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

摘要

The prediction of the maximum inclusionsize in a large volume of clean steel from data on smallspecimens is a key issue for steelmakers and users.The statistics of extremes has recently emerged as apowerful tool for this purpose. Murakami and coworkershave applied one branch of the theory to steel, basedon measuring the maximum inclusion size in a seriesof areas on the polished surface of the specimen. Thepresent authors have recently reported on theapplication to steels of another branch of the theory,using the Generalised Pareto Distribution(GPD), andin this paper the two methods are compared using dataon oxide inclusions obtained by quantitative imageanalysis on polished cross-sections. The mostimportant feature of the GPD method is that it predictsan upper limit to the inclusion size, in contrast tothe method of Murakami and coworders and indeed themore basic route of simply extrapolating the lognormaldistribution where, as the volume of steel isincreased, the size of the predicted maximum inclusionincreases. The existence of an upper limit is more inaccord with the practical expectations o fsteelmakers.