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

Very often, in dependability evaluation, the systems under study are assumed to have a Markovian behavior. This assumption highly simplifies the calculations, but introduces significant errors when the systems contain deterministic or quasi-deterministic processes, as it often happens with industrial systems. Existing methodologies for non-Markovian systems, such as device stage method [1], the supplementary variables method or the imbedded Markov chain method [2] do not provide an effective solution to deal with this class of systems, since their usage is restricted to relatively simple and small systems. This paper presents an analytical methodology for the dependability evaluation of non-Markovian discrete state systems, containing both stochastic and deterministic processes, along with an associated systematic resolution procedure suitable for numerical processing. The methodology was initially developed 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. Examples will be provided throughout the paper, in order to illustrate the fundamental concepts of the methodology, and to demonstrate its practical usefulness. (C) 2001 Elsevier Science Ltd. All rights reserved.