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On history-dependent mixed shock models
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- Journal:
- Probability in the Engineering and Informational Sciences / Volume 36 / Issue 4 / October 2022
- Published online by Cambridge University Press:
- 06 August 2021, pp. 1080-1097
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- Article
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In this paper, we consider a history-dependent mixed shock model which is a combination of the history-dependent extreme shock model and the history-dependent
$\delta$-shock model. We assume that shocks occur according to the generalized Pólya process that contains the homogeneous Poisson process, the non-homogeneous Poisson process and the Pólya process as the particular cases. For the defined survival model, we derive the corresponding survival function, the mean lifetime and the failure rate. Further, we study the asymptotic and monotonicity properties of the failure rate. Finally, some applications of the proposed model have also been included with relevant numerical examples.
