Statistical Modeling and Inference of the Effectiveness of Preventive Maintenance for Repairable Systems

The random effectiveness of preventive maintenance (PM) is not negligible when enacting the periodic PM policy. Hence, it is necessary to define an index that characterizes the random effectiveness of PM in the recurrent failure data analysis. Nevertheless, with purely the recurrent failure data, it is unreasonable to preset the index by a constant without knowing the specific physical mechanism of maintenance. In this paper, we propose a model based on the non-homogeneous Poisson process to account for both the inherent wear-out and the random effectiveness of PM for repairable systems. After each PM, the rate of occurrence of failures (ROCOF) of the system is multiplied by the index, which is modeled by a random variable following a gamma distribution. The Expectation-Maximum (EM) algorithm is then leveraged to estimate the parameters of the gamma distribution and the ROCOF. We apply the quasi-Monte Carlo method to approximate the multidimensional integration in the EM algorithm. The proposed model is validated by numerical simulations based on a real-world recurrent failure dataset of ambulances.