Joint optimization of condition-based maintenance and inventory control for a k-out-of-n:F system of multi-state degrading components

Maintaining a system of multiple degrading components requires having a supply of spare components to replace deteriorated ones in a timely manner. Decisions on whether to replace the deteriorated components are made based on the statuses of components and the system and are further restricted by the inventory level of spares. Inventory replenishment decisions themselves depend both on system status and maintenance policy. Both maintenance and replenishment decisions affect the system reliability and system maintenance and spare inventory cost. This paper considers the joint optimization of periodic condition-based replacement of components and inventory control for a k-out-of-n:F system of non-repairable degrading components under various system statuses. For modeling the degradation of components, both the Wiener process and gamma process are considered. We model the maintenance and inventory policy using the number of components in each discretized degradation state rather than the traditional approach, which uses the state of each component. Our approach considerably reduces the solution space. Based on that, we address the joint optimization using Markov decision process along with dynamic programming; we then analyze the complexity of the algorithm. We provide a numerical study on a 2-out-of-3:F system of components in three states to illustrate structural insights regarding the proposed model, including a sensitivity analysis on the length of inspection interval, system downtime cost, and inventory holding cost. We demonstrate the efficiency of the model and solution method by testing k-out-of-n:F systems with different numbers of components and discretized degradation states.