The preservation of stochastic orders by distortion functions has become a topic of increasing interest in the reliability analysis of coherent systems. The reason of this interest is that the reliability function of a coherent system with identically distributed components can be represented as a distortion function of the common reliability function of the components. In this framework, we study the preservation of the excess wealth order, the total time on test transform order, the decreasing mean residual live order, and the quantile mean inactivity time order by distortion functions. The results are applied to study the preservation of these stochastic orders under the formation of coherent systems with exchangeable components.

中文翻译：

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通过失真函数保留某些随机阶，并将其应用于具有可交换组件的相干系统

通过失真函数来保持随机阶数已经成为对相干系统的可靠性分析越来越感兴趣的话题。引起这种关注的原因是，具有相同分布的组件的相干系统的可靠性函数可以表示为组件的通用可靠性函数的失真函数。在此框架中，我们研究了畸变函数对超额财富阶数的保留，测试变换阶数上的总时间，平均剩余剩余生存阶数减少以及分位数平均非活动时间阶数。研究结果被用于研究在具有可交换成分的相干系统的形成下这些随机序的保存。