Reliability of non-repairable phased-mission systems with propagated failures

In this paper, we propose a recursive and exact method for reliability evaluation of phased-mission systems with failures originating from some system elements that can propagate causing the common cause failures of groups of elements. The system consists of multiple, consecutive, non-overlapping phases of operation, and non-identical binary non-repairable elements that can fail individually or due to propagated failures originating from other elements. The overall system can have binary states corresponding to the mission success and failure or multiple states characterized by different levels of system performance. Based on conditional probabilities as well as the branch and bound principle, the proposed method takes into account dynamic changes in system structure and demand across different phases. It also considers time-varying, phase-dependent failure rates and associated cumulative damage effects for the system elements. The main advantage of this method is that it does not require composition of decision diagrams and can be fully automated. Both an analytical example and a numerical example are analyzed to illustrate the proposed method.