Littlewood reliability model for modular software and Poisson approximation

James Ledoux (1)

1 IRMAR - Institut de Recherche Mathématique de Rennes

We 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.

Domaines: Probabilités [math.PR]; Statistiques [math.ST]; Théorie [stat.TH]; Performance et fiabilité [cs.PF]

James Ledoux. Littlewood reliability model for modular software and Poisson approximation. 3th Conference on Mathematical Methods in Reliability (MMR2002), 2002, Trondheim, Norway. pp.367-370. ⟨hal-00916258⟩