Toward a proper statistical description of defects

The Gumbel distribution (asymptotic theory) in conjunction with block maximum sampling is widely adopted to describe material defects. However, the appropriateness of asymptotic theory is questionable, as the block sizes are often relatively small due to practical limitations. In this paper, a recent and more appropriate sub-asymptotic extreme value distribution is presented and discussed in context of defects. Block maximum sampling scenarios with two different underlying defect size distributions (Weibull and log-normal) were simulated. It was demonstrated that the presented sub-asymptotic distribution is to a higher degree capable of capturing the actual extreme value behavior when compared to its asymptotic counterpart, i.e. Gumbel distribution. Furthermore, a comparison with the generalized extreme value distribution, which was adopted as an approximate/empirical distribution function, was also performed.