Joint Inspection and Inventory Models for k-out-of-n Systems

The objective is to study the relationship between maintenance and inventory for a k-out-of-n system. The component's failures are hidden and follow a non-homogeneous Poisson process. Two types of inspections are performed to reveal the failed components: periodic inspections and opportunistic inspections which are performed at system failure times (when n - k + 1 components are down at once). The failed components are, depending on their state, either minimally repaired or replaced with spare parts from the inventory. Our goal is to find the inspection frequency and the inventory replenishment policy such that the total cost is minimized over a finite planning horizon. Two models are considered. First we will assume that the periodic inspections and the inventory replenishments are performed simultaneously. Then we will relax this assumption and allow independent inspections and inventory reviews. A simulation model is developed and heuristic search methods are used to find the optimal solution.M.A.S