Sojourn times in semi-Markov reward processes: application to fault-tolerant systems modeling

Abstract

The paper considers fault-tolerant systems with operational periods in which the system works, and repair periods in which the system performs a reconfiguration from a recovering point. The aim is to obtain information about the successive operational periods before a fatal breakdown. In order to be able to deal with arbitrary probability distributions for the holding times in each state of the system, it is assumed that the system is modeled by a semi-Markov process. In this paper the distribution of the n th operational period is given. It often happens that the user wants to make a distinction among the operational states in order to get more detailed information. The use of rewards on the model states is then allowed, i.e. the results are presented for semi-Markov reward processes. An example illustrates this work.