This paper is concerned with two optimization problems for a k-out-of-n system consisting of dependent components such as finding the number of elements in the system that minimize the system’s mean cost rate and the system’s optimal replacement time. In previous studies, either system consisting of independent components or parallel systems, a particular case of the present study, was examined. In particular, we numerically examine how the components’ dependence affects the optimal number of units and replacement time for the system, minimizing mean cost rates. We consider when the components are exchangeable and dependent, that is, the system consists of dependent components. For three vastly used Clayton, Gumbel, and FGM copula functions, comparative numerical results are presented.

本文关注的是k -out-of- n 的两个优化问题由相关组件组成的系统，例如查找系统中使系统平均成本率和系统最佳更换时间最小的元素数量。在以前的研究中，检查了由独立组件或并行系统组成的系统，这是本研究的一个特殊案例。特别是，我们从数值上研究了组件的依赖性如何影响系统的最佳单元数和更换时间，从而最大限度地降低平均成本率。我们考虑什么时候组件是可交换和依赖的，即系统由依赖组件组成。对于三个广泛使用的 Clayton、Gumbel 和 FGM copula 函数，提供了比较数值结果。