In this paper, we investigate systems subject to random shocks that are classified into critical and noncritical categories, and develop two novel critical shock models. Classical extreme shock models and run shock models are special cases of our developed models. The system fails when the total number of critical shocks reaches a predetermined threshold, or when the system stays in an environment that induces critical shocks for a preset threshold time, corresponding to failure mechanisms of the developed two critical shock models respectively. Markov renewal processes are employed to capture the magnitude and interarrival time dependency of environment-induced shocks. Explicit formulas for systems under the two critical shock models are derived, including the reliability function, the mean time to failure and so on. Furthermore, the two critical shock models are extended to the random threshold case and the integrated case where formulas of the reliability indexes of the systems are provided. Finally, a case study of a lithium-ion battery system is conducted to illustrate the proposed models and the obtained results.

中文翻译：

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两种基于马尔可夫更新过程的新型临界冲击模型

在本文中，我们研究了受到随机冲击的系统，这些系统分为临界和非临界类别，并开发了两种新颖的临界冲击模型。经典的极端冲击模型和运行冲击模型是我们开发的模型的特例。当临界冲击的总数达到预定阈值时，或者当系统停留在诱发临界冲击的环境中达到预设的阈值时间时，系统就会失效，分别对应于所开发的两个临界冲击模型的失效机制。马尔可夫更新过程用于捕捉环境引起的冲击的幅度和到达间隔时间依赖性。推导出了两种临界冲击模型下系统的显式公式，包括可靠性函数、平均无故障时间等。此外，将两种临界冲击模型推广到随机阈值情况和综合情况，给出了系统可靠性指标的计算公式。最后，对锂离子电池系统进行了案例研究，以说明所提出的模型和获得的结果。