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SEQUENTIAL FIRST-CROSSING PROCEDURE FOR ASSESSING THE PERCENTAGE OF TOXIC ELEMENTS IN PRODUCTS
Abstract
In this paper the d-posterior approach to the problem of guaranteeing the statistical inference is used to estimate the average value ?? of the normal distribution under the prior truncated normal distribution of ??. It is assumed that the experimenter has prior information about the smallness of the mean parameter ?? of truncated normal distribution. Such statistical analysis scheme is applicable for example for estimation the percentage of rare elements or impurities in manufactured food or in other products. The constraints on percentage allow statistician to specify ?? even in absence of an archive of previous measurements of percentage. The unknown variance ??2 of thetruncated normal distribution can be found in the rated values of the applied analysis method or can be calculated from constraints determined by state standard for the discrepancy between parallel observations. It is assumed that the percentage of a rare element is observed in a series of runs in a sequential scheme. The results of observations have normal distribution with the parameters ?? and ??2, while ?? is the realization of a random variable with truncatednormal distribution. The first crossing procedure precedes the observations at the first step, when this posterior probability reaches the specified constraints on the accuracy and reliability of the estimation. The developed assessment procedure is illustrated on the data of determination of the percentage of rare elements (cadmium, arsenic, etc.) in manufactured food and water in accordance in accordance with Russian State Standards.
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References4
Salimov R., A sequential d-guaranteed test for distinguishing two interval hypotheses, Lobachevskii Journal of Mathematics, vol.37/issue 4, pp 500-503, 2016.
Salimov R.F, Yang S.-F, Turilova E.A, Volodin I.N., Estimation of the Mean Value for the Normal Distribution with Constraints on d-Risk, Lobachevskii Journal of Mathematics., vol.39/issue 3, pp 377-387, 2018.
Simushkin, S.V., An empirical d-a posteriori approach to the problem of statistical conclusion guarantee, Izvestiya vysshikh uchebnykh zavedenii matematika, vol. 11, pp 42-58, 1983.
Volodin I.N., Guarantied procedures of statistical inference (sample size determination), J.Soviet Math., Vol. 44, pp. 568-600, 1989.
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