A Weibull-based Recurrent Regression Model for Repairable Systems Considering Double Effects of Operation and Maintenance: A Case Study of Machine Tools

Abstract The failure processes of repairable systems may be impacted by operational conditions and repair activities. In reliability engineering, many real-life data have a bathtub-shaped failure intensity (FI). In order to handle the relationship between the effects of operational conditions and maintenance and bathtub-shaped FI, this paper proposes a double effects regression model in the context of the Weibull-based general renewal process. The model considers the multiplicative and cumulative effects of operational conditions, indicating both scale and shape parameters of the underlying Weibull distribution can potentially change with operational covariates and virtual age. It extends a recurrent regression model to the case of a bathtub-shaped FI and further provides more flexible FI shapes by setting different ranges of effect coefficients. An efficient parameter estimation procedure is illustrated to support the application of the proposed model. The proposed model is shown to more closely describe the bathtub-shaped failure process through several simulated and real-life examples.