Semi-Markov Processes and Reliability

ISBN-13: 9780817641962 / Angielski / Twarda / 2001 / 222 str.

Nikolaos Limnios; N. Limnios; G. Oprisan

Opis

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.

Recenzje

"The book presents an introductory and at the same time rather comprehensive treatment of semi-Markov processes and their applications to reliability theory. It also provides some general background (like measure theory, Markov processes and Laplace transform), which makes it accessible to a broader audience.... The book may be a useful tool for researchers and students interested in the theory of semi-Markov processes or its applications to reliability problems."

-Applications of Mathematics

Spis treści

(FULL TOC ATTACHED)1. Introduction and Renewal Process; 2. Markov Renewal Process, 3. Semi-Markov Process; 4. Countable State Space SMP; 5. Reliability of Semi-Markov Systems; 6 Examples of Reliability Evaluation; A. Measures and Probability; B. Laplace-Stieltjes Transform; c. Weak Convregence

O autorze

The book is a valuable resource for understanding the latest developments in Semi-Markov Processes and reliability. Practitioners, researchers and professionals in applied mathematics, control and engineering who work in areas of reliability, lifetime data analysis, statistics, probability, and engineering will find this book an up-to-date overview of the field.