This volume consists of twenty-four papers selected by the editors from the sixty-one papers presented at the 1st International Conference on Mathemati- cal Methods in Reliability held at the Politehnica University of Bucharest from 16 to 19 September 1997. The papers have been divided into three sections: statistical methods, probabilistic methods, and special techniques and appli- cations. Of course, as with any classification, some papers could be as well assigned to other sections. Problems in reliability are encountered in items in everyday usage. Relia- bility is an important feature of...

At first there was the Markov property. The theory of stochastic processes, which can be considered as an exten- sion of probability theory, allows the modeling of the evolution of systems through the time. It cannot be properly understood just as pure mathemat- ics, separated from the body of experience and examples that have brought it to life. The theory of stochastic processes entered a period of intensive develop- ment, which is not finished yet, when the idea of the Markov property was brought in. Not even a serious study of the renewal processes is possible without using the strong...

This book provides recent results on the stochastic approximation of systems by weak convergence techniques. General and particular schemes of proofs for average, diffusion, and Poisson approximations of stochastic systems are presented, allowing one to simplify complex systems and obtain numerically tractable models. The systems discussed in the book include stochastic additive functionals, dynamical systems, stochastic integral functionals, increment processes and impulsive processes. All these systems are switched by Markov and semi-Markov processes whose phase space is considered in...

Fault tree analysis is an important technique in determining the safety and dependability of complex systems. Fault trees are used as a major tool in the study of system safety as well as in reliability and availability studies. The basic methods - construction, logical analysis, probability evaluation and influence study - are described in this book. The following extensions of fault trees; non-coherent fault trees, fault trees with delay and multi-performance fault trees are explained. Classic algorithms for fault tree analysis are presented, as well as more recent algorithms based on...

Reliability and survival analysis are important applications of stochastic mathematics (probability, statistics, and stochastic processes) that are usually covered separately in spite of the similarity of the involved mathematical theory. This title aims to redress this situation.

William Q. Meeker has made pioneering and phenomenal contributions to the general areaofreliabilityand, inparticular, tothetopicsofdegradationandacceleratedtesting. Hisresearchpublicationsandthenumerouscitationshehasreceivedoverthepastthree decades provide an ample testimony to this fact. Statistical methods have become critical in analyzing reliability and survival data. Highly reliable products have necessitated the development of accelerated testing and degradation models and their analyses. This volume has been put together in order to (i) review some of the recent advances on accelerated...

This volume focuses on the latest statistical methods used to estimate the performance measures of reliability systems that operate under different conditions. It includes numerous techniques such as nonparametric estimation and lifetime regression analysis.

This volume consists of twenty-four papers selected by the editors from the sixty-one papers presented at the 1st International Conference on Mathemati- cal Methods in Reliability held at the Politehnica University of Bucharest from 16 to 19 September 1997. The papers have been divided into three sections: statistical methods, probabilistic methods, and special techniques and appli- cations. Of course, as with any classification, some papers could be as well assigned to other sections. Problems in reliability are encountered in items in everyday usage. Relia- bility is an important feature of...

This book presents a selection of papers presented to the Second Inter national Symposium on Semi-Markov Models: Theory and Applications held in Compiegne (France) in December 1998. This international meeting had the same aim as the first one held in Brussels in 1984: to make, fourteen years later, the state of the art in the field of semi-Markov processes and their applications, bring together researchers in this field and also to stimulate fruitful discussions. The set of the subjects of the papers presented in Compiegne has a lot of similarities with the preceding Symposium; this shows...