Geoffrey Lyman

A Statistical Theory for Sampling of Particulate Materials

  • Geology
  • Geotechnical Engineering and Engineering Geology
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The concepts currently applied to the sampling of broken minerals and particulate materials were recognised over 100 years ago. The first integrated theory of sampling for the mineral industries was proposed by Gy, who brought together means of estimation of the variance of sampling due to both the particulate nature of a broken ore and the time variation of composition of process streams. However, his theory deals only with sampling variance and cannot determine the full sampling distribution. The full distribution of the composition of potential samples arising from their particulate nature is developed in this paper based solely on the assumption that particle numbers in correct samples follow independent Poisson distributions. The enabling mathematical method is the use of the characteristic function of the sampling distribution. The practical means of calculating the full distribution completes the theory of sampling of particulate materials. The method is applied to a sample of gold ore to calculate the full sampling distribution and effectively clarifies several difficulties when sampling this material. The method has general applicability to all particulate materials, including foodstuffs.

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