On the prediction of future failures for a repairable equipment subject to overhauls

This paper deals with the prediction, from a Bayes viewpoint, of future failures for a repairable equipment subjected both to minimal repairs and periodic overhauls. The effect of major overhauls on the reliability of the equipment is modeled by a proportional age reduction model, while the failure process between two successive overhaul epochs is modeled by the power law process. Prediction both of the future failure times and of the number of failures in a future time interval are provided on the basis of the observed data and of a number of suitable prior densities, which reflect different degrees of belief on the failure mechanism and overhaul effectiveness. Finally, a numerical application illustrates the proposed prediction procedures and their use in assessing the adequacy of the model to describe the observed data set.