Metal fatigue, Wicksell transform and extreme values

The fatigue strength of high‐strength steel is closely related to the largest size of non‐metallic inclusions in the region of maximum stress of the steel. Hence, it is necessary to predict the largest size of the inclusions based on the size data measured in microscopic view‐fields of planar sections of a specimen. A statistical problem is the inference on the distribution of unmeasurable extreme values from the observations on its Wicksell transform. In this paper, the authors' previous works based on a parametric model are reviewed, and current research activities based on alternative models are introduced.