*System Reliability Theory* by Arnljot Høyland and Marvin Rausand

The first edition of

*System Reliability Theory: Models and Statistics Methods*, by Arnljot Høyland and Marvin Rausand was published in 1994. We present here an extract from the Preface together with extracts from some reviews of this work. We also present an extract from a review of the second edition which was published in 2004 after the death of Arnljot Høyland.**1. Preface.**

The main purpose of this book is to present a comprehensive introduction to system reliability theory. We have structured our presentation such that the book may be used as a text in introductory as well as graduate level courses. For this purpose we treat simple situations first. Then we proceed to more complicated situations requiring advanced analytical tools.

At the same time the book has been developed as a reference and handbook for industrial statisticians and reliability engineers.

The reader ought to have some knowledge of calculus and of elementary probability theory and statistics.

In the first five chapters we confine ourselves to situations where the state variables of components and systems are binary and independent. Failure models, qualitative system analysis, and reliability importance are discussed. These chapters constitute an elementary, though comprehensive introduction

The remaining part of the book is somewhat more advanced and may serve as a text for a graduate course. In Chapter 6 situations where the components and systems may be in two or more states are discussed. This situation is modelled by Markov processes. Renewal theory is treated in Chapter 7, and dependent failures in Chapter 8. A rather broad introduction to life data analysis is given in Chapter 9, accelerated life testing in Chapter 10, and Bayesian reliability analysis in Chapter 11. The book concludes with information about reliability data sources in Chapter 12.

The book contains a large number of worked examples, and each chapter ends with a selection of problems, providing exercises and additional applications.

A forerunner of this book, written in Norwegian by professor Arne T Holen and the present authors, appeared in 1983 as an elementary introduction to reliability analysis. It was published by TAPIR and reprinted in 1988. However, we have rewritten all the chapters of the earlier book and added new material as well as several new chapters. The present book contains approximately twice as many pages as its forerunner and can be considered as a completely new book.

We have already tried much of the material in the present book in courses on reliability and risk analysis at the university level in Norway and Sweden, including continuing education courses for engineers working in industry. The feedback from participants in these courses has significantly improved the quality of the book.

At the same time the book has been developed as a reference and handbook for industrial statisticians and reliability engineers.

The reader ought to have some knowledge of calculus and of elementary probability theory and statistics.

In the first five chapters we confine ourselves to situations where the state variables of components and systems are binary and independent. Failure models, qualitative system analysis, and reliability importance are discussed. These chapters constitute an elementary, though comprehensive introduction

**to**reliability theory. They may be covered in a one-semester course with three weekly lectures over fourteen weeks.The remaining part of the book is somewhat more advanced and may serve as a text for a graduate course. In Chapter 6 situations where the components and systems may be in two or more states are discussed. This situation is modelled by Markov processes. Renewal theory is treated in Chapter 7, and dependent failures in Chapter 8. A rather broad introduction to life data analysis is given in Chapter 9, accelerated life testing in Chapter 10, and Bayesian reliability analysis in Chapter 11. The book concludes with information about reliability data sources in Chapter 12.

The book contains a large number of worked examples, and each chapter ends with a selection of problems, providing exercises and additional applications.

A forerunner of this book, written in Norwegian by professor Arne T Holen and the present authors, appeared in 1983 as an elementary introduction to reliability analysis. It was published by TAPIR and reprinted in 1988. However, we have rewritten all the chapters of the earlier book and added new material as well as several new chapters. The present book contains approximately twice as many pages as its forerunner and can be considered as a completely new book.

We have already tried much of the material in the present book in courses on reliability and risk analysis at the university level in Norway and Sweden, including continuing education courses for engineers working in industry. The feedback from participants in these courses has significantly improved the quality of the book.

*Trondheim 1993***2. Review by: William Q Meeker.**

*SIAM Review*

**38**(1) (1996), 175-177.

During the quality revolution of the 1980s, there was widespresd implementation of statistical process monitoring and design of experiments for the purpose of improving the quality of manufactured products. These activities have had a positive effect on product reliability. Now, however, manufacturers have begun to focus more on implementing particular methods to improve product reliability. Høyland and Rausand provide timely, comprehensive treatment of the modern theory of system reliability. The ideas and method presented in the book will be important to practicing professionals as well as to students and others wanting an introduction to this interesting subject.

I enjoyed reading the book. I quickly gained an appreciation for the combination of practical and technical knowledge exhibited in the writing. New ideas are always motivated by clear real or realistic examples. The development is orderly and the writing style is clear and concise. Each chapter concludes with a number of interesting real/realistic problems that allow the reader to apply and explore the ideas that were developed in the chapter.

Most of the book deals with advanced probability models for reliability. The authors do, however, provide some coverage of analysis of reliability data. The mathematical level is higher than the standard engineering-oriented textbooks on the same subject. Readers without a strong calculus-based course in probability will have to struggle through some of the technical developments. Mathematical tools like matrix algebra, Laplace transform, and limiting arguments are used throughout. Høyland and Rausand cover all of the standard topics that one would expect to find in a book on system reliability. The book, however, is considerably broader than previous books in the area.

I enjoyed reading the book. I quickly gained an appreciation for the combination of practical and technical knowledge exhibited in the writing. New ideas are always motivated by clear real or realistic examples. The development is orderly and the writing style is clear and concise. Each chapter concludes with a number of interesting real/realistic problems that allow the reader to apply and explore the ideas that were developed in the chapter.

Most of the book deals with advanced probability models for reliability. The authors do, however, provide some coverage of analysis of reliability data. The mathematical level is higher than the standard engineering-oriented textbooks on the same subject. Readers without a strong calculus-based course in probability will have to struggle through some of the technical developments. Mathematical tools like matrix algebra, Laplace transform, and limiting arguments are used throughout. Høyland and Rausand cover all of the standard topics that one would expect to find in a book on system reliability. The book, however, is considerably broader than previous books in the area.

**3. Review by: Frank M Guess.**

*Journal of the American Statistical Association*

**91**(433) (1996), 436.

A key strength of this book lies in its having been well "wear-tested" by end users: students and practicing engineers. The authors write, "We have already tried much of the material in the present book in courses on reliability and risk analysis at the university level in Norway and Sweden, including continuing education courses for engineers working in industry. The feedback from participants in these courses has significantly improved the quality of the book."- A noble ancestor of this text was written in Norwegian by the two authors and Professor Arne Holen (appeared in 1983 and reprinted 1988). Høyland and Rausand (1994) commented, "We have rewritten all the chapters of the earlier book and added new material as well as several new chapters. The present book contains approximately twice as many pages as its forerunner." English readers will benefit by the ready accessibility of this new book. Reliability has grown greatly over the years in terms of applied methods, importance for industry and consumers, software tools for assessing and improving products, and the explosion of research papers in various journals. Some students earn a separate doctoral degree in reliability engineering (note, for example, the program at the University of Maryland and its extensive courses in reliability). This book clearly will not be able to cover the full scope of reliability. As the title implies, it focuses on the theory of system (and component) reliability, leaving, for example, structural reliability, software reliability, and human reliability to other tomes.

**4. Review by: Mark G Vangel.**

*Technometrics*

**38**(1) (1996), 79-80.

System reliability is obviously an important topic in applied statistics, and yet there are too few up-to-date books in this area that recognize the needs of practitioners without unduly sacrificing clarity and accuracy of the mathematics. In my opinion, this is one such book. The authors intend it to be a comprehensive introduction, suitable for use both as a handbook and as an elementary or graduate textbook for industrial statisticians or reliability engineers. The stated prerequisites are calculus, elementary probability theory, and statistics; in addition, I would suggest at least a co-requisite course in elementary stochastic processes, particularly if the material on Markov models or repairable systems is to be covered. This book is indeed comprehensive. A wide range of topics in system reliability are discussed in detail, and several peripheral areas are introduced, though perhaps too briefly. A notable feature is the wide range of worked examples and problems, many of them concerned with applications. Moreover, although the bibliography is of modest length, it includes many recent references. The mathematical level is intermediate, appropriate for a graduate-level statistics course but perhaps too mathematical for many engineers and reliability practitioners. Parts of the book are less technical than others, though, and the authors have put most of the less technical and simpler material at the beginnings of the chapters, which should help the reader less well prepared in mathematics. With its broad scope, many examples, and good bibliography, this book is particularly valuable as a reference. ... In conclusion, this book provides a valuable reference to practitioners and researchers in system reliability, as well as a good textbook for a graduate course on this topic. The exposition is clear, the coverage is comprehensive, and a serious attempt has been made to provide discussion.

**5. Review by: Eric R Ziegel.**

*Technometrics*

**46**(4) (2004), 495.

Here is the second edition of a book that received solid support for its excellence from the reviewer of the first edition, Vangel (1996). That review, which was replete with complimentary statements, concluded that the book "provides a valuable reference to practitioners and researchers in system reliability, as well as a good textbook for a graduate course on this topic. The exposition is clear, the coverage is comprehensive, and a serious attempt has been made to provide discussion, examples, and problems useful to engineers, while maintaining mathematical rigour." Appearing after 10 years in its second edition, the book is claimed by the authors to have had a "major upgrade," where "most of the original chapters have been significantly revised." In addition, there are new chapters on the reliability of maintained systems and on the reliability of safety systems. The authors conclude that "the second edition has more focus on the practical application of reliability than the first edition." Vangel (1996) previously commented on "the wide range of worked examples and problems."