Probabilities of mission success and system survival in multi-state systems with arbitrary structure

Many critical systems are designed with the rescue function to possibly survive the system in the event of the defined mission not being able to continue. Existing models have focused on binary-state systems with certain structures. Going beyond the state of the art in modeling the rescue possibility, this paper considers multi-state systems with arbitrary system structures and arbitrary element time-to-failure distributions. System elements have dynamic reliability and performance characteristics during the primary mission and the rescue procedure. A probabilistic approach is suggested for evaluating the mission success probability and system survival probability. The proposed approach is further extended for the element sensitivity analysis and optimal maintenance investment. The sensitivity analysis provides importance ranking of system elements with respect to their influence on the mission success or system survival, facilitating the determination of effective strategies to improve the mission success and system survival probabilities. The optimal maintenance investment problem is aimed at identifying the system element and its reliability improvement factor that minimize the expected losses cost. Two examples of wireless sensor networks and chemical reactor supply systems are analyzed to demonstrate the applications of the proposed method.