Abstract: The traditional Bootstrap method, when applied to small-sample fatigue test data, is limited by the fact that it can only resample from the original data, thereby constraining the amount of available information. To overcome this limitation, it is proposed to introduce grey system theory to process small-sample data by establishing grey differential equations that uncover hidden relationships within the original data, thus extracting additional implicit information. First, the original data are processed using grey system theory. Secondly, the bootstrap method is used to sample the processed data to obtain regenerated samples. Finally, the P-S-N curve of the small sample data was obtained by reprocessing the regenerated data. Through validation analysis, compared with the Bootstrap method, the grey Bootstrap method proposed in this paper has higher accuracy in processing the small sample P-S-N curve.

Key words: small samples, Bootstrap method, gray system theory, P-S-N curve