A contribution to the evaluation of imprecise availability of complex systems using markov models

When using classical methods for the availability assessment of a multi-state system, the precise values of state' probabilities are required. But, in many cases the available data does not describe the system's components, defining the system's state, precisely. To cope with this problem, the imprecision can be incorporated into the method in terms of imprecise rates [1] (failure and repair rates) by using imprecise probability theory [2]. Markov chain models are known for their simplicity and their great ability to model reparable systems, thus, they are well adapted for modeling stochastic failure and repair processes, where conditional probability distribution of future states depends only on the present state, and then computing the system's availability. To our best of knowledge, only a few works were developed in the context of imprecise continuous Markov chain [3]. The idea in this paper is to replace precise initial distributions and transition matrices by imprecise ones where imprecise rates are expressed in terms of intervals which are supposed to contain the true unknown initial probability and transition matrix. The contribution of this work is twofold: first, applying interval analysis techniques on existing algorithms for availability assessment of multi-state systems, and second, studying the stationarity, convergence and ergodicity properties related to the new proposed technique.