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The generalized renewal process (GRP) has been widely used for modeling repairable systems under general repairs. Unfortunately, most of the related work does not provide closed-form solutions for predicting the reliability metrics of such systems, such as the expected number of failures, and the expected failure intensity, at a future point in time. A technical approach reported in literature is to conduct simulations to predict the reliability metrics of interest; however, simulations can be time-consuming. To reduce computational efforts for failure prediction, we propose an analytical approach that does not rely on simulations. Our idea is to predict the system's mean residual life based on its virtual age after each repair. The predicted mean residual life is then used to determine the expected time to the next failure. To illustrate this approach, we use a log-linear failure intensity function, and provide a detailed procedure for obtaining the maximum likelihood estimates (MLE) of the model parameters. A numerical study shows that this simple yet effective approach can provide failure predictions as accurate as the simulation alternative. We then demonstrate how the proposed approach can evaluate different maintenance strategies more efficiently compared to using simulations. [ABSTRACT FROM PUBLISHER]

Numerous stochastic models for repairable systems have been developed by assuming different time trends, and repair effects. In this paper, a new general repair model based on the repair history is presented. Unlike the existing models, the closed-form solutions of the reliability metrics can be derived analytically by solving a set of differential equations. Consequently, the confidence bounds of these metrics can be easily estimated. The proposed model, as well as the estimation approach, overcomes the drawbacks of the existing models. The practical use of the proposed model is demonstrated by a much-discussed set of data. Compared to the existing models, the new model is convenient, and provides accurate estimation results. [ABSTRACT FROM AUTHOR]