Interval availability analysis using operational periods

Abstract

Consider a repairable computer system alternating periods during which it delivers useful service ( operational periods) with periods in which it is being repared ( unoperational periods). Interval availability is a dependability measure of such a system defined by the fraction of time during which a system is in operation over a finite observation period. In general, to evaluate the interval availability distribution of repairable computer systems analysts use Markov models. In this paper, we first deal with semi-Markov processes and under some conditions we develop a method to compute this distribution. It is based on the analysis of the length of the successive operational and unoperational periods. Particular attention is then devoted to the Markov case leading to a specific algorithm. As a byproduct, we obtain the distribution of the cumulative operational time up to the nth operational period.