Multi-state system reliability. Assessment, optimization and applications.

*(English)*Zbl 1030.90017
Series on Quality, Reliability and Engineering Statistics. 6. River Edge, NJ: World Scientific. xv, 358 p. (2003).

Controlling and improving complex systems is undoubtedly one of the most important tasks of future scientific efforts. Complex systems (here called multi-state systems, MSS) consists of a large number of elements where each element may adopt generally more than two levels of performance implying that the traditional binary reliability models cannot be applied. This book aims at giving a “comprehensive up-to-date presentation of MSS reliability theory”. It wants to “bridge the gap between theoretical advances and practical reliability engineering”.

The first chapter is devoted to the introduction of multi-state systems by defining a generic model and illustrating different types of MSS by means of real technical systems taken from various fields of application. There are various approaches to attack the problems arising in the context of multi-state systems reliability analysis. One approach is based on Boolean methods by trying to extent the analysis of binary systems to multi-state systems. A second approach uses stochastics processes, particularly Markov processes to model the timely development of MSS. A third not so widely known approach is based on a so-called universal generating function. Finally, Monte-Carlo based methods are often used for systems analysis.

Chapter 2 describes the Boolean approach, Chapter 3 the stochastic process approach and finally Chapter 4 the approach based on universal generating functions. The approach using Monte-Carlo methods is omitted as there is no essential difference between its application to binary systems and MSS.

Once an MSS is described by the one or the other method, the task of improving the performance of the system arises which can be achieved by altering its redundancy, by changing the adjustments or the geometric topology of the system, or by improving the elements’ performance. Mathematically, any improvement assumes a suitable optimization algorithm. In the fifth chapter the genetic algorithm is recommended and described in detail as a universally applicable optimization technique. Finally, there are a number of application problems listed and elaborated in Chapter 6.

The book is completed by some concluding remarks about future research.

All theoretical results presented in the chapters are illustrated by means of examples. Moreover, there are exercises and references stated at the end of each chapter.

The first chapter is devoted to the introduction of multi-state systems by defining a generic model and illustrating different types of MSS by means of real technical systems taken from various fields of application. There are various approaches to attack the problems arising in the context of multi-state systems reliability analysis. One approach is based on Boolean methods by trying to extent the analysis of binary systems to multi-state systems. A second approach uses stochastics processes, particularly Markov processes to model the timely development of MSS. A third not so widely known approach is based on a so-called universal generating function. Finally, Monte-Carlo based methods are often used for systems analysis.

Chapter 2 describes the Boolean approach, Chapter 3 the stochastic process approach and finally Chapter 4 the approach based on universal generating functions. The approach using Monte-Carlo methods is omitted as there is no essential difference between its application to binary systems and MSS.

Once an MSS is described by the one or the other method, the task of improving the performance of the system arises which can be achieved by altering its redundancy, by changing the adjustments or the geometric topology of the system, or by improving the elements’ performance. Mathematically, any improvement assumes a suitable optimization algorithm. In the fifth chapter the genetic algorithm is recommended and described in detail as a universally applicable optimization technique. Finally, there are a number of application problems listed and elaborated in Chapter 6.

The book is completed by some concluding remarks about future research.

All theoretical results presented in the chapters are illustrated by means of examples. Moreover, there are exercises and references stated at the end of each chapter.

Reviewer: Elart von Collani (Würzburg)

##### MSC:

90B25 | Reliability, availability, maintenance, inspection in operations research |

90-02 | Research exposition (monographs, survey articles) pertaining to operations research and mathematical programming |

93A30 | Mathematical modelling of systems (MSC2010) |