Statistical prediction of inclusion sizes in clean steels

Abstract

Predicting the maximum inclusion size in a large volume of clean steel from observations on a small volume is a key problem facing the steel industry. The maximum inclusion size controls fatigue behaviour and other mechanical properties. Recently manufacturers have started using the method evolved by Murakami and co-workers, which is based on the statistics of extreme values (SEV). Here an alternative method is described, based on a different branch of extreme value theory. This alternative method is termed the GPD method as it depends on the generalised Pareto distribution. There are three key points here. First, the SEV (Murakami) method predicts inclusion sizes which increase linearly with the logarithm of the volume of steel used for the prediction. In contrast, under certain conditions, the predictions with the GPD method tend to an upper limit and this is more in accord with the expectations from steelmaking practice. Second, the SEV method uses only the largest inclusion in each field in the analysis. Hence, much useful data about the large inclusions is being discarded. In contrast, the GPD method makes better use of the data including all inclusions over a certain threshold size. Third when the precision of the estimates from the two methods are compared, it appears that the SEV method gives narrower confidence intervals. However, in-depth understanding of the underlying statistics reveals that in the SEV method one of the variables is set to zero, hence artificially restricting the confidence intervals. In the GPD method, this is not the case.