Evaluation of maximum non-metallic inclusion sizes in engineering steels by fitting a generalized extreme value distribution based on vectors of largest observations

In the analysis of maximum sizes of large non-metallic inclusions in steels, the common extreme value analysis is only based on a sample of largest observations in control areas on polished planes, respectively. From a simulation study it is observed that this univariate set-up may lead to a high proportion of misspecifications of the true extreme value distribution. Due to their different tail behavior, a falsely determined extreme value distribution will lead to erroneous assertions about quantiles, which serve as characteristic quantities. A multivariate extreme value analysis incorporating data of the r largest observations in every control area will work satisfactorily and should be preferred. The effects of different choices of r are also illustrated by means of a real data set of oxide inclusions.