New method for availability computing of complex systems using imprecise Markov models

Abstract

The system availability is defined as the probability that the system is operational at a given time. To compute the availability of a multi-states system (the system and its components could have multi-states), we have to sum over all the probabilities of the components working states, therefore these probability precise values are required. In some cases (rare event failures, new components, ...), it isn't possible to obtain the working probabilities precisely because of the lack of data. In this work, we propose to apply imprecise continuous Markov chain where the failure and repair rates are imprecise. Only few works were developed using this concept. The precise initial distributions are replaced by intervals, which represents the unknown initial probabilities and the unknown transition matrix. The interval constraint propagation method is exploited for the first time, in availability modeling, to compute the imprecise multi-states system availability. The probability interval bounds associated to real variables are contracted, without removing any value that may be consistent with the set of constraints. The proposed methodology is guaranteed, and different examples of complex systems with some properties (convergence, ergodicity, ...) are studied. All the numerical examples and results will be discussed in the paper.

Methodology for the Assessment of Imprecise Multi-State System Availability

“…To our knowledge, the combination of a Markovian approach with interval contraction methods has not been investigated. Note that a preliminary work concerning our approach was briefly presented in our short conference papers [39,40]. Apart from the novelty of our proposed work, we can note many reasons to justify why such an extension is appealing:…”