The binomial failure rate mixture model for common cause failure data from the nuclear industry

A model for the lifetime of a system is considered in which the system is susceptible to simultaneous failures of two or more components, the failures having a common external cause. Three sets of discrete failure data from the US nuclear industry are examined to motivate and illustrate the model derivation: they are for motor-operated valves, cooling fans and emergency diesel generators. To achieve target reliabilities, these components must be placed in systems that have built-in redundancy. Consequently, multiple failures due to a common cause are critical in the risk of core meltdown. Vesely has offered a simple methodology for inference, called the binomial failure rate model: external events are assumed to be governed by a Poisson shock model in which resulting shocks kill X out of m system components, X having a binomial distribution with parameters ( m , p ), 0< p <1. In many applications the binomial failure rate model fits failure data poorly, and the model has not typically been applied to probabilistic risk assessments in the nuclear industry. We introduce a realistic generalization of the binomial failure rate model by assigning a mixing distribution to the unknown parameter p . The distribution is generally identifiable, and its unique nonparametric maximum likelihood estimator can be obtained by using a simple iterative scheme.