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## Book Description

Dependability metrics are omnipresent in every engineering field, from simple ones through to more complex measures combining performance and dependability aspects of systems. This book presents the mathematical basis of the analysis of these metrics in the most used framework, Markov models, describing both basic results and specialised techniques. The authors first present both discrete and continuous time Markov chains before focusing on dependability measures, which necessitate the study of Markov chains on a subset of states representing different user satisfaction levels for the modelled system. Topics covered include Markovian state lumping, analysis of sojourns on subset of states of Markov chains, analysis of most dependability metrics, fundamentals of performability analysis, and bounding and simulation techniques designed to evaluate dependability measures. The book is of interest to graduate students and researchers in all areas of engineering where the concepts of lifetime, repair duration, availability, reliability and risk are important.

1. Cover
2. Half-title page
3. Title
5. Contents
6. 1 Introduction
1. 1.1 Preliminary words
2. 1.2 Dependability and performability models
3. 1.3 Considering subsets of the state space
4. 1.4 The contents of this book
7. 2 Discrete-time Markov chains
8. 3 Continuous-time Markov chains
1. 3.1 Definitions and properties
2. 3.2 Transition function matrix
3. 3.3 Backward and forward equations
4. 3.4 Uniformization
5. 3.5 Limiting behavior
6. 3.6 Recurrent and transient states
7. 3.7 Ergodic theorem
8. 3.8 Absorbing Markov chains
9. 4 State aggregation
1. 4.1 State aggregation in irreducible DTMC
2. 4.2 State aggregation in absorbing DTMC
3. 4.3 State aggregation in CTMC
10. 5 Sojourn times in subsets of states
1. 5.1 Successive sojourn times in irreducible DTMC
2. 5.2 Successive sojourn times in irreducible CTMC
3. 5.3 Pseudo-aggregation
4. 5.4 The case of absorbing Markov chains
11. 6 Occupation times of subsets of states – interval availability
12. 7 Linear combination of occupation times – performability
1. 7.1 Backward and forward equations
2. 7.2 Solution
3. 7.3 Examples
4. 7.4 Algorithmic aspects
13. 8 Stationarity detection
1. 8.1 Point availability
2. 8.2 Expected interval availability analysis
3. 8.3 Numerical example
4. 8.4 Extension to performability analysis
5. 8.5 Conclusions
14. 9 Simulation techniques
1. 9.1 The standard Monte Carlo method
2. 9.2 Estimating the MTTF of a multicomponent repairable system
3. 9.3 Estimating the reliability of the system at time t
15. 10 Bounding techniques
1. 10.1 First part: Bounding the mean asymptotic reward
2. 10.2 Second part: Bounding the mean time to absorption
16. References
17. Index