Abstract: This paper focuses on an optimal maintenance policy of a system under three states with repair time limit under the discrete Markov renewal process. In our policy, the system undergoes a preventive replacement after operating continuously for a planned time interval T. When a failure arises prior to reaching time T, the system undergoes immediate corrective maintenance. Should the repair process conclude successfully prior to reaching the threshold $$T_0^*$$, normal operations recommence. Otherwise, it is replaced with a new one.To optimize this policy, we firstly give some key theorems concerning renewal functions and transition prob- abilities within a three-state Markov renewal process, where the states represent operation, repair, and replacement.Secondly, we propose two mathematical optimization models based on above foundations: Model I that minimizes the expected maintenance cost rate while ensuring a predefined system availability constraint. Model II that maximizes the expected reward rate, offering a computationally efficient alternative to Model I. Thirdly, we derive analytical solutions for the optimal repair time limit $$T_0^*$$ and the planned replacement time T∗ with a specified lifetime distribution. Finally, we employ numerical example and its parameters sensitivity analysis demonstrates the robustness and effectiveness of the proposed maintenance policy.

Keywords: Optimization policy, repair time limit, Markov renewal process, availability, maintenance cost, expected reward rate

Pages: 2601-2610