Cost effective scheduling of imperfect inspections in systems with hidden failures and rescue possibility

Abstract

• Inspected non-repairable systems subject to a delay-time failure are considered. • A hidden failure cannot stop system functioning while a fatal failure causes the entire system loss. • A probabilistic model for evaluating performance metrics of the system is suggested. • A problem of finding the inspection schedule minimizing the total expected loss is formulated and solved. • Examples demonstrating the effects of system parameters on the optimization solutions are provided. Motivated by real-world critical applications such as aircraft, medical devices, and military systems, this paper models non-repairable systems subject to a delay-time failure process involving hidden and fatal failures in two stages during their missions. A hidden failure cannot cause the system to stop functioning while a fatal failure causes the entire system loss. The system undergoes scheduled inspections for detecting the hidden failure. In the case of a positive inspection result, the system main mission is aborted and a rescue operation is started to mitigate the risk of the entire system loss. The inspections are imperfect and may produce false positive and negative failures. We propose probabilistic models for evaluating performance metrics of the system considered, including mission success probability, system survival probability, expected number of inspections during the mission, and total expected losses. Based on the evaluation models, we formulate and solve an optimization problem of finding the optimal inspection schedule on a fixed mission time horizon to minimize the total expected loss. Examples are provided to demonstrate the proposed methodology and effects of key system parameters on system performance and optimization solutions.