Bayesian inference in a discrete shock model using confounded common cause data

Abstract

We consider redundant systems of identical components for which reliability is assessed statistically using only demand-based failures and successes. Direct assessment of system reliability can lead to gross errors in estimation if there exist external events in the working environment that cause two or more components in the system to fail in the same deman period which have not been included in the reliability model. We develop a simple Bayesian model for estimating component reliability and the corresponding probability of common cause failure in operating systems for which the data is confounded; that is, the common cause failures cannot be distinguished from multiple independent component failures in the narrative event descriptions.