Computing bounds of the MTTF for a set of Markov chains

Abstract

We present an algorithm to find some upper and lower bounds of the Mean Time To Failure (MTTF) for a set of absorbing Discrete Time Markov Chains (DTMC). We first present a link between the MTTF of an absorbing chain and the steady-state distribution of an ergodic DTMC derived from the absorbing one. The proposed algorithm is based on the polyhedral theory developed by Courtois and Semal and on a new iterative algorithm which gives bounds of the steady-state distribution of the associated ergodic DTMC at each iteration. © 2013 Springer International Publishing.