Today, the alloy content in steel scrap deliveries in Sweden are determined by the waste management company by test melts. Random sampling analysis (RSA) is an alternative method, under development, to determine the alloy composition of steel scrap. This method evaluates the alloy composition of the steel delivery based on a number of randomly chosen steel scrap unit. RSA is a surface analysis, it is done on a distributed area where with the help of a grid, marks the random steel scrap units for evaluation. This means that the surface fraction determines the odds of analyzing the steel scrap. In a previous study of RSA, 100 random pieces of scrap units was evaluated for its alloy composition with Optical Emission Spectroscopy (OES). These scrap deliveries were thereafter sent to an Electric Arc Furnace for melting. This was done to compare the RSA analysis with samples taken after scrap melting. The RSA study however assumes that the scrap units have the same weight. In this study, the weights of the scrap units in the RSA was assumed to have a variance. Using MATLAB® and the alloy composition data acquired from the old study, a simulation was made where 100 pieces and 100 analyses was made to see what the margin of error in comparison to the old study. Another goal with this study was to see if the variance of the weight had any relation to the absolute deviation of each element in the alloy composition. The results showed that there was no relation between the absolute deviation of each element and the weight distribution in the population. This indicates that there are other factors involved other than the weight distribution in the samples. The average margin of error for all the elements was calculated to 5.94% for the weight distribution of 0.1:0.1:10 kg. This indicates that RSA is accurate or close in analysis for old steel scrap deliveries even if the weight distribution is 0.1:0.1:10kg. The highest margin of error was obtained for W, Ce and Ti with a margin of error of 18.6%, 14.89% and 10.71% respectively. All the other elements had a margin of error beneath 10%. This indicates that for RSA on old steel scrap deliveries a margin of error of 10% would be a good benchmark on the accuracy of the analysis.