An analytical methodology for the dependability evaluation of non-Markovian systems with multiple components

Very often, in dependability evaluation, the systems under study are assume d to have a Markovian behavior. This assumption highly simplifies the calcu lations, but introduces significant errors when the systems contain determi nistic or quasi-deterministic processes, as it often happens with industria l systems. Existing methodologies for non-Markovian systems, such as device stage method [1], the supplementary variables method or the imbedded Marko v chain method [2] do not provide an effective solution to deal with this c lass of systems, since their usage is restricted to relatively simple and s mall systems. This paper presents an analytical methodology for the dependability evaluat ion of non-Markovian discrete state systems, containing both stochastic and deterministic processes, along with an associated systematic resolution pr ocedure suitable for numerical processing. The methodology was initially de veloped in the context of a research work [3] addressing the dependability modeling, analysis and evaluation of large industrial information systems. This paper, extends the application domain to the evaluation of reliability oriented indexes and to the assessment of multiple components systems. Exa mples will be provided throughout the paper, in order to illustrate the fun damental concepts of the methodology, and to demonstrate its practical usef ulness. (C) 2001 Elsevier Science Ltd. All rights reserved.