Graphs and algoebra of words

摘要

An exponential approximation to estimate the reliability of large repairable systems, modeled by Markov-graph, was proposed a few years ago by J-L.Bon and J.Collec [1]. This approximation requires the computation of some sojourn times and the asymptotic probability of going from the perfect-operation state to the system-failure state. In order to compute this probability, an algorithm called SRI (french acronym for Sequences sans Retour vers l'etat Initial), suitable for semi-Markov Processes, was developed. The algorithm presents the particularity of exploring the Markov-graph sequences without exploring circuits but the computations take these circuits into account with asymptotic probabilites. This paper presents a generalisation of this algorithm in an algebraic context using Automata theory conepts.