Fatigue data arise in many research and applied areas and there have been statistical methods developed to model and analyze such data. The distributions of fatigue life and fatigue strength are often of interest to engineers designing products that might fail due to fatigue from cyclic-stress loading. Based on a specified statistical model and the maximum likelihood method, the cumulative distribution function (cdf) and quantile function (qf) can be estimated for the fatigue-life and fatigue-strength distributions. Likelihood-based confidence bands then can be obtained for the cdf and qf. This paper provides equivalence results for confidence bands for fatigue-life and fatigue-strength models. These results are useful for data analysis and computing implementation. We show (a) the equivalence of the confidence bands for the fatigue-life cdf and the fatigue-life qf, (b) the equivalence of confidence bands for the fatigue-strength cdf and the fatigue-strength qf, and (c) the equivalence of confidence bands for the fatigue-life qf and the fatigue-strength qf. Then we illustrate the usefulness of those equivalence results with two examples using experimental fatigue data.

翻译：疲劳数据广泛存在于众多研究与应用领域，针对此类数据的建模与分析方法已有统计学研究。在承受循环应力载荷可能发生疲劳破坏的产品设计中，工程师通常关注疲劳寿命与疲劳强度的分布特征。基于特定统计模型与极大似然方法，可对疲劳寿命分布与疲劳强度分布的累积分布函数(cdf)与分位数函数(qf)进行估计，进而获得基于似然比的累积分布函数与分位数函数置信带。本文给出了疲劳寿命与疲劳强度模型置信带的等价性结论，这些结果对数据分析与计算实现具有实用价值。我们证明了：(a)疲劳寿命累积分布函数置信带与疲劳寿命分位数函数置信带的等价性；(b)疲劳强度累积分布函数置信带与疲劳强度分位数函数置信带的等价性；(c)疲劳寿命分位数函数置信带与疲劳强度分位数函数置信带的等价性。最后通过两个实验疲劳数据实例，阐明了这些等价性结论的应用价值。