Condition-based maintenance for systems with aging and cumulative damage based on proportional hazards model

Bin Liu, Zhenglin Liang, Ajith Kumar Parlikad, Min Xie, Way Kuo

Research output: Contribution to journalArticlepeer-review

44 Citations (Scopus)
11 Downloads (Pure)


This paper develops a condition-based maintenance (CBM) policy for systems subject to aging and cumulative damage. The cumulative damage is modeled by a continuous degradation process. Different from previous studies which assume that the system fails when the degradation level exceeds a specific threshold, this paper argues that the degradation itself does not directly lead to system failure, but increases the failure risk of the system. Proportional hazards model (PHM) is employed to characterize the joint effect of aging and cumulative damage. CBM models are developed for two cases: one assumes that the distribution parameters of the degradation process are known in advance, while the other assumes that the parameters are unknown and need to be estimated during system operation. In the first case, an optimal maintenance policy is obtained by minimizing the long-run cost rate. For the case with unknown parameters, periodic inspection is adopted to monitor the degradation level of the system and update the distribution parameters. A case study of Asphalt Plug Joint in UK bridge system is employed to illustrate the maintenance policy.
Original languageEnglish
Pages (from-to)200-209
Number of pages10
JournalReliability Engineering and System Safety
Early online date13 Apr 2017
Publication statusPublished - 31 Dec 2017


  • Condition-based maintenance
  • aging and degradation
  • proportional hazards model
  • unknown distribution parameters
  • cumulative damage

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