Research on the Fitting Method for P‐S‐N Curves With Extremely Small Sample Experiment Data: Improved Backwards Statistical Inference Method

ABSTRACT This study focuses on an improved statistical processing method for extremely small sample probabilistic S‐N (P‐S‐N) curve test data and proposes an improved backwards statistical inference method. By employing a quantile consistency principle, an equivalent large sample of fatigue lives can be obtained by congregating all test data, which enables high‐precision estimation of distribution parameters with limited data at each stress level. The logarithmic life standard deviation is assumed to have a logarithmic linear relationship with the stress levels. A method for revealing the relationship is proposed, and all of the fatigue life data can be equivalently congregated to determine the P‐S‐N curve. The test results demonstrate that this improved method delivers superior fitting results compared to other methods in scenarios with extremely small sample sizes. Additionally, this method imposes no constraints on sample format and allows for flexible setting of stress levels and sample sizes.