Optimal age-replacement time with minimal repair based on cumulative repair cost limit and random lead time

We consider an age-replacement model with minimal repair based on a cumulative repair cost limit and random lead time for replacement delivery. A cumulative repair cost limit policy uses information about a system's entire repair cost history to decide whether the system is repaired or replaced; a random lead time models delay in delivery of a replacement once it is ordered. A general cost model is developed for the average cost per unit time based on the stochastic behavior of the assumed system. The minimum-cost policy time is derived, its existence and uniqueness is shown, and structural properties are presented. Various special cases are included. Because the framework and analysis are general, the proposed model extends several existing results.