Reliability analysis of static and dynamic fault-tolerant systems subject to probabilistic common-cause failures

Fault-tolerant systems designed with redundancy techniques are typically subject to common-cause failures, which are multiple dependent component failures caused by a shared root cause or a common cause (also known as a shock). There are two types of shocks: fatal and non-fatal. A fatal shock (FS) will fail all components of a system. A non-fatal shock (NFS) will affect only a subset of system components. Most of the existing shock models have assumed that the occurrence of an NFS results in deterministic and simultaneous failures of the affected components. In practice, however, the occurrence of an NFS may result in failures of different components with different probabilities of occurrence. This behaviour is referred to as probabilistic NFS. In this paper, we consider the effects of probabilistic NFS in the reliability analysis of fault-tolerant systems. Both an explicit method and an implicit method are proposed for incorporating probabilistic NFS in the reliability analysis of static systems. A Markov approach combined with the Poisson decomposition law is proposed for incorporating probabilistic NFS in the reliability analysis of dynamic systems. The proposed approaches are illustrated through the analyses of several examples.