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.

翻译：失真函数对随机序的保持性已成为相干系统可靠性分析中日益受到关注的研究课题。这种关注的原因在于，具有同分布部件的相干系统的可靠性函数可以表示为部件共同可靠性函数的失真函数。在此框架下，我们研究了失真函数对超额财富序、总试验时间变换序、递减平均剩余寿命序以及分位数平均不活动时间序的保持性。所得结果被应用于研究在构建具有可交换部件的相干系统时，这些随机序的保持性。