Joint optimization of maintenance and spare parts provisioning for multi-unit systems

Performance of a deteriorating system depends on the planned maintenance actions and on the availability of spare parts. As a result, maintenance control and inventory control of spare parts should be considered jointly. This study investigates the joint optimization of condition-based maintenance and spare parts provisioning for multi-unit systems. We consider a system consisting of N identical units, where each unit deteriorates independently. We model the deterioration process of each unit as a three-state continuous time homogeneous Markov chain with two working states and a failure state. The deterioration level of each unit and the spare parts inventory state can be revealed by periodic inspections at discrete time epochs. Decisions to perform maintenance or to order spare parts at each inspection time are determined by the number of units in the failure state. Our objective is to determine jointly the optimal number of failed units to initiate maintenance or to place an order, minimizing the long run expected average cost per time unit. The problem is formulated and solved in the semi-Markov decision process (SMDP) framework. A numerical example is developed to demonstrate the proposed model.