Optimal age-replacement policy of a system subject to shocks with random lead-time

This paper considers a generalized age-replacement policy of a system subject to shocks with random lead-time. A system is subject to shocks that arrive according to a non-homogeneous Poisson process. A model is developed for the average cost per unit time and is based on the stochastic behavior of the assumed system and reflects the cost of storing a spare as well as the cost of system downtime. The minimum-cost policy time is described and discussed. Various special cases are considered. Because the model and its analysis are general, several existing results are shown to be subsumed by this model.