Issue 11, p. 425 (2022)


Gy’s discrete heterogeneity and the grouping and segregation variance

  • Geoffrey J. Lyman  
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Materials Sampling & Consulting
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This paper returns to Gy’s work to make a recapitulation of his derivation of the constitutional and distributional heterogeneity of a particulate material with a careful delineation of the assumptions that he employed to arrive at expressions for the fundamental sampling variance and the variance due to distributional heterogeneity or the grouping and segregation variance. Gy derives a link between the constitutional and distributional heterogeneity based on the assumption that increments are ‘similar’. This in fact requires that potential increments contain the same number of particles which is very restrictive. Gy’s expressions are explored with numerical examples which demonstrate that these may be valid only under limited circumstances. The second part of the paper provides a derivation that presents an alternative approach to the variance of sampling of a highly segregated particulate material. It is shown that when all particles have the same mass as can be expected under Gy’s assumptions, the new expression coincides with Gy’s. The new derivation is essentially free of assumptions regarding particle numbers and masses in increments and appeals to common sense regarding the extraction of samples by mechanically correct samplers. The new approach provides an expression for the variance due to grouping and segregation which involves the properties of the particulate material and the same variable used by Gy to expresses the extent of segregation of the lot. The grouping factor γ used by Gy is eliminated from consideration.




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