An optimal maintenance strategy for multi-state deterioration systems based on a semi-Markov decision process coupled with simulation technique

•An estimation approach to obtain the high-precision transition probability matrix is proposed.•An algorithm to calculate the summation of coefficients in Laplace transform domain is developed.•A highly efficient optimal maintenance strategy is developed to avoid the curse of dimensionality. Maintenance optimization of multi-state systems is a research topic of practical significance for various manufacturing systems. Nevertheless, design of satisfactory maintenance strategies remains a challenging problem due to the complex industrial field and large strategy space for maintenance optimization of such systems. In this study, a model of the deterioration process of multi-state systems with the multi-phase property was constructed by utilizing semi-Markov decision theory and linear systems of integral equation. An efficient maintenance strategy was developed with the purpose of maximizing the net revenue per unit period based on the simulation technique. In the constructed model, a system of linear integral equations with a recursive structure was constructed to obtain all possible transition probabilities between the states. Due to this recursive structure, conventional solutions of linear integral equations are not capable of solving this equation. For this reason, an algorithm was developed that was instrumental in resolving this issue. In the designed maintenance strategy, to avoid the potential curse of dimensionality resulting from the scales of the systems and the strategy space, a semi-Markov decision process coupled with the simulation technique was adopted in each decision period to reduce the search space by eliminating unreachable states. Finally, numerical examples of two systems with different scales based on real data of the inspection record database at Dongbei Special Steel Group Co., Ltd. are given to illustrate the effectiveness of the proposed model and the performance of the designed strategy. The numerical results demonstrate the high efficiency of the optimal strategy, especially for large-scale systems.