An optimal maintenance strategy for multi-state systems based on a system linear integral equation and dynamic programming

An optimal preventive maintenance strategy for multi-state systems based on an integral equation and dynamic programming is described herein. Unlike traditional preventive maintenance strategies, this maintenance strategy is formulated using an integral equation, which can capture the system dynamics and avoid the curse of dimensionality arising from complex semi-Markov processes. The linear integral equation of the system is constructed based on the system kernel. A numerical technique is applied to solve this integral equation and obtain all of the mean elapsed times from each reliable state to each unreliable state. An analytical approach to the optimal preventive maintenance strategy is proposed that maximizes the expected operational time of the system subject to the total maintenance budget based on dynamic programming in which both backward and forward search techniques are used to search for the local optimal solution. Finally, numerical examples concerning two different scales of systems are presented to demonstrate the performance of the strategy in terms of accuracy and efficiency. Moreover a sensitivity analysis is provided to evaluate the robustness of the proposed strategy.