This paper studies the optimal allocation policy of a coherent system with independent heterogeneous components and dependent subsystems, the systems are assumed to consist of two groups of components whose lifetimes follow proportional hazard (PH) or proportional reversed hazard (PRH) models. We investigate the optimal allocation strategy by finding out the number $k$ of components coming from Group A in the up-series system. First, some sufficient conditions are provided in the sense of the usual stochastic order to compare the lifetimes of two-parallel–series systems with dependent subsystems, and we obtain the hazard rate and reversed hazard rate orders when two subsystems have independent lifetimes. Second, similar results are also obtained for two-series–parallel systems under certain conditions. Finally, we generalize the corresponding results to parallel–series and series–parallel systems with multiple subsystems in the viewpoint of the minimal path and the minimal cut sets, respectively. Some numerical examples are presented to illustrate the theoretical findings.

本文研究了具有独立异构组件和依赖子系统的相干系统的最优分配策略，假设系统由两组组件组成，其寿命遵循比例风险（PH）或比例反向风险（PRH）模型。我们通过找出数字$k$来研究最优分配策略来自上系列系统中 A 组的组件。首先，在通常的随机顺序意义上提供了一些充分条件来比较具有依赖子系统的两个并联-串联系统的寿命，并且我们得到了当两个子系统具有独立寿命时的危险率和逆向危险率顺序。其次，在某些条件下，双串并联系统也获得了类似的结果。最后，我们分别从最小路径和最小割集的角度将相应的结果推广到具有多个子系统的并联-串联和串-并系统。给出了一些数值例子来说明理论发现。