On the asymptotic analysis of Littlewood's reliability model for modular software

James Ledoux (1, 2)

1 IRMAR - Institut de Recherche Mathématique de Rennes
2 INSA Rennes - Institut National des Sciences Appliquées - 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 behavior 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]; Performance et fiabilité [cs.PF]; Statistiques [math.ST]; Théorie [stat.TH]

James Ledoux. On the asymptotic analysis of Littlewood's reliability model for modular software. B. H. Lindqvist, K. A. Doksum. Mathematical and Statistical Methods in Reliability, World Scientific, pp.521-536, 2003. ⟨hal-00916262⟩