Nonzero repair times dependent on the failure hazard

Richard Arnold*, Stefanka Chukova, Yu Hayakawa, Sarah Marshall

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


It is common in the literature on the reliability and maintenance of repairable systems to model the repair times as instantaneous. However, this is an unreasonable assumption for some complex systems, especially those requiring a high level of reliability, and such systems may spend a significant proportion of their lifetimes under maintenance and repair. We model the ageing of such a system with alternating stochastic processes. Operational times are generated at random and may have an increasing failure rate. Repair times are generated from a random process where the repair time is related to the hazard rate at failure. This yields lengthened repair times at late stages in a system subject to an increasing failure hazard rate but also accommodates long repair times at young ages in systems with a bathtub-shaped hazard rate function. We derive analytic results for a set of special cases of the model, show how simulation and inference can be carried out, and apply our method to real data from a large car manufacturer.

Original languageEnglish
Pages (from-to)988-1004
Number of pages17
JournalQuality and Reliability Engineering International
Issue number3
Publication statusPublished - 2020 Apr 1


  • bathtub hazard rate
  • failure distributions
  • nonzero repair times
  • stochastic process
  • warranty analysis

ASJC Scopus subject areas

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


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