Issue 7, p. 7 (2017)


Pierre Gy’s development of the Theory of Sampling: a retrospective summary with a didactic tutorial on quantitative sampling of one-dimensional lots

  • R. C.A. Minnitt  
  • K. H. Esbensen
Consultant, adj. professor (
[email protected]
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 Corresponding Author
School of Mining Engineering, University of Witwatersrand, Private Bag 3, WITS. 2050, South Africa
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Corrected version with changes to Table 3 published 14 March 2017.
This paper presents an overview of the pioneering work of Pierre Gy on the Theory of Sampling (TOS) over a period of 66 years—a monumental legacy of dedicated work to the science of sampling. It starts with the early years, beginning in 1949, when Gy worked tirelessly, often in isolation, and not without resistance from other scientists, to create a systematic, mathematically based framework within which every error arising from sampling of a heterogeneous material can be identified (named), analysed and explained. Gy is widely remembered for “The Formula”, which expresses the variance of the fundamental sampling error (FSE) in terms of the mass, fragment top-size and various other compositional attributes of the minerals of interest. But as early as 1947 the seeds of two related questions were planted: “How... to sample” and “How much... material should one take”, which eventually evolved to become the Theory of Sampling, essentially completed in 1975. Presentation of this famous equation to the scientific community led to a period of intense practical experimentation on stationary lots that continues to this day. Gy also addressed the challenge of sampling from fluxes and here identified the variability due to autocorrelation between samples taken from flowing streams that led ultimately to the discipline of chronostatistics, a study of variability in one-dimensional streams. The scope and depth of Gy’s research endeavours grew during the 1960s and led to his encounter with metallurgical balance and reconciliation. As a result, Gy developed the idea of proportional sampling that allows several material streams to be sampled according to the same selection probability with very efficient reconciliation benefits. The TOS was also further extended to include the problems that producers faced in regard to bed blending. Gy was a prolific writer and published over 250 different articles and books, with his last four papers published in the Proceedings of the First World Conference on Sampling and Blending, WCSB1 (2003), Esbjerg, Denmark. In these papers, Gy left us a personal history of the development of TOS as well as three fundamental tutorials, with practical examples, summarising how to manage both the qualitative and quantitative aspects of sampling of discrete materials. This tribute focuses especially on Pierre Gy“s pioneering applications of variography to understanding the large-scale variability in process plants and process control from as early as the 1950s, and he devoted a major part of the development period of TOS to this critically important subject. The variogram allows one to identify sources of variability and provides valuable insight into correlations between successive samples. Poor understanding of the analytical capabilities of the variogram mean that it has not been widely applied in process control. Failure to address the concept of stream heterogeneity means that conventional statistics and statistical process control (SPC) fail to identify and distinguish the sources of variability in a process stream. For each type of heterogeneity, there is a matching variety of process variability. Although the method is powerful in terms of the insights one is able to gain in regard to plant performance and management, there are surprisingly few examples of its application in the literature, although there has been greater acceptance of the method. The authors believe the concluding didactic presentation of Pierre Gy’s approach to process sampling may be a useful starting point for newcomers to TOS.




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