A unified approach for reliability and performability evaluation of semi-Markov systems (Q2711704)

The mathematical models based on semi-Markov processes are well adapted for the study of the real systems (reliability indicators, evaluation of the performability, optimization, etc.). Many of these investigations become easier if a previous study of some additive functionals of a semi-Markov process is made. 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, \(\alpha\)-reliable mission time, mean time to failure, performability, throughput availability, maintainability, etc. It is considered the evolution of the system described by a semi-Markov process \((Z_{t}; t\in R_{+})\) with an arbitrary state space \(E\) and the accumulated reward \(W_{t}.\) Some general results concerning the Markov renewal equation for a process with general state space are given. Markov renewal equations are derived for some functionals of the semi-Markov processes. Existence and uniqueness of the solutions for these equations are discussed. It is shown how the functionals introduced can be used to analyse reliability and performability of the systems.