N. Limnios - Böcker

Presents thirty-one chapters that provide a survey of models and methods for reliability analysis and applications in science, engineering, and technology. This book contains coverage of the developments and innovative techniques in a range of theoretical and numerical issues in the field of statistical and probabilistic methods in reliability.

This work provides an overview of semi-Markov processes and their applications in reliability. It contains examples which aid in the understanding of the theoretical notions and shows how to apply them to concrete physical situations including algorithmic simulations. Many examples of the concrete applications in reliability are given. The topics covered in the book include: processes associated to semi-Markov kernel for general and discrete state spaces; asymptotic theory of processes and of additive functionals; statistical estimation of semi-Markov kernel and of reliability function; and Monte Carlo simulation.

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 tool of Markov processes. The modern theory of Markov processes has its origins in the studies by A. A: Markov (1856-1922) of sequences of experiments "connected in a chain" and in the attempts to describe mathematically the physical phenomenon known as Brownian mo­ tion. Later, many generalizations (in fact all kinds of weakenings of the Markov property) of Markov type stochastic processes were proposed. Some of them have led to new classes of stochastic processes and useful applications. Let us mention some of them: systems with complete connections [90, 91, 45, 86]; K-dependent Markov processes [44]; semi-Markov processes, and so forth. The semi-Markov processes generalize the renewal processes as well as the Markov jump processes and have numerous applications, especially in relia­ bility.