Computer simulation of the estimation of the maximum inclusion size in clean steels by the generalized Pareto distribution method

Abstract The Generalized Pareto Distribution (GPD) method has recently been applied to the estimation of the characteristic size of the maximum inclusion in clean 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 in a large volume of steel, a parameter of importance to steel users. The methodology 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 between the GPD parameters ( ξ and σ ′), 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 confidence intervals increase with an increase of ξ and σ ′, ξ being the dominant parameter. Small negative ξ values give bigger values for the characteristic size and confidence intervals than more negative ξ values. The information given here allows an experimentalist to determine how many inclusions to measure for a desired precision on the estimation to be obtained.