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.

预防性维护（Preventive Maintenance，以下简称PM）在工程实践中被广泛应用，旨在改善系统健康状态并降低突发故障发生风险。然而，若PM作业执行不当，则可能对系统可靠性产生负面影响。我们基于某服务车辆车队四年的运行数据，对其PM方案的有效性开展评估时，便观察到了这一现象。该现象在车辆与航空器的维护领域亦有诸多报道。受此观察结果启发，我们将PM可能带来的负面影响纳入考量，针对可修复系统提出了一种统计模型。在该模型的构建中，未受PM影响的基准故障过程采用非齐次泊松过程（Nonhomogeneous Poisson Process）进行建模。当执行PM作业时，其对故障过程的影响被建模为对系统故障发生率的乘性随机效应。本文探讨了该模型下的统计推断方法，并进一步构建了拟合优度检验流程，以验证该模型的适用性。上述服务车辆运行数据集被用于验证所提方法的有效性。