Statistical Reasoning and Methods

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  • This article was downloaded by: [West Virginia University]On: 15 October 2014, At: 20:45Publisher: Taylor & FrancisInforma Ltd Registered in England and Wales Registered Number: 1072954 Registered office: MortimerHouse, 37-41 Mortimer Street, London W1T 3JH, UK

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    Statistical Reasoning and MethodsRobert A. Lordo aa BattellePublished online: 12 Mar 2012.

    To cite this article: Robert A. Lordo (1999) Statistical Reasoning and Methods, Technometrics, 41:3, 269-270

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    in this collection point up another interesting phenomenon: Not too far beyond the basics, the landscape gets tortuous very quickly. This means that it usually requires a great deal of work (detail? cleverness?) to create a model that applies to a messy real situation, and the results are rarely transferable to other situations without extensive revision. I could cite as examples any of the papers that deal with analysis of real held reliabil- ity data and that try to account for such phenomena as random environ- ments, missing data, or other such wrinkles that the basic models do not include.

    Please do not think that all of the preceding is a negative review of the book. It is not. It is just that the book is another example of how the ap- plied statisticians job is challenging and interesting along the dimension of adapting someone elses results for a novel analysis. That said, I want to tell you about some of my favorite papers in this collection. Gasmi and Kahles paper, despite its misleading title, is a good description of a gen- eral repair model for maintained systems. It includes both modeling and parameter estimation in a few short pages. Fergers paper covers a very important idea in statistical process control (SPC)-namely, determination of whether there has been a change in process characteristics, and, if so, at what time? Gob develops a general model of production processes that re- quire the application of both SPC and engineering process control (EPC). Along the way, it presents a concise review of SPC and EPC and their use together. Wendts paper covers a basic model for the reliability of a unit suffering shocks with accumulating damage. The Heiligers and Ruf paper provides a new model for returns incorporating both failures and returns mandated by new recycling laws. I was also drawn to the papers in the network analysis section, perhaps because that is where my responsibili- ties are heading currently. You will certainly have other favorites. I found little that I thought was inappropriate for inclusion under the stated head- ing, and that is probably due more to my ignorance than to the editors error.

    Birkhauser has done a good job with the production. The paper is acid- free, typos are few and far between, and the mathematical typesetting, tables, and figures are mostly attractively done (although there are a few in-line mathematical expressions that look squeezed). Some of the notation is unusual and explained (e.g., p. 300) and some of it is unusual and not explained (e.g., p. 4). Some of the references are obscure. For example, reference 8 on page 75 is to Bericht 95/l 1 without any clues as to whose report series this is.

    If you are a specialist in any of the fields covered here, there is much here to interest you. If you are an applied statistician looking for that certain result that will help you analyze that reliability dataset, you might find some ideas here on how to create your own solution, but the chances that you will find that solution already crafted here are slim. If you are a student, mastering the concepts in these papers is great exercise, and when you are done you will have a better foundation than you can get from most textbooks-but you will probably need some help. If you are an engineer, despite the promise of the Preface, this book is rough going unless you are also mathematically sophisticated.

    Michael TORTORELLA Bell Laboratories

    Mathematical Theory of Reliability of Time Depen- dent Systems With Practical Applications, by Igor N. KOVALENKO, Nickolaj Yu. KUZNETSOY, and Philip A. PEGG, Chichester, U.K.: Wiley, 1997, ISBN O-471- 95060-2, ix + 303 pp., $79.95.

    The authors have set out to write a book on the mathematical theory of reliability. They have done an excellent job of achieving that objective with an approach that uses applied probability and stochastic processes. The issues of statistical inference are left to other books. Its lack of problems or exercises at the end of chapters may hinder its use as a textbook; however, it has an excellent set of references and will be a valuable addition to the shelves of those researchers interested in the mathematical theory. Some graduate training in stochastic processes would be advisable for optimal use of this book.

    Chapter 1 is a basic introduction to the mathematical theory covering the basic context and definitions, coherent structure functions, reliability, failure rates, and other things that might constitute the first few chapters in some other books.

    Chapters 2 and 3 make substantial use of stochastic processes. Chapter 2 is a presentation of the notions of a Markov and a semi-Markov process.

    Some applications to reliability and queuing theory are made. A separate section treats important special cases such as birth and death processes and alternating renewal processes. Chapter 3 is devoted to homogeneous and nonhomogeneous point processes with an indication to the way in which reliability theorists can use this material.

    Chapters 4. 5, and 6 discuss topics that are commonly treated in reliabil- ity books. Chapter 4 is devoted to fault-tree analysis and its current state of research. Chapter 5 treats the theory of redundant systems and makes extensive and interesting use of queuing-theory techniques. Chapter 6 dis- cusses Monte Carlo methods; random-variable generation and the model- ing of nonhomogeneous Poisson processes and continuous-time Markov chains are some of the topics.

    Chapter 7 presents a discussion of perturbation methods with sections on Markov reliability models, phase-type and matrix-exponential approx- imations, and infinitesimal perturbation analysis. Chapter 8 is devoted to stiff processes. Various variance reduction methods are presented in Chap- ter 9, and Chapter 10 covers the rapid simulation of repairable systems. The final chapter is devoted to a study of several measures of component importance that have been introduced over the years.

    Overall, this book is geared toward the researcher in the mathematical theory rather than the statistical theory of reliability and succeeds nicely in accomplishing its intent.

    William S. GRIFFITH University of Kentucky

    Statistical Reasoning and Methods, by Richard A. JOHNSON and Kam-Wah TSUI, New York: Wiley, 1998. xiv + 589 pp., $75.95.

    The title for this book well represents the approach taken throughout. Although much of this book presents the same basic statistical methods as do many other books that are currently used in elementary statistics courses, it places considerable emphasis on statistical reasoning and how the concepts apply to everyday life or occupational situations. Although many students can learn statistical methods well enough to score highly on homework and examinations, they may fail to fully understand how to apply these methods appropriately to real-world problems. This book takes a large step in bridging this gap by introducing concepts and methods, then encouraging the student to reason how to apply the methods to solve a problem.

    This book contains 12 chapters that, according to the authors. can be covered in a one-quarter or one-semester elementary statistics course. An instructor wishing to cover certain issues in detail, however, will likely need two courses in which to cover the entire book. Many useful fea- tures exist within each chapter to broaden the students understanding. For example, the first page of each chapter contains a list of chapter ob- jectives that the student can revisit after completing the chapter to de- termine whether each objective is understood and can be accomplished. Statistical Reasoning blocks are extended examples of how to apply a specific method to a particular topic. For example, within a chapter on linear regression, the authors discuss how to select variables that can most accurately predict the amount of time one has to wait in line at a grocery store. Similarly, a brief illustration of how bias can enter into a survey through how questions are worded is included in the section on analyzing categorical data. Sections titled Using a Computer show how to ap- ply methods on a computer, with examples of Minitab code. Key Ideas and Formulas are occasional quick reviews of definitions and formulas that were introduced earlier in the chapter. Perhaps of most long-term benefit to the student, ideas for student projects are given to reinforce the understanding of concepts covered in the chapter and to allow the student to experience how these concepts would be applied in the real world. These special features add to the overall value of this book to the student.

    The chapters are grouped according to five specific statistical concepts. Chapters l-3 emphasize the need for statistics and sampling. how to de- sign a sampling process and collect data. how to portray the data graph- ically, and how to measure the central tendency and variance of a data distribution. Chapters 4-7 introduce the concept of statistical inference by presenting mathematical probability, discrete and continuous distributions, and the role of normal distributional assumptions and how to test that these assumptions hold. Chapters 8-10 focus on statistical inference on the mean and variance of a distribution by introducing hypothesis testing, point estimation, and confidence intervals and how to properly interpret





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    these concepts. The discussion can get quite technical because such issues as statistical power (within the notion of selecting sample size) and Type I and II errors are addressed. Inferences on proportions are discussed in Chapter 1 I. Finally, Chapter 12 introduces simple linear regression, in- cluding inference on predicted values and diagnostic checks such as tests on residuals. Statistical formulas, tables of random digits and common distributions, data used in examples through the text, and answers to se- lected exercises are included in appendixes. Although not available for review, the authors also offer an instructors manual, a test bank of ad- ditional exercises (available in hard copy and PC format), and large exam- ple datasets in ASCII format (which can be obtained from the publishers website).

    Due to its considerable mathematical content, much of this book may not be appropriate for use in basic statistics courses that minimize the technical nature of the subject. For example, the chapter entitled Normal Distributions (an inaccurate title because it addresses continuous data dis- tributions as well as the standard normal distribution) discusses probability density functions, area under the curve, and the central limit theorem in a mathematical context but without specific references to calculus. The book uses formulas and mathematical notation quite liberally for an ele- mentary textbook, but includes an appendix on summation notation to as- sist students who are uncomfortable with such notation. Despite the books technical approach, definitions are often basic and nontechnical (e.g., a discrete variable takes values that are distinct numbers with gaps between them.). This book would be excellent for students entering into scientific disciplines such as engineering.

    This book is sure to challenge the student in a first statistics course with its mathematical approach and the technical subject matter that the book occasionally tackles. Throughout the book, however, the student is encouraged to apply statistical reasoning to situations that are encountered in everyday life, such as current issues addressed by the news media. This is a much-welcomed approach that makes this book highly recommended for todays statistics instructor and a useful reference for the industrial statistician.

    Robert A. LORDO Battelle

    Introductory Statistics and Random Phenomena, by Manfred DENKER and Wojbor A. WOYCZYNSKI, Boston: Birkhauser, 1998, ISBN o-8176-4031-2, xxiv + SO9 pp., $65.

    This is an innovative book, fitting well the authors claim that the books novelty is integration of ideas about statistics of random phenom- ena stemming from three distinct viewpoints: algorithmic/computational complexity, classical probability theory, and chaotic behavior in nonlin- ear systems (p. xv). Indeed, the topics covered in this book range from the basics of mathematical statistics through Kolmogorovian randomness to dynamical systems; the latter two topics are rarely seen in common statistical textbooks. Two additional features include annotated biblio- graphic notes at the end of each chapter and, in almost every section, well-constructed computer exercises with a bundled easily used software package Mathematics@ Uncertain Virtual WorldsT. The computer simulation...


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