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Cost Limit Replacement Policy under Imperfect Repair with Inspection Error

A replacement policy with repair cost limit is discussed. When a system fails, the repair cost is estimated by inspection and repair is then 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 probability(l-p) or is minimally repaired with probability p. It is assumed that repair cost can not be estimated exactly because of inspection error. 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.