In δ-shock modeling, the life behavior of systems suffering from random shocks depends on the length of inter-arrival times between successive shocks. In this paper, a generalized version of the classical δ-shock model is studied, under which the system fails when the inter-arrival time falls in the interval [α,δ] for 0≤α<δ. Furthermore, with an innovative approach, the classical δ-shock model is studied under this new assumption that the inter-arrival times are overdispersed in the critical interval of the model. This is a new assumption compared to the traditional assumptions in the context of shock models and actually introduces a situation wherein the system is under pressure to fail. Under this assumption, two situations are considered for the system, which are regular and critical situations, and then the reliability behavior of the system's lifetime is investigated under these situations. Some examples are also provided to illustrate the theoretical results of the application.

中文翻译：

---

δ 冲击建模的一些新方法


在 δ 冲击建模中，遭受随机冲击的系统的寿命行为取决于连续冲击之间的到达时间间隔的长度。本文研究了经典 δ 冲击模型的广义版本，在该模型下，当到达间隔时间落入区间 [α,δ]（0≤α<δ）时系统就会失效。此外，采用创新方法，在模型临界区间内到达间隔时间过度分散的新假设下研究了经典δ冲击模型。与冲击模型背景下的传统假设相比，这是一个新的假设，并且实际上引入了系统面临失败压力的情况。在此假设下，系统考虑两种情况，即常规情况和临界情况，然后研究这些情况下系统寿命的可靠性行为。还提供了一些例子来说明应用的理论结果。