Comparison of extreme value statistics methods for predicting maximum inclusion size in clean steels

Abstract

The prediction of the maximum inclusion size in a large volume of clean steel from data on small specimens is a key issue for steelmakers and users. The statistics of extremes has recently emerged as a powerful tool for this purpose. Murakami and coworkers have applied one branch of the theory to steels, based on measuring the maximum inclusion size in a series of areas on the polished surface of the specimen. The present authors have recently reported on the application to steels of another branch of the theory, using the Generalised Pareto Distribution (GPD), and in this paper the two methods are compared using data on oxide inclusions obtained by quantitative image analysis on polished cross-sections. The most important feature of the GPD method is that it predicts an upper limit to the inclusion size, in contrast to the method of Murakami and coworkers and indeed the more basic route of simply extrapolating the log- normal distribution where, as the volume of steel is increased, the size of the predicted maximum inclusion increases. The existence of an upper limit is more in accord with the practical expectations of steelmakers.