Modeling and Estimating Small Unreliabilities for Static Networks with Dependent Components

¹ School of Mathematics and Statistics, The University of New South Wales, Sydney, NSW 2052, Australia
² DIRO, Université de Montreal, Pav. Aisenstadt, C.P. 6128, Succ. Centre-Ville, Montréal (Québec), H3C 3J7, Canada
³ INRIA Rennes Bretagne Atlantique, Campus Universitaire de Beaulieu, 35042 Rennes Cedex, FRANCE

Abstract

We study static network reliability models in which the component failures are not independent. To model the dependence and also to develop effiective simulation methods that estimate the system unreliability, we extend the static model into an auxiliary dynamic model where the components fail at random time, according to a Marshall-Olkin multivariate exponential distribution. We examine and compare diffierent versions of this model and develop efficient unreliability estimation methods based on conditional Monte Carlo and on a generalized splitting methodology.