Heterogeneous Non-Repairable Warm Standby Systems With Periodic Inspections

Abstract

Motivated by practical applications (for example production systems, flow transmission systems, and transportation systems), this paper considers 1-out-of- $N$ : G warm standby systems subject to periodic inspections. Periodic inspections are performed to detect failures of system components. If an online operating component failure is detected during inspection, an available warm standby component is activated to take over the mission task. The mission succeeds if system components can complete a pre-specified amount of work. A state space event transition based numerical algorithm is first suggested for evaluating important mission performance indices including mission success probability, expected mission cost, expected mission time, expected mission completion delay over a desired time, and expected uncompleted work of the considered standby system. Based on the proposed evaluation algorithm, inspection interval optimization problems are formulated and solved, which find the optimal value of the inspection interval to minimize the expected total mission cost subject to providing a desired level of mission success probability, expected completion time, and delay. Further, combined component sequencing and inspection interval optimization problems are solved, for minimizing the expected total mission cost, or maximizing the mission success probability. As illustrated through examples, the proposed methodology can also facilitate solving dynamic optimization problems that update the optimal solution after each component failure, leading to further improvements of various mission indices.