Reliability of Systems with Simultaneous and Consecutive Failures

A new non-homogeneous shock model for common-cause failure analysis is proposed in this paper. The reliability of a $k$–out-of– $n$ system and a consecutive $k$–out-of– $n$ system subjected to shock and considering the simultaneous failures are discussed. Component failures including common-cause failures are assumed to occur as the result of the occurrence of external shocks. With the assumption that common-cause failures occur within the components located close each other (simultaneous and consecutive failure), the reliabilities of redundant systems are derived. The signed domination is applied to the formulation of a $k$–out-of– $n$ system. The reliability is compared to that of the conventional homogeneous model in numerical example.