In this paper, we discuss stochastic orderings of lifetimes of two heterogeneous parallel and series systems with heterogeneous dependent components having generalized Birnbaum–Saunders distributions. The comparisons presented here are based on the vector majorization of parameters. The ordering results are established in some special cases for the generalized Birnbaum–Saunders distribution based on the multivariate elliptical, normal, t, logistic, and skew-normal kernels. Further, we use these results by considering Archimedean copulas to model the dependence structure among systems with generalized Birnbaum–Saunders components. These results have been used to derive some upper and lower bounds for survival functions of lifetimes of parallel and series systems.

中文翻译：

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包含具有广义 BIRNBAUM-SAUNDERS 分布的异构相关组件的并联和串联系统寿命的随机排序

在本文中，我们讨论了具有广义 Birnbaum-Saunders 分布的异构依赖组件的两个异构并行和串联系统的生命周期的随机排序。这里提出的比较是基于参数的向量主要化。排序结果是在一些特殊情况下基于多元椭圆、正态、吨，逻辑和偏斜正态内核。此外，我们通过考虑 Archimedean copulas 来使用这些结果来模拟具有广义 Birnbaum-Saunders 组件的系统之间的依赖结构。这些结果已被用于推导出并联和串联系统寿命生存函数的一些上限和下限。