A Poisson limit theorem for reliability models based on Markov chains

James Ledoux (1, 2)

1 IRMAR - Institut de Recherche Mathématique de Rennes
2 INSA Rennes - Institut National des Sciences Appliquées - Rennes

In 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.

Mots clés: Discrete-time multivariate point process; time inhomogeneous Markov chain; Compound Poisson approximation; filtering

Domaines: Probabilités [math.PR]

James Ledoux. A Poisson limit theorem for reliability models based on Markov chains. Communications in Statistics - Theory and Methods, 2006, 35 (1), pp.173-196. ⟨10.1080/03610920500439331⟩. ⟨hal-00452069⟩