Edited by Connie M. Borror

Chance Encountersby Christopher J. Wilder and George A. F. Seber — Lloyd S. Nelson

Linear Models: A Mean Model Approach

by Barry Kurt Moser — Charles W. Champ

Multivariate Quality Control: Theory and Applications

by Camil Fuchs and Ron S. Kenett — Steven E. Rigdon

Statistical Quality Assurance Methods for Engineers

by S. B. Vardeman and J. M. Jobe —Marvin M. Kilgo, III

**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:

- What is Statistics
- Tools for Exploring Univariate Data
- Exploratory Tools for Relationships
- Probabilities and Proportions
- Discrete Random Variables
- Continuous Random Variables
- Sampling Distributions of Estimates
- Confidence Intervals
- Significance Testing: Using Data to Test Hypotheses
- Data on a Continuous Variable
- Tables of Counts
- Relationships between Quantitative Variables: Regression and Correlation.

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 interesting—and 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
data—employing case studies and MINITAB^{TM}computer
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:

- Quality Control with Multivariate Data
- The Multivariate Normal Distribution in Quality Control
- Quality Control with Externally Assigned Targets
- Quality Control with Internal Targets—Multivariate Process Capability Studies
- Quality Control with Targets from a Reference Sample
- Analyzing Data with Multivariate Control Charts
- Detection of Out-of-Control Characteristics
- The Statistical Tolerance Regions Approach
- Multivariate Quality Control with Units in Batches
- Applications of Principal Components
- Additional Graphical Techniques for Multivariate Quality Control
- Implementing Multivariate Quality Control

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

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:

- Phase I, n = 1
- Phase I, n > 1
- Phase II, n = 1
- Phase II, n > 1

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. 800–810.

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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