On the overhaul effect for repairable mechanical units: a Bayes approach

This paper deals with the statistical analysis, from a Bayes viewpoint, of the failure data of repairable mechanical units subjected to minimal repairs and periodic overhauls. A proportional age reduction model is assumed to model the effect of overhauls on the reliability of the unit, whereas the failure process between two successive overhaul epochs is modeled by the power law process. Point and interval estimation of model parameters, as well as of quantities of large interest, are provided on the basis of a number of suitable prior densities, which reflect different degrees of belief on the failure/repair process. Hypothesis tests on the effectiveness of performed overhauls are developed on the basis of Bayes factor, and some guidelines to perform sensitivity analysis versus the prior information are provided. Finally, a numerical application illustrates the proposed inference and testing procedures.