A unified approach for reliability and performability evaluation of semi-Markov systems
Nikolaos Limnios, Gheorghe Oprian · Applied Stochastic Models in Business and Industry · 1999
The aim of this paper is to give a unified approach for the evaluation of reliability- and performability-related indicators of semi-Markov systems: reliability, availability, α-reliable mission time, mean time to failure, performability, throughput availability, maintainability, etc. For a semi-Markov processes, (Zt; t ∈ ℝ+) say, with an arbitrary state space E, we associate to every state a reward rate (or a performance level), then the accumulated reward until time t, denoted by Wt, is an additive functional of the process. The above-stated indicators are obtained by some distribution functions of the process (Zt, Wt; t ∈ ℝ+) by means of the Markov renewal theory, as well as the joint distribution of (ZT, WT), where T is the first hitting time of a subset of states. Copyright © 1999 John Wiley & Sons, Ltd.