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. Language: English