Classical Optimal Replacement Strategies Revisited

This paper considers the generalization of the classical optimal age replacement strategy to the case when the system's output is modelled by the decreasing deterministic function. This function describes an additional source of system's deterioration with time. We derive and analyze the long-run expected cost per unit of time and consider the corresponding optimal replacement problem. Our results show that additional source of degradation decreases the optimal replacement time as compared with the case without output or with a constant in time output. Furthermore, the optimal replacement time can now exist and be finite when the failure time of our system is described by the exponential, non-aging distribution. The cases of periodic replacement and of stochastic output are also considered and analyzed. Some simple examples illustrating our results are given.