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Reliability Modeling with Hidden Markov and semi-Markov Chains

Vlad-Ştefan BARBU

Université de Rouen

France

Abstract: Semi-Markov processes and Markov renewal processes represent a class of stochastic processes that generalize Markov and renewal processes. As it is well known, for a discrete-time (respectively continuous-time) Markov process, the sojourn time in each state is geometrically (respectively exponentially) distributed. In the semi-Markov case, the sojourn time distribution can be any distribution on N* (respectively on R+ ). This is the reason why the semi-Markov approach is much more suitable for applications than the Markov one.

The purpose of our talk is doublefold:

(i) to make a general introduction to semi-Markov processes;

(ii) to investigate some survival analysis and reliability problems for this type of system

We start by briefly introducing the discrete-time semi-Markov framework, giving some basic definitions and results. These results are applied in order to obtain closed forms for some survival or reliability indicators, like survival/reliability function, availability, mean hitting times, etc; we also discuss the particularity of working in discrete time.