Two-threshold control limit policy in condition-based maintenance

Ahmad Al Hanbali*, Haitham Saleh, Noman Ullah

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

3 Scopus citations


In this paper, we consider a component exhibiting a continuous monotone degradation modeled as a Gamma process. The maintenance policy is of condition-based type with periodic inspections. It follows the two threshold control limit policy with a preventive maintenance limit, a switching limit, and a given failure limit. Our interest is to minimize the annual expected maintenance cost subject to a constraint on the average availability. The decision variables are the preventive limit, the switching limit, and the inspections schedule. We derive exact results for the key performance indicators, but since they are numerically involved, we propose a simple, that is, involving necessary spreadsheet calculations, accurate approximation. We apply our model to a case from the process industry, namely, a carbon steel hydrogen dryer consisting of a cylindrical pressure vessel. This vessel suffers from corrosion with thickness growth modeled as a Gamma process. The optimization results show that although the annual maintenance cost increases with the mean and the coefficient of variation of the yearly corrosion thickness, its mean has a higher impact on cost. Based on the cost sensitivity analysis, we find that the impact of a vast increase of the corrective maintenance cost for the same inspection and preventive costs can be mitigated by appropriately reducing the corrective maintenance probability. Finally, we empirically show that the two threshold policy achieves an annual cost savings up to (Formula presented.) compared to the single threshold policy.

Original languageEnglish
Pages (from-to)2170-2187
Number of pages18
JournalQuality and Reliability Engineering International
Issue number4
StatePublished - Jun 2022

Bibliographical note

Funding Information:
The authors would like to thank the deanship of scientific research at King Fahd University of Petroleum and Minerals for their support under Grant SR181012.

Publisher Copyright:
© 2022 John Wiley & Sons Ltd.


  • Gamma process
  • condition-based maintenance
  • control limit policy
  • optimization
  • periodic monitoring

ASJC Scopus subject areas

  • Safety, Risk, Reliability and Quality
  • Management Science and Operations Research


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