| Semi-Markov Processes and Reliability 2001 Edition Contributor(s): Limnios, N. (Author), Oprisan, G. (Author) |
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ISBN: 0817641963 ISBN-13: 9780817641962 Publisher: Birkhauser OUR PRICE: $104.49 Product Type: Hardcover - Other Formats Published: February 2001 Annotation: The theory of stochastic processes, for science and engineering, can be considered as an extension of probability theory allowing modeling of the evolution of systems over time. The modern theory of Markov processes has its origins in the studies of A.A. Markov (1856-1922) on sequences of experiments "connected in a chain" and in the attempts to describe mathematically the physical phenomenon Brownian motion. The theory of stochastic processes entered in a period of intensive development when the idea of Markov property was brought in. This book is a modern overall view of semi-Markov processes and its applications in reliability. It is accessible to readers with a first course in Probability theory (including the basic notions of Markov chain). The text contains many 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. Features: * 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 * Monte Carlo simulation * Applications in reliability and maintenance 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. |
| Additional Information |
| BISAC Categories: - Technology & Engineering | Industrial Engineering - Mathematics | Applied - Mathematics | Probability & Statistics - General |
| Dewey: 006.3 |
| LCCN: 00060866 |
| Series: Statistics for Industry and Technology |
| Physical Information: 0.66" H x 7.25" W x 10.29" (1.27 lbs) 222 pages |
| Descriptions, Reviews, Etc. |
| Publisher Description: 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. |