Joint optimization of preventive maintenance and triggering mechanism for k-out-of-n: F systems with protective devices based on periodic inspection

Systems with protective devices (PDs) have attracted increasing research interests due to their extensive engineering applications. In practice, the PDs are triggered to function under certain conditions. However, existing studies focus on the reliability modelling and analysis for such systems, and the joint optimization of maintenance and PD's triggering mechanism has not been investigated. Consequently, this paper explores the joint optimization of maintenance and triggering mechanism for k-out-of-n: F systems with PDs. A new triggering mechanism of the PD is proposed based on the number of failed or unhealthy components. The working PD can reduce the impacts of shocks on components. Based on the detected system status through periodic inspections, corresponding actions including corrective maintenance for components or the PD, preventive maintenance for components or shutting down the PD can be decided to improve the system reliability. The operation process of the established system is modelled by Markov decision process, and optimal actions under diverse system states are obtained via value iteration algorithm. The optimal inspection interval and triggering mechanism are derived by solving the optimization model aiming to minimize the expected total cost. Finally, the applicability of the proposed model is validated by abundant numerical examples.