A practical method for reliability analysis of phased-mission systems

Many practical systems are phased-mission systems where the mission consists of multiple, consecutive, non-overlapping phases. For the mission to be a success, the system must operate successfully during each of the phases. In each phase, the system has to accomplish a specific task and may be subject to different stresses. Thus, the system configuration, success criteria, and component failure behavior may change from phase to phase. An accurate reliability analysis of these systems must consider the statistical dependencies of component states across the phases. The consideration of these dynamic dependencies poses unique challenges to existing reliability analysis methods. In this paper, we propose an efficient method for exact reliability evaluation of a special class of phased-mission systems containing multiple subsystems where all components within a subsystem are identical. The configuration of each subsystem can change with the phases, including their active and inactive status, redundancy type, and minimum required working components. If any one of the required (active) subsystems is failed in a phase, the system is considered to be failed in that phase. We also consider the time-varying and phase-dependent failure rates and associated cumulative damage effects. From the published examples, it can be shown that the mild restrictions imposed on the system configuration are applicable for a wide range of practical systems. The proposed method, which can be applied to very large-scale systems, is based on conditional probabilities and an efficient recursive formula to compute these probabilities. The main advantage of this method is that both the computational time and memory requirements of the method are linear in terms of the system size. We demonstrate the efficiency of the proposed method using medium-scale to large-scale systems. The proposed method provides a simple, efficient, and accurate reliability analysis of practical and large-scale phased-missi on systems.