Optimal inventories for repairable redundant systems with aging components

In a recent paper, Lawrence and Schaefer determined the optimal maintenance center inventories for fault-tolerant repairable systems. They found optimal maintenance center inventories for machines containing several sets of redundant systems under a budget constraint on total inventory investment. This article extends that work in several important ways. First, the authors relax the assumption that the parts have constant failure rates. In this model, component failure rates increase as the parts age. Second, the authors determine the optimal preventive maintenance policy, calculating the optimal age at which a part should be replaced even if it has not failed because the probability of subsequent failure has become unacceptably high. Third, they relax the earlier assumption that component repair times are independent, identically distributed random variables. In this article the authors allow congestion to develop at the repair shop, making repair times longer when there are many items requiring repair. Fourth, they introduce a more efficient solution method, marginal analysis, as an alternative to dynamic programming, which was used in the earlier paper. Fifth, the authors modify the model in order to deal with an alternative objective of maximizing the job-completion rate. In this article, the notation and assumptions of the earlier model are reviewed. The requisite changes in the model development and solution in order to extend the model are described. Several illustrative examples are included.