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Construction of copulas for bivariate failure rates

Author

Listed:
  • Shaomin Wu

    (University of Kent)

  • Hongyan Dui

    (Zhengzhou University)

  • Linmin Hu

    (Yanshan University)

Abstract

This paper aims to develop a method to construct an asymmetric copula, based on which a closed form of the cumulative bivariate failure rate can be obtained. The construction method differs from existing ones. This new method can facilitate the derivation of some results such as the estimation of the expected number of occurrences for a system whose failure process is modelled by a bivariate stochastic process or the expected cost in optimisation of maintenance policies.

Suggested Citation

  • Shaomin Wu & Hongyan Dui & Linmin Hu, 2024. "Construction of copulas for bivariate failure rates," Annals of Operations Research, Springer, vol. 341(2), pages 1177-1189, October.
    • Handle: RePEc:spr:annopr:v:341:y:2024:i:2:d:10.1007_s10479-024-06053-x
    DOI: 10.1007/s10479-024-06053-x
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    References listed on IDEAS

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    1. Alessandro Barbiero, 2022. "Discrete analogues of continuous bivariate probability distributions," Annals of Operations Research, Springer, vol. 312(1), pages 23-43, May.
    2. Alessandro Barbiero, 2022. "Properties and estimation of a bivariate geometric model with locally constant failure rates," Annals of Operations Research, Springer, vol. 312(1), pages 3-22, May.
    3. Wu, Shaomin, 2024. "A copula-based approach to modelling the failure process of items under two-dimensional warranty and applications," European Journal of Operational Research, Elsevier, vol. 314(3), pages 854-866.
    4. Wu, Shaomin, 2014. "Construction of asymmetric copulas and its application in two-dimensional reliability modelling," European Journal of Operational Research, Elsevier, vol. 238(2), pages 476-485.
    5. Liebscher, Eckhard, 2008. "Construction of asymmetric multivariate copulas," Journal of Multivariate Analysis, Elsevier, vol. 99(10), pages 2234-2250, November.
    6. Johnson, N. L. & Kotz, Samuel, 1975. "A vector multivariate hazard rate," Journal of Multivariate Analysis, Elsevier, vol. 5(1), pages 53-66, March.
    7. M. Kayid & Antonio Di Crescenzo, 2022. "Characterizations of the Weak Bivariate Failure Rate Order and Bivariate IFR Aging Class," Journal of Mathematics, Hindawi, vol. 2022, pages 1-9, April.
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