Optimal replacement policy under a general failure and repair model: Minimal versus worse than old repair

F. G. Badía, M. D. Berrade, Ji Hwan Cha, Hyunju Lee

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30 Scopus citations


We analyze the optimal replacement policy for a system subject to a general failure and repair model. Failures can be of one of two types: catastrophic or minor. The former leads to the replacement of the system, whereas minor failures are followed by repairs. The novelty of the proposed model is that, after repair, the system recovers the operational state but its condition is worse than that just prior to failure (worse than old). Undertrained operators or low quality spare parts explain this deficient maintenance. The corresponding failure process is based on the Generalized Pólya Process which presents both the minimal repair and the perfect repair as special cases. The system is replaced by a new one after the first catastrophic failure, and also undergoes two sorts of preventive maintenance based on age and after a predetermined number of minor failures whichever comes first. We derive the long-run average cost rate and study the optimal replacement policy. Some numerical examples illustrate the comparison between the as bad-as-old and the worse than old conditions.

Original languageEnglish
Pages (from-to)362-372
Number of pages11
JournalReliability Engineering and System Safety
StatePublished - Dec 2018

Bibliographical note

Funding Information:
The work of F.G. Badía and M.D. Berrade has been supported by the Spanish Ministry of Economy and Competitiveness under Project MTM2015-63978-P. The work of Ji Hwan Cha was supported by Priority Research Centers Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology ( 2009-0093827 ). The authors acknowledge the helpful comments of the editor and anonymous reviewers which significantly improved the paper.

Publisher Copyright:
© 2018 Elsevier Ltd


  • Generalized Pólya Process
  • Maintenance
  • Optimum policy
  • Worse-than-minimal-repair


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