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On a multivariate IFR and positively dependent lifetime model induced by multiple shot-noise processes

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  • Hyunju Lee

    (Ewha Womans University)

  • Ji Hwan Cha

    (Ewha Womans University)

Abstract

In reliability and survival analysis, the shot-noise processes have been intensively employed as a useful tool for modeling the impact of a dynamic environment (in the form of the point process of stresses) on survival characteristics of systems and organisms. However, the studies on the shot-noise processes have been mostly focused on the univariate analysis. In this paper, we develop a class of multivariate stochastic failure models based on a dynamic shock model induced by multiple shot-noise processes and study its properties. Explicit parametric forms for the multivariate survival functions are suggested. Multivariate ageing properties and dependence structures of the class are discussed as well.

Suggested Citation

  • Hyunju Lee & Ji Hwan Cha, 2021. "On a multivariate IFR and positively dependent lifetime model induced by multiple shot-noise processes," Statistical Papers, Springer, vol. 62(2), pages 561-590, April.
    • Handle: RePEc:spr:stpapr:v:62:y:2021:i:2:d:10.1007_s00362-019-01099-7
    DOI: 10.1007/s00362-019-01099-7
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    References listed on IDEAS

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    1. Toshio Nakagawa, 2007. "Shock and Damage Models in Reliability Theory," Springer Series in Reliability Engineering, Springer, number 978-1-84628-442-7, June.
    2. Montoro-Cazorla, Delia & Pérez-Ocón, Rafael, 2011. "Two shock and wear systems under repair standing a finite number of shocks," European Journal of Operational Research, Elsevier, vol. 214(2), pages 298-307, October.
    3. Xiaohu Li & Guoxin Qiu, 2007. "Some preservation results of NBUC aging property with applications," Statistical Papers, Springer, vol. 48(4), pages 581-594, October.
    4. Arjun Gupta & Johanna Orozco-Castañeda & Daya Nagar, 2011. "Non-central bivariate beta distribution," Statistical Papers, Springer, vol. 52(1), pages 139-152, February.
    5. Maxim Finkelstein & Ji Hwan Cha, 2013. "Burn-in for Heterogeneous Populations," Springer Series in Reliability Engineering, in: Stochastic Modeling for Reliability, edition 127, chapter 0, pages 261-312, Springer.
    6. Ji Hwan Cha & Maxim Finkelstein, 2013. "On generalized shock models for deteriorating systems," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 29(5), pages 496-508, September.
    7. D. Al-Mutairi & M. Ghitany & D. Kundu, 2011. "A new bivariate distribution with weighted exponential marginals and its multivariate generalization," Statistical Papers, Springer, vol. 52(4), pages 921-936, November.
    8. Maxim Finkelstein & Ji Hwan Cha, 2013. "Shocks as Burn-in," Springer Series in Reliability Engineering, in: Stochastic Modeling for Reliability, edition 127, chapter 0, pages 313-361, Springer.
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