A Poisson limit theorem for reliability models based on Markov chains

International audienceIn this article, we deal with a class of discrete-time reliability models. The failures are assumed to be generated by an underlying time inhomogeneous Markov chain. The multivariate point process of failures is proved to converge to a Poisson-type process when the failures are rare. As a result, we obtain a Compound Poisson approximation of the cumulative number of failures. A rate of convergence is provided