标题： 在随机冲击下阿基米德copula中串联和并联系统寿命的随机比较 显示英文标题

标题： Stochastic comparison of series and parallel systems lifetime in Archimedean copula under random shock

摘要： 本文研究了由具有相依性和异质性部件组成的串联系统和平联系统的寿命，这些系统经历随机冲击，并表现出不同的相依结构。 我们确立了关于单个部件寿命的某些条件，其中部件之间的相依性由阿基米德copulas定义，以及随机冲击对整个系统寿命的影响，以得出结果。 我们考虑的部件生存函数是所涉及参数的增加对数凹函数或减少对数凸函数。 这些条件使得可以使用通常的随机顺序框架来比较两个系统的寿命。 此外，我们提供了示例和图形表示来阐明我们的理论发现。 显示英文摘要

摘要： In this paper, we studied the stochastic ordering behavior of series as well as parallel systems' lifetimes comprising dependent and heterogeneous components, experiencing random shocks, and exhibiting distinct dependency structures. We establish certain conditions on the lifetime of individual components where the dependency among components defined by Archimedean copulas, and the impact of random shocks on the overall system lifetime to get the results. We consider components whose survival functions are either increasing log-concave or decreasing log-convex functions of the parameters involved. These conditions make it possible to compare the lifetimes of two systems using the usual stochastic order framework. Additionally, we provide examples and graphical representations to elucidate our theoretical findings.