In this paper, delta and extreme shock models and a mixed shock model which combines delta-shock and extreme shock models are studied. In particular, the interarrival times between successive shocks are assumed to belong to a class of matrix-exponential distributions which is larger than the class of phase-type distributions. The Laplace -Stieltjes transforms of the systems’ lifetimes are obtained in a matrix form. Survival functions of the systems are approximated based on the Laplace-Stieltjes transforms. The results are applied for the reliability evaluation of a certain repairable system consisting of two components.

中文翻译：

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一类特殊的冲击时间分布的冲击模型评估

在本文中，研究了δ和极限冲击模型以及结合了delta-shock和极限冲击模型的混合冲击模型。特别地，假设连续的冲击之间的到达间隔时间属于一类矩阵指数分布，该矩阵指数分布大于相类型分布的类别。系统寿命的Laplace -Stieltjes变换以矩阵形式获得。系统的生存功能是基于Laplace-Stieltjes变换进行估算的。该结果用于由两个部分组成的某个可修复系统的可靠性评估。