Statistical Modeling of the Effectiveness of Preventive Maintenance for Repairable Systems

Preventive maintenance (PM) is commonly adopted in practice to improve a system’s health condition and reduce the risk of unexpected failures. When a PM action is poorly performed, however, it is likely to have adverse effects on system reliability. We observe this phenomenon when evaluating the effectiveness of a PM program for a fleet of service vehicles based on their four-year operating data. This phenomenon is also commonly reported in the maintenance of vehicles and aircraft. Motivated by this observation, we propose a statistical model for repairable systems by taking potential PM adverse effects into account. In the formulation, the baseline failure process without PM effects is modeled by a nonhomogeneous Poisson process. When a PM action is performed, its effect on the failure process is modeled as a multiplicative random effect on the system rate of occurrence of failures. Statistical inference under the proposed model is discussed, and we further develop goodness-of-fit test procedures to validate the adequacy of this model. The above-mentioned service vehicle operating data are used to demonstrate the proposed methods.