Many systems experience gradual degradation while simultaneously being exposed to a stream of random shocks of varying magnitudes that eventually cause failure when a shock exceeds the residual strength of the system. In this paper, we present a family of stochastic processes, called shock-degradation processes, that describe this failure mechanism. In our failure model, system strength follows a geometric degradation process. The degradation process itself is any Lévy process, that is, any stochastic process with stationary independent increments. The shock stream is a Fréchet stochastic process, a process derived from the Fréchet extreme-value distribution. Finally, the shock-degradation process is a convolution of the Fréchet shock process and any one of the candidate degradation processes. The system fails at the first occasion when a shock takes system strength across a threshold at zero. The paper presents results for Wiener diffusion processes and gamma processes as examples of Lévy degradation processes. The paper develops key statistical properties of the process model and its survival distribution, including several that are important for its practical application. As the failure mechanism is a first hitting time event, applications that require regression structures fall within the domain of threshold regression methodology.

中文翻译：

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遭受冲击的降解过程的新型生存分布

许多系统会逐渐退化，同时会受到一系列大小不定的随机冲击的冲击，当冲击超过系统的剩余强度时，这些冲击最终会导致故障。在本文中，我们介绍了描述这种失效机制的一系列随机过程，称为冲击降解过程。在我们的故障模型中，系统强度遵循几何退化过程。降级过程本身是任何Lévy过程，即具有固定独立增量的任何随机过程。冲击流是Fréchet随机过程，该过程是从Fréchet极值分布得出的。最后，冲击降解过程是Fréchet冲击过程与任何候选退化过程的卷积。当电击使系统强度超过零阈值时，系统首次出现故障。本文介绍了维纳扩散过程和伽马过程的结果，作为李维降解过程的例子。本文开发了过程模型及其生存分布的关键统计属性，包括对其实际应用很重要的几个属性。由于故障机制是最重要的事件，因此需要回归结构的应用程序属于阈值回归方法论的范畴。包括对其实际应用很重要的几种。由于故障机制是最重要的事件，因此需要回归结构的应用程序属于阈值回归方法论的范畴。包括对其实际应用很重要的几种。由于故障机制是最重要的事件，因此需要回归结构的应用程序属于阈值回归方法论的范畴。