Optimal Condition-based Opportunistic Maintenance and Spare Parts Provisioning for a Two-unit System using a State Space Partitioning Approach

Making optimal decisions on preventive maintenance (PM) and spare parts provisioning for a multi-unit system is a practical problem in many industrial applications. In practice, decision makers must deal with a high level of complexity because of complex interactions among multiple units. In this work, we study optimal conditionbased opportunistic maintenance (CBOM) and spare parts provisioning policies for a two-unit system experiencing continuous deterioration. A state space partitioning approach considering the deterioration states of the system along with the spare parts inventory state is proposed to analyse the requirements and actions for different maintenance types under the constraints of spare parts and those for spare parts holding and ordering. The explicit representations of stationary probability densities of combined states and their numerical solutions are deduced to obtain the corresponding probabilities of interest. Based on the results and the semi-regenerative process theory, an expected long-run cost rate model is developed to determine the optimal joint strategy. To illustrate the use of the proposed approach in practice, a wind turbine system consisting of main bearings and gearboxes is studied. The numerical results and sensitivity analysis validate the proposed approach and its practical values in solving such complex industrial problems.