Dynamic populations of manufactured items under shocks

Populations of manufactured degrading items that are incepted into operation with a given rate are considered. The impact of shocks on the dynamic populations’ age structures is described. The relevant stochastic comparisons between random ages before and after a single shock and for a population under a point process of shocks and without this impact are obtained. Optimal preventive maintenance (replacements) policy for populations of items that are subject to the Poisson process of external shocks is discussed in the framework of the extreme shock model. Numerical examples illustrating the optimal replacement policy are provided.