Functional estimation for a multicomponent age replacement model

We consider a multicomponent system with identical components subject to failures, controlled by a replacement rule based on age thresholds. We show how to estimate the expected cost of operating the system as a function of one of the thresholds, in functional form, by simulation. The efficiency of the approach is analyzed for two types of performance measures of the system: (i) The total expected cost over a finite time horizon and (ii) the average cost over an infinite time horizon. For the average cost case, we show under mild conditions that the system is geometrically ergodic, uniformly over the parameter set of interest. Our numerical illustrations suggest that the proposed approach is viable from the practical viewpoint.