Heterogeneous 1-Out-of-N Warm Standby Systems With Dynamic Uneven Backups

Abstract

In this paper, mission reliability, expected mission completion time, and cost of non-repairable 1-out-of- $N$ : G warm standby sparing systems subject to uneven backup actions are modeled and optimized. The backup actions are used to facilitate the data recovery process in the case of an online operating element failure, which enables an activated standby element to take over the mission task through subsequent data retrievals. Both data backup and retrieval times are dynamic, and physically dependent on the amount of work performed. The system elements are not necessarily identical; each element can be characterized by a different time-to-failure distribution, a different performance, and a different level of readiness to take over the system task during the warm standby mode. An iterative numerical method is first proposed to simultaneously evaluate mission reliability, expected mission completion time, and the cost of the considered heterogeneous warm standby systems. Due to the non-monotonic effect of the backup distribution on the mission reliability, time, and cost, we formulate and solve the optimal backup distribution problem considering different combinations of optimization objectives and constraints. In the case of system elements being non-identical, their activation order can influence the mission reliability, expected mission completion time, and mission cost significantly. Therefore, we also formulate and solve the optimal element sequencing problem for the considered system. Furthermore, new integrated optimization problems are formulated and addressed. The integrated optimization aims to identify the optimal combination of backup distribution and element activation order that maximizes the mission reliability, or minimizes the expected mission time or mission cost. As shown through examples, the proposed methodology can implement a tradeoff analysis among the three mission requirements of reliability, cost, and completion time, leading to the optimal decision on both backup and standby policies of warm standby systems.