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On Optimal Replacement Policies - Random Horizon

A system with a functional life of T units of time requires a certain functional part for its operation. If this part fails before the failure of the system, it has to be replaced immediately to keep the system in operation. Two brands are available for replacements. These two brands differ in unit costs and life distributions. The objective is to determine a time-dependent replacement policy that minimizes the expected operational cost. We show that if certain conditions are satisfied, then the optimal policy exists and has a simple intuitive structure.