Determination of the fatigue P-S-N curves – A critical review and improved backward statistical inference method

•The optimal fatigue parameters for the small-number samples were acquired by using the search path searching to quantify the lifetime with stress levels.•The equivalent lives corresponding to different stress levels could be well correlated with the fatigue data under the highest stress level.•The predicted fatigue P-S-N curves were more accurate with small-number data at the low stress level when considering the variable standard deviation.•For small sample fatigue data, improved backward statistical inference approach can achieve more conservative fatigue life curves than the traditional group method. To increase the prediction accuracy of small-number sample life data, improved backward statistical inference approach (ISIA) was formulated using the modified distribution coefficients while fitting the fatigue probabilistic S-N (P-S-N) curve. Based on the search path searching for fatigue parameters, the novel scheme captures the optimal coefficients that can efficiently correlate the life distribution and stress levels. The equivalent lives can be obtained through the conversion of fatigue life to the highest stress level. To acquire a realistic P-S-N curve of full-scale components, the life distribution effect of small-number samples can be considered when fitting curves. Results show that for a set of data with an accurate standard deviation at the first stress level, the predicted lifetime using the ISIA is approximately 8.7% of the conventional group method and is only 10.5% of the original backwards statistical inference method. Meanwhile, by comparing the predicted results with the fatigue life testing data of full-scale alloy steel EA4T axles, the accuracy of fatigue P-S-N curves by using ISIA is further confirmed. For the modern axle materials and welded structures widely used in railway vehicles, the newly-proposed ISIA can not only achieve a reliable fatigue life, particularly in the high cycle fatigue regime, but also provide a more conservative fatigue P-S-N curve than traditional fitting methods.