Sampling with discrete contamination
Résumé
The sampling variance for a process stream which carries fluctuating levels of the sought-after analyte and is subject to mass flow variation can be estimated
from the covariance function of the analyte fluctuation and the covariance function of the mass flow when these covariance functions are well-defined
and can be considered to be a stationary property of the process stream. However, in the case of sampling a flow of material (a one-dimensional lot) or from material removed from the hold of a ship (a three-dimensional lot)
which does not possess a covariance function for the analyte of interest, a different approach must be taken. An important example of such a case is a shipment of grain that is contaminated by some component such as
genetically modified organisms (GMOs) or by mycotoxins. Depending on the manner of contamination, the regions of the lot that carry contamination can be considered as randomly located distributions of concentration. The distributions themselves may be stochastic in that their mean concentrations and extents may be statistically defined rather than fixed. This paper develops the sampling variance for ‘slugs’ of contamination with a uniform concentration distribution and regular spacing of the sample increments, based on the assumption that the origins of the slugs are uniformly and randomly located (a Poisson point process).
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