Statistical Modeling of the Effectiveness of Preventive Maintenance for Repairable Systems

Abstract

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.

KEYWORDS:

• EM algorithm
• Goodness-of-fit tests
• Nonhomogeneous Poisson process
• Preventive maintenance
• Quasi-Monte Carlo method

Supplementary Materials

Supplementary document: (a) implementation details of the Bayesian estimation procedure; (b) derivations of the system ROCOF, complete-data log-likelihood function, Q-function, and the product integral term in the likelihood function; (c) discussions on the applicability of the proposed method to the non-periodic PM or condition-based PM setting; (d) comparisons between the Monte Carlo method and quasi-Monte Carlo method from both theoretical and empirical perspectives; (e) evaluation on the proximities between the observed data and the estimated models based on the martingale residuals; and (f) the additional figures and parameter estimation results.

Source code files: the R code of the proposed method in the numerical experiments (Table 4), as well as the dataset of the real case study.

Acknowledgments

The authors are grateful to the editor, an associate editor, and two anonymous referees for their valuable insights and constructive suggestions, which have considerably helped improve an earlier version of this article.

Disclosure Statement

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this article.

Additional information

Funding

This work was supported by the Future Resilient Systems project at the Singapore-ETH Centre (SEC) established by Singapore’s National Research Foundation under its CREATE programme.