THE BINOMIAL FAILURE RATE MIXTURE MODEL FOR COMMON-CAUSE FAILURE DATAFROM THE NUCLEAR INDUSTRY

A model for the lifetime of a system is considered in which the system is susceptible to simultaneous failures of two OF more components, th e failures having a common external cause. Three sets of discrete fail ure data from the US nuclear industry are examined to motivate and ill ustrate the model derivation: they are for motor-operated valves, cool ing fans and emergency diesel generators. To achieve target reliabilit ies, these components must be placed in systems that have built-in red undancy. Consequently, multiple failures due to a common cause are cri tical in the risk of core meltdown. Vesely has offered a simple method ology for inference, called the binomial failure rate model: external events are assumed to be governed by a Poisson shock model in which re sulting shocks kill X out of m system components, X having a binomial distribution with parameters (m, p), 0 < p < 1. In many applications t he binomial failure rate model fits failure data poorly, and the model has not typically been applied to probabilistic risk assessments in t he nuclear industry. We introduce a realistic generalization of the bi nomial failure rate model by assigning a mixing distribution to the un known parameter p. The distribution is generally identifiable, and its unique nonparametric maximum likelihood estimator can be obtained by using a simple iterative scheme.