Optimal Replacement Policies Based on Cumulative Damage and Inspection Cost Limit

This article considers periodic inspection and replacement policies under the cumulative damage model, considering the inspection cost limit. The system is subject to two types of shocks: type I shock, which causes additive damage to the system, and type II shock, which results in system failure. The system performs a preventive replacement at the th inspection or at the time when the total inspection cost exceeds an inspection cost limit for the first time, whichever occurs first or last, depending on whether the replacement first (RF) or replacement last (RL) policy is applied. Meanwhile, a corrective replacement of the system is performed at the next inspection after the accumulative damage exceeds the damage level , or after a type II shock occurs, whichever occurs first, for the RF and RL policies. The RF and RL policies are used to derive optimal numbers of inspections, optimal inspection cost limits and optimal long‐run expected cost rates. Comparisons between RF and RL policies are discussed in terms of long‐run expected cost rate. Finally, both numerical and real‐world examples are provided to illustrate our results and to guide decisions on which policy should be adopted under different conditions.