In this article, we study a load-sharing redundancy system in the presence of statistical dependence between base and redundancy component lifetimes when they are under partial workload. We derive the system reliability function in terms of reliability functions and the copula function of the base and redundancy component lifetimes. Further, in the setting of some aging properties, the base component and absolute continuous copula, we develop the hazard rate order, the reversed hazard rate order, and the likelihood ratio order between the system lifetime and the base component lifetimes. Two typical scenarios with independence between the base and redundancy component lifetimes are discussed in particular. Several numerical examples are presented to illustrate the theoretical findings as well.

中文翻译：

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具有统计相关冗余的负载共享系统的随机比较

在本文中，我们研究了负载共享冗余系统，当它们在部分工作负载下时，基本组件和冗余组件的寿命之间存在统计相关性。我们根据可靠性函数和基本和冗余组件寿命的 copula 函数推导出系统可靠性函数。此外，在设置一些老化属性、基础组件和绝对连续 copula 时，我们开发了系统寿命和基础组件寿命之间的危险率顺序、反向危险率顺序和似然比顺序。特别讨论了基本和冗余组件寿命之间独立的两种典型情况。给出了几个数值例子来说明理论发现。