We consider coherent systems with independent and identically distributed components. While it is clear that the system’s life will be stochastically larger when the components are replaced with stochastically better components, we show that, in general, similar results may not hold for hazard rate, reverse hazard rate, and likelihood ratio orderings. We find sufficient conditions on the signature vector for these results to hold. These results are combined with other well-known results in the literature to get more general results for comparing two systems of the same size with different signature vectors and possibly with different independent and identically distributed component lifetimes. Some numerical examples are also provided to illustrate the theoretical results.

中文翻译：

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使用签名的相干系统随机比较的一些新结果

我们考虑具有独立且相同分布的组件的相干系统。虽然很明显，当用随机更好的组件替换组件时，系统的寿命会随机变长，但我们表明，一般而言，类似的结果可能不适用于风险率、反向风险率和似然比排序。我们在签名向量上找到了足以使这些结果成立的条件。这些结果与文献中其他众所周知的结果相结合，以获得更通用的结果，用于比较具有不同特征向量以及可能具有不同独立且相同分布的组件寿命的两个相同大小的系统。还提供了一些数值例子来说明理论结果。