Optimal Backup Distribution in 1-out-of- ${N}$ Cold Standby Systems

This paper considers nonrepairable 1-out-of-N: G cold standby (CS) systems subject to uneven backup actions as well as dynamic backup and retrieval times. In such systems, only one element is online and operates with the rest of the elements waiting in the unpowered CS mode. The operating element performs data backup actions when certain fractions of the mission task are accomplished. The backup actions facilitate data recovery in case of an operating element failure, which allows an activated standby element to take over the task through data retrieval. Backup distribution can have a nonmonotonic effect on mission reliability, time, and cost, leading to the optimal backup distribution problem. In this paper, we first suggest a numerical method to model and evaluate mission reliability, expected time, and cost simultaneously for the considered CS systems with uneven backup actions and dynamic backup and retrieval times. Based on the suggested evaluation method and genetic algorithm, the optimal backup distribution problem is then formulated and solved with the objective to minimize the expected mission cost subject to meeting certain levels of mission reliability and expected mission time. Examples show that the proposed methodology can facilitate a tradeoff study between mission reliability, and time and cost, which assists in the optimal decisionmaking for the backup policy used in the practical design of CS systems.