Del i serien Statistics for Industry and Technology

Semi-Markov Processes and Reliability

Inbunden, Engelska, 2001

AvN. Limnios,G. Oprisan

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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.

Produktinformation

Utgivningsdatum2001-02-16
Mått178 x 254 x 17 mm
Vikt576 g
FormatInbunden
SpråkEngelska
SerieStatistics for Industry and Technology
Antal sidor222
Upplaga2001
FörlagBirkhauser Boston Inc
ISBN9780817641962

Tillhör följande kategorier

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.

"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