A novel fatigue design modeling method under small-sample test data with generalized fiducial theory.

• Proposing a fiducial-based fatigue design model for small-sample test data. • The quantile score considering overestimation and underestimation impacts is employed for fatigue design validation. • The proposed method outperforms the ISO method on small and medium sample data. • The proposed method performs comparably to the ISO method on extensive data. Understanding the correlation between the fatigue life of engineering materials and the applied stress is a crucial aspect of reliability and safety design. However, small data observations frequently occur in fatigue testing due to factors like time and budget limitations, as well as constraints related to the availability of testing materials and resources. In this article, fiducial inference method is employed for modeling P - S - N curves to deal with scenarios with small sample sizes. Fiducial inference can be seen as a procedure that provides a measure within a parameter space while requiring fewer assumptions than Bayesian inference (no prior). The performance of the proposed method is evaluated by comparing it with the ISO method using statistical simulation data and aluminum alloy 2524-T3 data. In scenarios with ample data (no less than 15 observations at each of the four stress levels), the proposed fiducial-based method yields results comparable to those obtained through the ISO method. When dealing with small-sample data (around 2–4 observations for each of the four stress levels) and medium-sample data (about 5–10 observations per stress level), the proposed fiducial-based method consistently outperforms the ISO method in terms of the quantile scores (also known as pinball loss). This shows the advantageous performance of the fiducial method under conditions of limited data availability. Besides, the consistency in performance across varying data size scenarios underscores the reliability and robustness of the fiducial-based approach in estimating probabilistic S - N curves. [ABSTRACT FROM AUTHOR]