Purpose The purpose of this paper is to introduce error ellipse into the bootstrap method to improve the reliability of small samples and the credibility of the S-N curve. Design/methodology/approach Based on the bootstrap method and the reliability of the original samples, two error ellipse models are proposed. The error ellipse model reasonably predicts that the discrete law of expanded virtual samples obeys two-dimensional normal distribution. Findings By comparing parameters obtained by the bootstrap method, improved bootstrap method (normal distribution) and error ellipse methods, it is found that the error ellipse method achieves the expansion of sampling range and shortens the confidence interval, which improves the accuracy of the estimation of parameters with small samples. Through case analysis, it is proved that the tangent error ellipse method is feasible, and the series of S-N curves is reasonable by the tangent error ellipse method. Originality/value The error ellipse methods can lay a technical foundation for life prediction of products and have a progressive significance for the quality evaluation of products.

In the engineering application of high strength steel and surface strengthening steel, fisheye failure is often happened in high cycle fatigue. To explore the effect of fisheye failure on high cycle fatigue properties of materials, a high cycle fatigue life model was established based on the Murakami and Tanaka’s fatigue strength models. The model introduces the error circle to evaluate fisheye size, and discusses the influencing factors of fatigue strength. The results show that the size and depth of fisheye failure will affect performance of materials. The proposed model considering the size and depth of defect quantitatively shows the influence of fisheye details on material performance, and effectively predicts the high/ultra-high cycle fatigue life.