Repair cost limit replacement policy under imperfect inspection

A replacement policy with minimal repair cost limit is discussed. When a system fails, the repair cost is estimated by inspection and minimal repair is the undertaken if the estimated cost is less than a predetermined limit L; otherwise, the system is replaced. It is assumed that repair cost can not be estimated exactly because of imperfect inspection. When the failure time follows a Weibull distribution and repair cost a normal distribution, the value of repair cost limit minimizing the expected cost rate is shown to be finite and unique.