapter 3, along with a discussion of the use of average run length (ARL) to characterize the performance of a chart. The fourth chapter introduces more advanced techniques such as exponentially weighted moving average (EWMA), CUSUM, and multivariate charts.
An interesting inclusion in Chapter 3 is a section discussing "engineering control," specifically a PID control scheme. The authors stress the complementary nature of engineering control and SPC techniques for process operation. This is a valuable point that is seldom made in introductory SPC texts.
The fifth chapter is entitled "Process characterization and process analysis." Additional graphical techniques such as box plots and Q-Q plots are presented, as are discussions of process capability indices, interval estimation, and propagation of error.
The next two chapters focus on experimental design. The first of these, Chapter 6, provides introductory material, through 2 level factorial designs, while Chapter 7 addresses more advanced topics such as fractional factorials, response surface methods and mixture experiments.
Chapter 8 discusses sampling inspection. Sampling plans for both attributes and variable characteristics are discussed, and Mil Std 105 is introduced. The chapter ends with a discussion of the role of acceptance sampling in practice.
The final chapter is a very brief discussion of the philosophy underlying TQM. This is a useful summary of the context in which the tools presented in the preceding chapters will be implemented.
This book provides a broad introduction to SQC techniques. Although it is primarily intended as an undergraduate textbook, it would be useful to engineers new to the field, and, for example, for preparation for the CQE exam. It also provides a good background from which to approach more advanced books on SPC, acceptance sampling, and design of experiments. Many fine introductory SQC books are available, but this text by Vardeman and Jobe deserves serious consideration for a spot on the bookshelf.
Ott, E. R. (1975). Process Quality Control. McGraw-Hill, New York, NY.
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