A dependability measure for Markov models of repairable systems: Solution by randomization and computational experience

✍ Scribed by A. Csenki

• Publisher: Elsevier Science
• Year: 1995
• Tongue: English
• Weight: 779 KB
• Volume: 30
• Category: Article
• ISSN: 0898-1221
• DOI: 10.1016/0898-1221(95)00079-e

✦ Synopsis

Irreducible, continuous-time Markov models for reliability analysis axe considered whose finite state space is partitioned as G U B, where G and B stand for the set of system up ('good') and down ('bad') states, respectively. For a fixed length of time to > 0, let TG(to ) and Ns(t0) stand, respectively, for the total time spent in G and the number of visits to B during [0, to].

The dependability measure considered here is P(TG(to) > t, Ns(t0) _~ n), i.e., the probability that during [0, to] the cumulative system up-time exceeds t(< to) and the system does not suffer more than n failures. Using the randomization technique and some recent tools from the theory of sojourn times in finite Maxkov chains, a closed form expression is obtained for this dependability measure. The scope of the practical computational utility of this analytical result is explored via its Mat-Lab implementation for the Maxkov model of a system comprising two parallel units and a single repairman.