OPTIMAL REPLACEMENT PERIOD WITH REPAIR COST LIMIT AND CUMULATIVE DAMAGE MODEL

This paper deals with periodical replacement model with single repair cost limit under cumulative damage process. The system is subject to two types of shocks. Type I shock causes damage to the system. The total damage is additive, and it causes a serious failure eventually if the total additive damage exceeds a failure level K. Type II shock causes the system to a minor failure, which can be maintained by minimal repair if the estimated repair cost is smaller than a predetermined repair-cost limit L-S or by preventive replacement if the estimated repair cost is larger than LS. The system is also replaced at scheduled time T or at serious failure. The long-term expected cost per unit time is derived using the expected costs as the optimality criterion. The minimum-cost policy is derived, and existence and uniqueness are proved.