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Semi-Markov Processes and Reliability

BuchGebunden
222 Seiten
Englisch
Springererschienen am16.02.2001
Not even a serious study of the renewal processes is possible without using the strong tool of Markov processes. The semi-Markov processes generalize the renewal processes as well as the Markov jump processes and have numerous applications, especially in relia­ bility.mehr
Verfügbare Formate
BuchGebunden
EUR113,50
BuchKartoniert, Paperback
EUR106,99
E-BookPDF1 - PDF WatermarkE-Book
EUR96,29

Produkt

KlappentextNot even a serious study of the renewal processes is possible without using the strong tool of Markov processes. The semi-Markov processes generalize the renewal processes as well as the Markov jump processes and have numerous applications, especially in relia­ bility.
Details
ISBN/GTIN978-0-8176-4196-2
ProduktartBuch
EinbandartGebunden
Verlag
Erscheinungsjahr2001
Erscheinungsdatum16.02.2001
ReiheStatistics for Industry and Technology
Seiten222 Seiten
SpracheEnglisch
Gewicht580 g
IllustrationenXII, 222 p.
Artikel-Nr.11746148

Inhalt/Kritik

Inhaltsverzeichnis
1 Introduction to Stochastic Processes and the Renewal Process.- 1.1 Preliminaries.- 1.2 Stopping Times.- 1.3 Important Families of Stochastic Processes.- 1.4 Renewal Processes.- 1.5 Regenerative Processes.- 2 Markov Renewal Processes.- 2.1 The Semi-Markov Kernel.- 2.2 Processes Associated to a Semi-Markov Kernel.- 2.3 Specification of a Markov Renewal Process.- 2.4 Robustness of Markov Renewal Processes.- 2.5 Korolyuk´s State Space Merging Method.- 3 Semi-Markov Processes.- 3.1 Basic Definitions and Properties.- 3.2 Markov Renewal Equation.- 3.3 Functional of the Semi-Markov Process.- 3.4 Associated Markov Processes.- 3.5 Asymptotic Behavior.- 4 Countable State Space Markov Renewal and Semi-Markov Processes.- 4.1 Definitions.- 4.2 Classification of States.- 4.3 Markov Renewal Equation.- 4.4 Asymptotic Behavior.- 4.5 Finite State Space Semi-Markov Processes.- 4.6 Distance Between Transition Functions.- 4.7 Phase Type Semi-Markov Kernels.- 4.8 Elements of Statistical Estimation.- 5 Reliability of Semi-Markov Systems.- 5.1 Introduction.- 5.2 Basic Definitions.- 5.3 Coherent Systems.- 5.4 Reliability Modeling in the Finite State Space Case.- 5.5 Methods for Obtaining Transition Probabilities.- 5.6 Reliability and Performability Modeling in the General State Space Case.- 6 Examples of Reliability Modeling.- 6.1 Introduction.- 6.2 A Three-State System.- 6.3 A System with Mixed Constant Repair Time.- 6.4 A System with Multiphase Repair.- 6.5 Availability of a Series System.- 6.6 A Maintenance Model.- 6.7 A System with Nonregenerative States.- 6.8 A Two-Component System with Cold Standby.- 6.9 Markov Renewal Shock Models.- 6.10 Stochastic Petri Nets.- 6.11 Monte Carlo Methods.- A Measures and Probability.- A.I Fundamentals.- A.2 Conditional Distributions.- A.3 FundamentalFormulas.- A.4 Examples.- B Laplace-Stieltjes Transform.- C Weak Convergence.- References.- Notation.mehr
Kritik
"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 Mathematicsmehr

Schlagworte

Autor

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.
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Oprisan, G.