An Analytical Approach to Failure Prediction for Systems Subject to General Repairs

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.