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.

在本文中，我们考虑了一个历史相关的混合冲击模型，它是历史相关的极端冲击模型和历史相关的$\delta$ -shock模型的组合。我们假设冲击发生在广义 Pólya 过程中，包括齐次 Poisson 过程、非齐次 Poisson 过程和 Pólya 过程作为特例。对于定义的生存模型，我们推导出相应的生存函数、平均寿命和故障率。此外，我们研究了故障率的渐近性和单调性特性。最后，提出的模型的一些应用也包括在相关的数值例子中。