Two definitions of Birnbaum’s importance measure for coherent systems are studied in the case of exchangeable components. Representations of these measures in terms of distribution functions of the ordered component lifetimes are given. As an example, coherent systems with failure-dependent component lifetimes based on the notion of sequential order statistics are considered. Furthermore, it is shown that the two measures are ordered in the case of associated component lifetimes. Finally, the limiting behavior of the measures with respect to time is examined.

中文翻译：

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具有可交换组件的相干系统的组件重要性表示

在可交换组件的情况下，研究了相干系统的 Birnbaum 重要性度量的两个定义。给出了这些度量在有序组件寿命分布函数方面的表示。例如，考虑基于顺序统计概念的具有与故障相关的组件寿命的相干系统。此外，这表明在相关组件寿命的情况下，这两个度量是有序的。最后，检查措施相对于时间的限制行为。