A random walk model for a multi-component deteriorating system

We consider a Markovian l-unit system which is subject to shocks causing it to deteriorate in each of its stochastically dependent components. The net reward produced by the system is assumed to be an l-dimensional function of the amounts of deterioration of the components. After every shock the controller has the option to replace the system by a new one. The objective is to maximize the long-run average reward. Under natural conditions we prove the existence of an optimal control-limit policy and the unimodality of the long-term reward as a function of the threshold value.