Inspection policy optimization for a k-out-of-n/Cl(k′,n′;F) system considering failure dependence: a case study

This study presents the reliability and inspection optimization of a novel k-out-of-n: G system with linear consecutive k′-out-of-n′ load-sharing subsystems, abbreviated as k-out-of-n/Cl(k′,n′;F), motivated by a roller system. The subsystems are identical and mutually independent and the system works when at least k subsystems function. Within a subsystem, failure dependence among components exists since the carried load is unequally shared by surviving components. We model the load-sharing effect by the tempered failure rate model. The failure sequence diagram (FSD) is constructed to describe possible events of a subsystem evolution in the present of the states of components. A regular inspection policy is proposed, upon which hidden failures at the component level can be revealed. The system is preventively maintained upon an inspection or at its failure, which occurs first. The long-run expected cost per unit time is minimized, and a coupling search FSD and sampling algorithm is designed to search for the optimal inspection interval. A case study is presented to show the applicability of the proposed model, where we show the reliability variation and indicate that the current one-week-inspection policy is too conservative. Sensitivity analysis is provided to examine the impact of cost parameters on the optimal decision.