Investigation of the Instrumental Components in Uncertainty of Extreme Random Observations
In this paper the instrumental components in the uncertainty of extreme observations are analyzed and quantitatively evaluated. In practice this method can be used to evaluate the uncertainty results of testing products, when during testing the most informative parameter is not the arithmetic mean but the extreme (minimal or maximal) observation. In the paper two main components of the uncertainty for such testing are studied: the statistical component - the variation of the measured parameter of a few tested specimens and the instrumental component - uncertainty of the measurement result of the appropriate parameter for each tested specimen. It is shown that the uncertainty of extreme observations depends in different ways on systematic and random effects in the measurements. If the standard uncertainty evaluated using the type B method (instrumental components) does not exceed (approximately) 1/3 of the standard uncertainty determined using the type A method (deviation values of observations), then the value of a coefficient which is used to calculate one-side expanded uncertainty of extreme observation can be determined approximately using a simplified method based on the ratio of both components of the standard uncertainty. The results of the research can be used to evaluate the uncertainty results in the quality testing of a wide variety of products in industry, agriculture and medicine when the result of the test depends on the minimum or maximum value of the parameter in the tested specimens.
KeywordsMeasurement Random Systematic effects Uncertainty Extreme (minimal, maximal) observation Monte carlo method
This work is financed by Polish Ministry of Science and Higher Education under the program “Regional Initiative of Excellence” in 2019–2022. Project number 027/RID/2018/19, funding amount 11 999 900 PLN.
- 1.D 638 Test Method for Tensile Properties of Plastics Annual Book of ASTM Standards, Vol 08.01Google Scholar
- 2.ASM International. Tensile Testing, Second Edition (2004)Google Scholar
- 3.GOST 11262-80, GOST 26277-84, GOST 12423-66. Ukraine standards of testing methods and conditions of plastic materials and productsGoogle Scholar
- 7.Burke, S.: Missing Values, Outliers, Robust Statistics & Non-parametric Methods. Statistics and data analysis. LC•GC Europe Online Supplement (2001)Google Scholar
- 8.Guide to the Expression of Uncertainty in Measurement. GUM. First ed. 1993 ISO Switzerland, last corrected ed. JCGM BIPM 100 (2008)Google Scholar
- 10.Dorozhovets, M,. Popovych I., Warsza Z.L.: Method of evaluation the measurement uncertainty of the minimal value of observations and its application in testing of plastic products. Advanced Mechatronics Solutions. Advances in Intelligent Systems and Computing. Springer International Publishing Switzerland Vol. 393, 421–430 (2016)Google Scholar
- 11.Dorozhovets, M., Bubela, I.: Computing uncertainty of the extreme values in random samples. Int. J. Comput. 15(2), 127–135 (2016)Google Scholar
- 12.Gumbel, E.: Statistics of Extremes, New York (1962)Google Scholar
- 13.Dietrich, C.F.: Uncertainty, Calibration and Probability. The Statistics of Scientific and Industrial Measurement. Second Edition. The Adam Hilger Series on Measurement Science and Technology, p. 535 (1991)Google Scholar
- 14.Dorozhovets, M., Popovych, I.: Processing of the random observations with Flatten-Gaussian distribution by approximate order statistics method. In: Proceedings of the 2015 IEEE 8th International Conference on Intelligent Data Acquisition and Advanced Computing Systems: Technology and Applications, IDAACS 2015. Vol. 1, pp. 149–152Google Scholar
- 15.JCGM 101: Evaluation of measurement data—Supplement 1 to the ‘Guide to the Expression of Uncertainty in Measurement’—Propagation of distributions using a Monte-Carlo method. BIPM, IEC, IFCC, ILAC, ISO, IUPAC, IUPAP and OIML (2008)Google Scholar