Author | Limnios, N. author |
---|---|
Title | Semi-Markov Processes and Reliability [electronic resource] / by N. Limnios, G. Opriลan |
Imprint | Boston, MA : Birkhรคuser Boston : Imprint: Birkhรคuser, 2001 |
Connect to | http://dx.doi.org/10.1007/978-1-4612-0161-8 |
Descript | XII, 222 p. online resource |
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 Korolyukโs 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 Fundamental Formulas -- A.4 Examples -- B Laplace-Stieltjes Transform -- C Weak Convergence -- References -- Notation