Extreme value models for the assessment of steels containing multiple types of inclusion

Statistical methods based on extreme value theory have recently proved useful for estimating the sizes of large inclusions in clean steels. Observational evidence, however, suggests that for some steels the methods need modification to account for the presence of different types of inclusions. A new model on which estimations may be based is proposed for cases when two or more types of inclusion are present. The paper shows that the new model is more realistic than an earlier mixture model and that it fits data equally well. It may be used to give extended guidance about sampling strategies when the presence of two or more types of inclusion is suspected. The new model also enables the rate of occurrence of different inclusion types to be estimated without identification of the types of individual inclusions, and it allows the effect on maximum inclusion size to be predicted when inclusion characteristics are modified.