Maintenance policies for systems that are subject to stochastic failures have been treated extensively in the past two decades. But most of them have assumed implicitly that there are an unlimited number of spare units available for replacement and did not consider the inventory problem of spare units involved in the maintenance policies.
This study is concerned with the optimal inventory system for the economical implementation of maintenance policies, and divided into the following four parts:
First, ordering and replacement policies for a nonrepairable unit with general lifetime and lead time distributions are considered. Some properties regarding the optimum ordering time and the optimum ordering policy are derived.
Second, ordering and replacement policies with minimal repair are considered. Two policies, which include the periodic replacement with minimal repair at failure of Barlow and Hunter as a special case, are proposed and analyzed.
Third, a joint stocking and preventive age replacement policy is considered for a non-repairable unit assuming instantaneous replenishment. Recursive relationships among the optimal preventive replacement ages are obtained, which show that the optimal preventive replacement ages in a replenishment cycle form an increasing sequence due to the inventory carrying cost. Using these relationships, a procedure is given for determining how many units to purchase on each order and when to replace each unit after it has begun operating so as to minimize the cost rate.
Finally, a joint stocking and periodic replacement policy with minimal repair is considered. The procedure for determining order quantity and replacement ages is very similar to that of non-repairable unit case.