"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

• 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

• 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.