This paper deals with the Bayes prediction of the future failures of a deteriorating repairable mechanical system subject to minimal repairs and periodic overhauls. To model the effect of overhauls on the reliability of the system a proportional age reduction model is assumed and the 2-parameter Engelhardt-Bain process (2-EBP) is used to model the failure process between two successive overhauls. 2-EBP has an advantage over Power Law Process (PLP) models. It is found that the failure intensity of deteriorating repairable systems attains a finite bound when repeated minimal repair actions are combined with some overhauls. If such a data is analyzed through models with unbounded increasing failure intensity, such as the PLP, then pessimistic estimates of the system reliability will arise and incorrect preventive maintenance policy may be defined. On the basis of the observed data and of a number of suitable prior densities reflecting varied degrees of belief on the failure/repair process and effectiveness of overhauls, the prediction of the future failure times and the number of failures in a future time interval is found. Finally, a numerical application is used to illustrate the advantages from overhauls and sensitivity analysis of the improvement parameter carried out. 1. Introduction A repairable system is a system that, after failing to perform one or more of its functions satisfactorily, can be restored to satisfactory performance. Most repairable mechanical systems are subjected to degradation phenomena with operating time, so that the failures become increasingly frequent with time. Such systems often undergo a maintenance policy. Maintenance extends system's lifetime or at least the mean time to failure, and an effective maintenance policy can reduce the frequency of failures and the undesirable consequences of such failures. Maintenance can be categorized into two classes: corrective and preventive actions. Corrective maintenance, called repair, is all actions performed to restore the system to functioning condition when it fails. Preventive maintenance is all actions performed to prevent failures when the system is operating. Corrective and preventive maintenance actions are generally classified in terms of their effect on the operating conditions of the system. Pham and Wang [1] classified them as perfect maintenance, minimal maintenance, imperfect maintenance, and worse maintenance. At one extreme is the assumption of perfect maintenance, that a system is restored to good-as-new condition after maintenance. At the other extreme is the
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