Periodic Replacement with Increasing Minimal Repair Costs at Failure

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Abstract
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.

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