APPLICATION OF THE GENERALIZED PARETO DISTRIBUTION TO THE ESTIMATION OF THE SIZE OF THE MAXIMUM INCLUSION IN CLEAN STEELS

摘要

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 beha- viour and other mechanical properties. A statistical method based on the Generalized Pareto Distribution, which has not previously been applied to inclusions, is described and used to analyse results from two steels with different cleanness levels. The predictions of maximum size in larger volumes are compared with those from extrapolating the log-normal curve which fits the size distribution of inclusions observed on the surface of cold crucible remelted buttons of the steels. If the predicted maximum inclusion size is plotted against increasing volume of steel, there is a continuous increase for the log-normal extrapolation but for the Generalized Pareto Distribution method the curve tends towards an upper limit. This is of great signifi- cance to steelmakers because the existence of an upper limit is more in accord with the expectation from steelmaking practice.