Abstract
This paper models a hybrid standby system subject to periodic inspections and condition-based standby mode transfers during a mission. At the beginning of the mission only one element is online and operating. The second element waits in a hot standby mode being ready to replace the failed online element at any time. Other elements wait in less-stressful and less-costly warm standby mode. During the mission periodic inspections are performed for checking conditions of the online and hot standby elements and subsequently triggering necessary mode transfer(s) of available warm standby element(s) to replace the failed hot standby element and/or online element. We suggest an efficient numerical method to assess availability and expected total mission cost (including standby cost, operation cost and mode transfer cost of system elements, inspection cost, system interruption or idle cost) of the considered system. The algorithm is flexible and applicable to arbitrary type of time-to-failure distributions. Then we formulate and solve new optimization problems that identify the optimal combination of inter-inspection interval and element activation sequence to minimize expected total mission cost while satisfying a certain constraint on system availability. As illustrated through examples, the optimization results can facilitate cost-effective and availability-aware planning of system inspection and operation.