Abstract Considering the unconvincing results produced by probability theory when dealing with small sample data, this paper introduces uncertainty theory (a branch of axiomatic mathematics parallel to probability theory) to model and estimate the uncertainty of fatigue life with the small sample of fatigue test data. A new method called α -S-N curves is firstly proposed to describe the relationship between fatigue life and stress levels. Subsequently, general procedures are established for the determination of α -S-N curves based on the four basic assumptions to improve the information utilized in the estimation process and overcome the large-scatter of the small sample fatigue failure data. Finally, the developed procedures are verified by the data of aluminum alloy data and laminate panel data. The precision and stability of the developed procedures are validated by the index relative slope in comparison with the method stated in ISO 12107.

中文翻译：

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α-SN曲线：一种新的基于不确定性理论的小样本测试数据下的SN曲线建模方法

摘要 考虑到概率论在处理小样本数据时产生的结果不令人信服，本文引入不确定性理论（与概率论平行的公理数学的一个分支），对疲劳试验数据小样本的疲劳寿命不确定度进行建模和估计。首次提出了一种称为α-SN曲线的新方法来描述疲劳寿命与应力水平之间的关系。随后，基于四个基本假设建立了确定 α -SN 曲线的一般程序，以改进估计过程中使用的信息并克服小样本疲劳失效数据的大分散。最后，通过铝合金数据和层压板数据对开发的程序进行了验证。