Age‐based preventive replacement policy has been extensively studied in the literature. Upon an unexpected failure, most studies assume that only one type of maintenance actions can be executed to restore the system back to work. For example, minimal repair or corrective replacement that bring the system to respective as‐bad‐as‐old and as‐good‐as‐new states. Few studies consider both two types of maintenance actions, while predetermine the structure of the maintenance policy. Modern systems are becoming increasingly complex. Besides minimal repair and corrective replacement, imperfect repair can also be carried out to restore a failed system back to work, which brings it to a state between as‐bad‐as‐old and as‐good‐as‐new. This study investigates an optimal age‐based replacement policy, where minimal repair, corrective replacement, and imperfect repair can be carried out upon an unexpected failure with different maintenance effects. We formulate the problem as a semi‐Markov decision process (SMDP), and prove the existence of the stationary optimal policy. The optimal preventive replacement age threshold and the corresponding optimal maintenance action upon each failure are jointly obtained to minimize the long‐term average maintenance cost per time unit. A numerical study is provided to illustrate the effectiveness of our proposed model.

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