Abstract
•Inspected 1-out-of-n standby system is considered.•Operating and standby elements are exposed to random common shocks.•Operating element is also exposed to operational shocks.•An algorithm for evaluating expected mission losses is suggested.•Optimal inspection and standby element addition policy is obtained.
Motivated by practical applications like data storage, product defect detection, medical imagining, and sensing, this paper puts forward a new inspected standby system model where only one element can be online operating and only one element can stay in the standby mode at any time. Both operating and standby elements are exposed to random common shocks, causing their deterioration and even failures. The operating element may also be deteriorated by random operational shocks. The system undergoes periodic inspections to determine the refill of the operating or standby element. A new optimization problem is formulated and solved to determine the inspection and standby element addition policy with the objective to minimize the expected mission cost (EMC) attributed to factors including system downtime, number of inspections, element modes and failures, element activation and mode transitions. A new and efficient system state transition-based numerical algorithm is proposed to evaluate the EMC. A case study of a standby sensor system is provided to demonstrate the proposed model and impacts of several cost parameters as well as shock rates on the EMC and the optimal inspection and standby element addition policy, leading to insightful managerial guidelines for the system design and operation.