Cost limit replacement policy under imperfect repair

A repair cost limit policy is studied for a system whose repair cost can be estimated by inspection. When a system fails, the repair cost is estimated and repair is undertaken if the estimated cost is less than a predetermined limit L; otherwise, the system is replaced. After repair, the system is as good as new with ($\text{1−p}$) or is minimally repaired with p. The s-expected cost rate is used as a criterion for optimization. The existence and uniqueness of optimum L are studied for the case of Weibull time-to-failure distribution and negative exponential repair cost distribution.