Reliability modeling with hidden Markov and semi-Markov chains

Abstract

Abstract form only given. 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 basicdefinitions and results. These results are applied in order to obtain closed forms for some survival orreliability indicators, like survival/reliability function, availability, mean hitting times, etc; we alsodiscuss the particularity of working in discrete time.