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Steady-state imperfect repair models

Author

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  • Liu, Xingheng
  • Finkelstein, Maxim
  • Vatn, Jørn
  • Dijoux, Yann

Abstract

Imperfect maintenance models are widely used in reliability engineering. This paper discusses relevant asymptotic properties for the steady-state virtual age processes. It is shown that the limiting distributions of age, the residual lifetime and the spread that describe an ordinary renewal process can be generalized to the stable virtual age process, although the cycles of the latter are not independent. Asymptotic distributions of the virtual age at time t, as well as of the virtual ages at the start and the end of a cycle containing t (as t tends to infinity) are explicitly derived for two popular in practice imperfect maintenance models, namely, the Arithmetic Reduction of Age (ARA) and the Brown–Proschan (BP) models. Some applications of the obtained results to maintenance optimization are discussed.

Suggested Citation

  • Liu, Xingheng & Finkelstein, Maxim & Vatn, Jørn & Dijoux, Yann, 2020. "Steady-state imperfect repair models," European Journal of Operational Research, Elsevier, vol. 286(2), pages 538-546.
    • Handle: RePEc:eee:ejores:v:286:y:2020:i:2:p:538-546
    DOI: 10.1016/j.ejor.2020.03.057
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    References listed on IDEAS

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    2. Dimitrakos, T.D. & Kyriakidis, E.G., 2007. "An improved algorithm for the computation of the optimal repair/replacement policy under general repairs," European Journal of Operational Research, Elsevier, vol. 182(2), pages 775-782, October.
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    6. Nguyen, Dinh Tuan & Dijoux, Yann & Fouladirad, Mitra, 2017. "Analytical properties of an imperfect repair model and application in preventive maintenance scheduling," European Journal of Operational Research, Elsevier, vol. 256(2), pages 439-453.
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    Cited by:

    1. Liu, Xingheng & Vatn, Jørn & Dijoux, Yann & Toftaker, Håkon, 2020. "Unobserved heterogeneity in stable imperfect repair models," Reliability Engineering and System Safety, Elsevier, vol. 203(C).
    2. Syamsundar, A. & Naikan, V.N.A. & Wu, Shaomin, 2021. "Extended Arithmetic Reduction of Age Models for the Failure Process of a Repairable System," Reliability Engineering and System Safety, Elsevier, vol. 215(C).

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