Modeling and estimating small unreliabilities for static networks with dependent components

Generally nuclear safety depends on a chain of very low probability events. In this article we study static network reliability models in which the component failures are not independent. To model the dependence and also to develop effective 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 different versions of this model and develop efficient unreliability estimation methods based on conditional Monte Carlo and on a generalized splitting methodology. (authors)