On Robust Markov Analysis for Reliability Assessment of Complex Systems using Imprecise Markov Chains

Markov analysis is a wide-spread tool for modelling interactions among components in complex systems. It is based on modelling the evolution of system’s component states by Markov Chains. But, as in many other uncertainty models, it might often be overly optimistic to assume that we can construct a precise stochastic model which properly captures the uncertainties present in the investigated system. This issue is addressed by the theory of Imprecise Probabilities and, specifically for stochastic processes, by the theory of Imprecise Markov Chains. In this paper, we will demonstrate how Imprecise Markov Chains can not only serve as a robust alternative to classical stochastic models, but also how they can facilitate analyses by the means of problem dimension reduction and also, by die means of deliberate model construction, enable analyses which would not be possible by using solely precise probability models.