A comparative analysis of dependability assessment methodologies for markovian and non-markovian systems

Abstract

This paper presents a comparative analysis of several reliability evaluation methodologies for discrete-state markovian, semi-markovian, and non-markovian systems, and discusses the situations where the use of each one of these approaches seems to be the more appropriate one. The first part of the paper reviews these three classes of systems, along with the mathematical foundations of the corresponding evaluation methodologies. The emphasis is put on continuous Markov processes and embedded Markov chains, respectively, for markovian and semi-markovian systems. For non-markovian systems, the device of stages and the DepCim methodologies will be introduced together with the Monte Carlo simulation techniques. The second part of the paper analyses the error introduced in the reliability indexes when the system under study contains non-exponential but, for evaluation purposes, is adopted the usual assumption that the systems has a markovian behaviour pattern, i.e. all their processes have exponential distributions so that the transition rates between states are constant. In the final part of the paper, a set of heuristic rules will be proposed allowing to foresee, from the structure of the models and the distributions of their individual processes, the situations where the error is more likely to be significant, so that a non-markovian evaluation methodology should be employed.