Ebook: Semi-Markov Processes and Reliability
Author: N. Limnios G. Oprişan (auth.)
- Tags: Computational Intelligence, Quality Control Reliability Safety and Risk
- Series: Statistics for Industry and Technology
- Year: 2001
- Publisher: Birkhäuser Basel
- Edition: 1
- Language: English
- pdf
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.
Content:
Front Matter....Pages i-xii
Introduction to Stochastic Processes and the Renewal Process....Pages 1-29
Markov Renewal Processes....Pages 31-49
Semi-Markov Processes....Pages 51-83
Countable State Space Markov Renewal and Semi-Markov Processes....Pages 85-120
Reliability of Semi-Markov Systems....Pages 121-151
Examples of Reliability Modeling....Pages 153-176
Back Matter....Pages 177-222
Content:
Front Matter....Pages i-xii
Introduction to Stochastic Processes and the Renewal Process....Pages 1-29
Markov Renewal Processes....Pages 31-49
Semi-Markov Processes....Pages 51-83
Countable State Space Markov Renewal and Semi-Markov Processes....Pages 85-120
Reliability of Semi-Markov Systems....Pages 121-151
Examples of Reliability Modeling....Pages 153-176
Back Matter....Pages 177-222
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