A Conditional Probability Approach to Reliability with Common-Cause Failures

This paper presents a conditional probability method to evaluate the reliability or availability of a system whose components failures can be s-independent or have a common-cause. Different failure types can be in each cut-set. By applying pivotal decomposition, the chain rule of conditional probability, and the recursive rule of probability of a union of events, I obtain the steady-state system unavailability. This approach requires the failure & repair rates of each component due to s-independent causes, the occurrence rate of each common-cause failure, and the mean duration of each common-cause. Hence it is practical and useful. The general model in the adverse environment assumes s-dependency and faces the dilemma of how to estimate the transition rates of each component.