LAUSR

This paper develops a joint strategy of condition-based maintenance and spare ordering for a multistate system that is subject to competing failures due to external shocks and self-degradation. Failures of this system are hidden and can be divided into two types: a one-stage hard failure and a two-stage soft failure. The states of the system are identified by periodic inspections and replacement is executed preventively or correctively in response to the defective or failed state. When the operating time of the system is reached the predetermined threshold $\tau $ , the spare is ordered. Furthermore, a threshold level $z$ is introduced to postpone the preventive replacement (PR) when the ordered spare is delivered before the defective state is first detected. Depending on the state of the ordered spare when replacement is required and the fault cause of the system when a corrective replacement (CR) is needed, all possible renewal events are analyzed to establish the joint optimization model. A modified artificial bee colony algorithm and discrete simulation algorithm are adopted to find the optimal solutions, and the correctness of the proposed model is verified by a numerical example. Moreover, the results from the numerical example indicate that the proposed strategy is superior to the comparative model, thus the applicability and effectiveness of the proposed model are illustrated.