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Shock models and the MIFRA property

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  • Savits, Thomas H.
  • Shaked, Moshe

Abstract

Marshall and Shaked [6] have shown that some multivariate life distributions obtained from their shock model satisfy the IFRA conditions A and B of Esary and Marshall [5]. Block and Savits [2] have introduced a multivariate IFRA condition which is stronger than Conditions A and B. In this paper it is shown that the multivariate life distributions of Marshall and Shaked actually satisfy the Block-Savits MIFRA condition. As a consequence it follows that the damage processes associated with the Marshall-Shaked shock models are multivariate strongly IFRA in the sense of Block and Savits [3].

Suggested Citation

  • Savits, Thomas H. & Shaked, Moshe, 1981. "Shock models and the MIFRA property," Stochastic Processes and their Applications, Elsevier, vol. 11(3), pages 273-283, August.
    • Handle: RePEc:eee:spapps:v:11:y:1981:i:3:p:273-283
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    Cited by:

    1. Ji Cha & Maxim Finkelstein, 2015. "A dynamic stress–strength model with stochastically decreasing strength," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 78(7), pages 807-827, October.
    2. Li, Haijun & Xu, Susan H., 2001. "Stochastic Bounds and Dependence Properties of Survival Times in a Multicomponent Shock Model," Journal of Multivariate Analysis, Elsevier, vol. 76(1), pages 63-89, January.
    3. Pellerey, Franco, 1999. "Stochastic Comparisons for Multivariate Shock Models," Journal of Multivariate Analysis, Elsevier, vol. 71(1), pages 42-55, October.

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