An algorithm for estimating the effect of maintenance on aggregated covariates with application to railway switch point machines

We propose an algorithm for estimating the effectiveness of maintenance on both age and health of a system. One of the main contributions is the concept of virtual health of the device. It is assumed that failures follow a nonhomogeneous Poisson process (NHPP) and covariates follow the proportional hazards model (PHM). In particular, the effect of maintenance on device’s age is estimated using the Weibull hazard function, while the effect on device’s health and covariates associated with condition-based monitoring (CBM) is estimated using the Cox hazard function. We show that the maintenance effect on the health indicator (HI) and the virtual HI can be expressed in terms of the Kalman filter concepts. The HI is calculated from Mahalanobis distance between the current and the baseline condition monitoring data. The effect of maintenance on both age and health is also estimated. The algorithm is applied to the case of railway point machines. Preventive and corrective types of maintenance are modelled as different maintenance effect parameters. Using condition monitoring data, the HI is calculated as a scaled Mahalanobis distance. We derive reliability and likelihood functions and find the least squares estimates (LSE) of all relevant parameters, maintenance effect estimates on time and HI, as well as the remaining useful life (RUL).