Optimal and suboptimal strategies for group preventive replacement

The group preventive replacement problem is formulated in continuous time for a multicomponent system having identical elements. The Dynamic Programming equation is obtained in the framework of the theory of optimal control of Jump processes. A discrete time version of the model is used for the numerical computation of optimal and suboptimal strategies of group preventive replacement. A monotonicity property of the Bellman functional (or cost-to-go function) is stated and serves to reduce the size of the computational problem.