Periodic Replacement with Increasing Minimal Repair Costs at Failure

When an expensive one unit system fails or breaks down, it is often more practical to perform “minimal repair” than to make a replacement or perform a complete overhaul. Instead replacements or complete overhauls are made periodically at fixed multiples of some predetermined time T. In this paper we treat a model for this minimal repair-periodic replacement policy, and consider the problems of determining: (1) the period T which minimizes the total expected cost of repair and replacement over a fixed time horizon [0, t), and (2) the period T which minimizes the total expected cost per unit time over an infinite time horizon.