Littlewood reliability model for modular software and Poisson approximation

International audienceWe consider a Markovian model, proposed by Littlewood, to assess the reliability of a modular software. Speci cally , we are interested in the asymptotic properties of the corresponding failure point process. We focus on its time-stationary version and on its ehavior when reliability growth takes place. We prove the convergence in distribution of the failure point process to a Poisson process. Additionally, we provide a convergence rate using the distance in variation. This is heavily based on a similar result of Kabanov, Liptser and Shiryayev, for a doubly-stochastic Poisson process where the intensity is governed by a Markov process