In this paper, particular shock models are studied for the case when the times between successive shocks and the magnitudes of shocks have discrete phase-type distributions. The well-known shock models such as delta shock model, extreme shock model, and the mixed shock model which is obtained by combining delta and extreme shock models are considered. The probability generating function and recursive equation for the distribution of the system's lifetime are obtained for the cases when the interarrival times between shocks and the magnitudes of shocks are independent and when they are dependent. System reliability is computed for particular interarrival distributions such as geometric, negative Binomial and generalized geometric distributions.

中文翻译：

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通过相型分布对离散时间冲击模型进行可靠性评估

在本文中，针对连续冲击之间的时间和冲击的幅度具有离散相位型分布的情况，研究了特定的冲击模型。考虑了著名的冲击模型，如 delta 冲击模型、极端冲击模型以及 delta 和极端冲击模型结合得到的混合冲击模型。分别在冲击间隔时间与冲击强度独立和相互依赖的情况下，得到了系统寿命分布的概率生成函数和递推方程。系统可靠性是针对特定的到达间隔分布计算的，例如几何分布、负二项分布和广义几何分布。