G. Shi et al., Computer simulation of the estimation of the maximum inclusion size in clean steels by the generalized Pareto Distribution method, ACT MATER, 49(10), 2001, pp. 1813-1820
The Generalized Pareto Distribution (GPD) method has recently been applied
to the estimation of the characteristic size of the maximum inclusion in cl
ean steels for the first time. This allows data on inclusion sizes in small
samples of steel to be used to predict the size of the maximum inclusion i
n a large volume of steel, a parameter of importance to steel users. The me
thodology for finding the confidence limits for the estimate has also been
developed, again using data from real experimental samples. Here, computer
simulation of data (using the Monte Carlo method) allows a much wider range
of data sets to be explored quickly and efficiently. The relationship betw
een the GPD parameters (xi and sigma'), the number of simulated inclusions,
the volume of steel used for the prediction, the predicted characteristic
size and the width of the associated confidence intervals on size has been
determined using simulated data. The characteristic size and width of confi
dence intervals increase with an increase of xi and sigma', xi being the do
minant parameter. Small negative 5 values give bigger values for the charac
teristic size and confidence intervals than more negative 5 values. The inf
ormation given here allows an experimentalist to determine how many inclusi
ons to measure for a desired precision on the estimation to be obtained. (C
) 2001 Acta Materialia Inc. Published by Elsevier Science Ltd. All rights r
eserved.