Nonzero repair times dependent on the failure hazard

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  • Richard Arnold
    School of Mathematics and Statistics Victoria University of Wellington Wellington New Zealand
  • Stefanka Chukova
    School of Mathematics and Statistics Victoria University of Wellington Wellington New Zealand
  • Yu Hayakawa
    School of International Liberal Studies Waseda University Tokyo Japan
  • Sarah Marshall
    School of Mathematics and Statistics Auckland University of Technology Auckland New Zealand

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<jats:title>Abstract</jats:title><jats:p>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.</jats:p>

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