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COMPUTING UNCERTAINTY OF THE EXTREME VALUES IN RANDOM SAMPLES

Mykhaylo Dorozhovets, Ivanna Bubela

Abstract


This paper proposes and analyses a statistical method for uncertainty evaluation of extreme values (minimal or maximal) for measurement results with significantly limited number of observations n = 3…10 and considerable deviation of observation probability density function (PDF) from normal distribution. The method is based on properties of order statistics. It can be used for the uncertainty evaluation of mechanical properties of testing products in a food industry (when minimal values of measurement results are observed) and for the investigation of a number of harmful elements (when maximal values of measurement results are observed).

Keywords


measurement; extremal values; minimal value of observations; maximal value of observations; uncertainty; distribution.

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References


Guide to the Expression of Uncertainty in Measurement, First ed. 1993 ISO Switzerland, last corrected ed. JCGM BIPM 100, 2008 and Supplement 1– Propagation of distributions using a Monte-Carlo method.

M. Dorozhovets, I. Popovych, “Processing of the random observations with Flatten-Gaussian distribution by approximate order statistics method,” in Proceedings of the IEEE 8th International Conference on Intelligent Data Acquisition and Advanced Computing Systems: Technology and Applications (IDAACS’2015), Warsaw, Poland, 24-26 September 2015, vol. 1, pp. 149-152.

M. Dorozhovets, I. Popovych, “Processing of the random observations with Flatten-Gaussian distribution by approximate order statistics method,” in Proceedings of the Ukrainian scientific-technical conference of young scientists in the field of metrology “Technical Using of Measurement 2015,” Slavsko, Ukraine, February 1-5, 2016, pp. 119-121. (in Ukrainian).

O. V. Avramenko, M. M. Dorozhovets, I. V. Popovych, “Evaluation of uncertainty of measurement results in testing of percent elongation and tensile strength of plastic products,” Automation, Measurement and Control, Lviv Polytechnic National University, 2014. (in Ukrainian).

M. Dorozhovets, I. Popovych, Z. L. Warsza, “Method of evaluation the measurement uncertainty of the minimal value of observations and its application in testing of plastic products,” Advanced Mechatronics Solutions, vol. 393 of the series Advances in Intelligent Systems and Computing, Springer International Publishing Switzerland, pp. 421-430, 2015.

M. Dorozhovets, Z. L. Warsza, I. Popovych, “Uncertainty evaluation of the minimal value measurements,” Measurement Automation Monitoring, vol. 61, no. 08, pp. 395-398, August 2015.

O. V. Avramenko, M. M. Dorozhovets, I. V. Popovych, “Evaluation of uncertainty of measurement results in testing of percent elongation and tensile strength of plastic products,” in Proceedings of the Ukrainian scientific-technical conference of young scientists in the field of metrology “Technical Using of Measurement 2015,” Slavsko, Ukraine, February 2-6, 2015, pp. 94-96. (in Ukrainian).

M. Dorozhovets, I. Popovych, Z. Warsza, “Evaluation of the measurement uncertainty of the minimal value of observations,” in Proceedings of the XI Scientific-Technical Conference on Problems and Progress in Metrology, Kościelisko, Poland, June 07-10, 2015, pp. 60-66.

Tensile Testing, ASM International, Second Edition, 2004.

D 638 Test Method for Tensile Properties of Plastics, Annual Book of ASTM Standards, Vol 08.01.

GOST 11262-80, GOST 26277-84, GOST 12423-66, Ukraine standards of testing methods and conditions of plastic materials and products.

M. Fisz, Probability Theory and Mathematical Statistics, John Willey & Sons, London, 1963.

P. V. Novitski, I. A. Zograf, Evaluation of measurement result errors, Leningrad, Energoatomizdat, 1985, 248 p. (in Russian).

O. A. Botsiura, Yu. G. Zharko, I. P. Zakharov, “Measurement uncertainty evaluation of the maximum observed value of the test parameter,” Information Processing Systems, issue 2(127), Kharkiv, pp. 21-23, 2015. (in Russian).


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