An experimental comparison of Gy?s sampling model with amore general model for particulate material sampling

Gy's formula for the variance of the fundamental sampling error (FSE) is based on a model that assumes independent selections of particles. A generalization of this model, which can theoretically lead to more realistic representation of actual sampling processes, was, for the first time, experimentally verified by repeated sampling from a well-mixed batch consisting of particles of zirconium silicate of two different sizes. The predictions for the sampling variance made in Gy?s theory and in the more general model were compared with the experimentally observed sampling variance. During the experiment performed here, the variance prediction made in the theory of Gy ranges from 0.96 × 10?7(g2/g2) to 0.95 × 10?7(g2/g2), which is approximately a factor 60 lower than the experimentally observed variance (5.76 × 10?6(g2/g2)). The difference between the Gy prediction and the experimentally observed variance cannot be fully explained by the uncertainty in the experimentally obtained variance due to the finite number of degrees of freedom. Therefore, the difference is likely to be a significant effect. This shows that, under the experimental conditions, Gy?s formula for the variance of the FSE probably undervalues the sampling variance, unless an empirical correction factor for grouping and segregation is applied in the theory of Gy. The new theory resulted in a variance prediction of 6.00 × 10?6(g2/g2), which is much closer to the observed variance than the Gy prediction. This indicates that the generalization of Gy?s theory offers an outlook for providing a better variance prediction than the Gy predictor in the case of dependencies between particle selections. The results are discussed. Keywords: sampling, variance, parameter for the dependent selection of particles, Gy, experiment.