Effects of residual variances on the estimation of the variance of the Fundamental Error

Recent literature suggests difficulties calculating the variance of the Fundamental Error using Gyʹs Sampling Theory, especially for fine materials. There is a mineral grinding explanation, as some minerals of interest, such as gold, chromite, molybdenite, and many others are affected by delayed comminution, which is addressed in the Sampling Theory. Another problem is the contribution, sometimes obscure, of the analytical procedure variance, which may become significant if not effectively estimated and accounted for prior to calculating the Constant Factor of Constitution Heterogeneity. Results from experiments for gold and copper minerals suggest the Analytical Error must be considered in conjunction with Heterogeneity Tests to prevent empirical mixing of variances from different origins. Furthermore, the contribution of the variance of the Grouping and Segregation Error is often vastly underestimated. Solutions are proposed.