A periodical replacement model based on cumulative repair-cost limit

This paper considers a periodical replacement model based on a cumulative repair-cost limit whose concept uses the information of all repair costs to decide whether the system is repaired or replaced. The failures of the system can be divided into two types. One is minor failure that is assumed to be corrected by minimal repair, while the other is serious failure where the system is damaged completely. When a minor failure occurs, the corresponding repair cost is evaluated and minimal repair is then executed if this accumulated repair cost is less than a pre-determined limit L, otherwise, the system is replaced by a new one. The system is also replaced at scheduled time T or at serious failure. Long-run expected cost per unit time is formulated and the optimal period T minimizing that cost is also verified to be finite and unique under some specific conditions.