Optimal maintenance strategy for systems with two failure modes

This paper considers a single-unit system subject to two types of failures: a traditional catastrophic failure and a two-stage delayed failure. Periodic inspections are carried out to identify the defective stage of the two-stage failure process, whereas preventive replacements are implemented to avoid any potential failure due to the catastrophic failure mode. We construct a basic maintenance model and then extend it to the cases of imperfect inspections (i.e., inspections that do not always notice a defective state). We analyze the renewal process of the system and establish the expected long-run cost rate (ELRCR). The optimal inspection period and preventive replacement interval are determined by minimizing the ELRCR. A case study on infusion pumps is presented to illustrate the proposed model.