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DOI: 10.5593/SGEM2016/HB14/S01.023

SEQUENTIAL PROCEDURES FOR ASSESSING THE PERCENTAGE OF HARMFUL IMPURITIES WITH THE GIVEN LIMITATIONS ON THE ACCURACY AND RELIABILITY OF STATISTICAL INFERENCE

R. Salimov, E. Turilova, I. Volodin
Friday 11 November 2016

References: 16th International Multidisciplinary Scientific GeoConference SGEM 2016, SGEM Vienna GREEN Extended Scientific Sessions, www.sgemviennagreen.org, SGEM2016 Conference Proceedings, ISBN 978-619-7105-80-3 / ISSN 1314-2704, 2 - 5 November, 2016, Book 1 Vol. 4, 175-180pp, DOI: 10.5593/SGEM2016/HB14/S01.023

ABSTRACT

In this article we consider the problem of statistical estimation of impurity content in some product. It is assumed that the observed data have a normal distribution and impurities have the extremely low percentage. The latter circumstance is formalized in the form of a normal prior distribution of the parameter being evaluated, a probability mass is concentrated in the state standardized range content of harmful impurities. Usually this type of interval is written like [0; a]. For such Bayesian model random variable with normal distribution with mean θ and variance σ2 is observed; unknown value of the parameter θ is treated as the true value of the harmful impurities content. We should assess this value. At the same time the estimated value θ is treated as a realization of a random variable having a normal distribution with mean μ and variance τ2.
We offer two assessment procedures, one of which guarantees the absolute accuracy of estimation, another - relative estimation precision; both procedures guarantee a predetermined level of reliability assessment. The procedure for guaranteeing the absolute error value is based on a fixed number of observations; a formula for the required number of observations is given further. The procedure for guaranteeing the relative error value of observation is sequential procedure of first crossing by posteriori probability of a specified level of reliability assessment (for description of such procedure see [1]). For certain values of the parameters μ and τ of the prior distribution, which can be estimated from the data archive, only one observation is enough to make for the first procedure, to ensure the required accuracy and reliability. The proposed procedure is illustrated by the example of estimation of total sulfur content according to the analysis of diesel fuel.

Keywords: normal-normal model, sequential procedure, estimation of impurities in diesel fuel, d-posterior approach.

PAPER DOI: 10.5593/SGEM2016/HB14/S01.023, SEQUENTIAL PROCEDURES FOR ASSESSING THE PERCENTAGE OF HARMFUL IMPURITIES WITH THE GIVEN LIMITATIONS ON THE ACCURACY AND RELIABILITY OF STATISTICAL INFERENCE

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