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A bivariate failure time model with random shocks and mixed effects

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  • Mercier, Sophie
  • Pham, Hai Ha

Abstract

Two components are considered, which are subject to common external and possibly fatal shocks. The lifetimes of both components are characterized by their hazard rates. Each shock can cause the immediate failure of either one or both components. Otherwise, the hazard rate of each component is increased by a non fatal shock of a random amount, with possible dependence between the simultaneous increments of the two failure rates. An explicit formula is provided for the joint distribution of the bivariate lifetime. Aging and positive dependence properties are described, thereby showing the adequacy of the model as a bivariate failure time model. The influence of the shock model parameters on the bivariate lifetime is also studied. Numerical experiments illustrate and complete the study. Moreover, an estimation procedure is suggested in a parametric framework, under a specific observation scheme.

Suggested Citation

  • Mercier, Sophie & Pham, Hai Ha, 2017. "A bivariate failure time model with random shocks and mixed effects," Journal of Multivariate Analysis, Elsevier, vol. 153(C), pages 33-51.
    • Handle: RePEc:eee:jmvana:v:153:y:2017:i:c:p:33-51
    DOI: 10.1016/j.jmva.2016.09.008
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    References listed on IDEAS

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    Cited by:

    1. Gobbi, Fabio & Kolev, Nikolai & Mulinacci, Sabrina, 2021. "Ryu-type extended Marshall-Olkin model with implicit shocks and joint life insurance applications," Insurance: Mathematics and Economics, Elsevier, vol. 101(PB), pages 342-358.
    2. Sophie Mercier & Carmen Sangüesa, 2023. "A general multivariate lifetime model with a multivariate additive process as conditional hazard rate increment process," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 86(1), pages 91-129, January.
    3. Mei-Ling Ting Lee & G. A. Whitmore, 2019. "A new class of survival distribution for degradation processes subject to shocks," Journal of Statistical Distributions and Applications, Springer, vol. 6(1), pages 1-24, December.
    4. Hyunju Lee & Ji Hwan Cha, 2021. "A general multivariate new better than used (MNBU) distribution and its properties," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 84(1), pages 27-46, January.

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