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Filtering lack of microhomogeneity in reference materials for microanalytical methods
van den Boogaart, K. G.; Renno, A. D.; Tolosana-Delgado, R.;
Homogeneity is a relative property of a sample in relation to the measurement (analytical method), the analyte, and the intended purpose, like the usage as a reference material (RM). The verification of homogeneity is essential to define a RM as fit for purpose. In this context, there have been recent efforts to check the possible superiority of synthetic RMs over natural ones. The assessment of homogeneity is an integral part of these synthesis tests and of the following certification for use as RM. With regard to their spatial variability, five types of microheterogeneity of RMs can be found in the literature, depending on which is the source of heterogeneity that it presents: random, systematic, periodic, nugget and island.

This contribution presents a first attempt towards such tests of microhomogeneity for discussion. In a first step, we define a stochastic random function model that will describe each of the types of microheterogeneity mentioned before. Then, in a quite natural manner a particular sampling strategy for each of them is derived in the second step, with the goal to filter out the undesired source of variability. In the third step, we derive a strategy of characterization of the material, namely a strategy of estimation of the heterogeneity properties of the RM that should be used to certify the reference nature of the material. These the adequacy of these strategies is shown in this contribution by using simulations of the several heterogeneity structures and of the proposed sampling and characterization strategies.

For instance, for the case of a random heterogeneity we may assume that the concentration of the target element is described by a random function (RF). If the covariance function of this RF would be known, the sampling strategy would be to repeat measurements on random positions of a very fine regular grid in such a way that the variance of their average decreases as fast as possible, using as many locations as necessary to ensure that it falls below the method specifications. Finally, the way to characterise the RM would require calibrating the concentration of the target element on a coarser grid, on as many locations as necessary to appropriately set the covariance function, using classical concepts and models of Geostatistics. Similar strategies can be derived for the rest of the heterogeneity structures, like robust methods for nugget heterogeneity or geostatistical concepts related to intrinsic functions of order k for systematic heterogeneity
  • Lecture (Conference)
    MATHMET 2016 - International Workshop on Mathematics and Statistics for Metrology, 07.-09.11.2016, Berlin, Deutschland

Publ.-Id: 24911