A stochastic control approach to group preventive replacement in a multicomponent system

A 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. For a discrete time version of the model, the numerical computation of optimal and suboptimal strategies of group preventive replacement are done. A monotonicity property of the Bellman functional (or cost-to-go function) is used to reduce the size of the computational problem. Some counterintuitive properties of the optimal strategy are apparent in the numerical results obtained.