|
Article information
2017 , Volume 22, ¹ 2, p.85-98
Kumkov S.I., Ignatenkova L.A.
Interval approach to estimation of stability for characteristics of standard samples
We consider the problem for estimation of the stability for characteristics of a standard sample (SS), either still in use or expired. Due to operation, the characteristics of the sample are subject to “ageing”, that is falling out of the assigned bounds. This process can be described by instability model - a function containing parameters of the sample, which include the certified value of its characteristic and the uncertainty of this value. During the useful life of the standard sample we measure the value of its certified characteristic. The deviation from the accumulated set of measurements is then estimated. The question on whether to exploit or not the standard sample any further is resolved based on the discrepancy between the measured and the certified values. However, in practice, any information about the probabilistic distribution of the errors is unavailable. In addition, the instability model is not known either. Hence, it is hardly possible to strictly substantiate the use of the standard statistical methods for estimating the stability characteristics of the standard sample, thus these techniques can only be applied formally. Under such conditions, the use of methods of interval analysis is a reasonable complement to already existing techniques that evaluate the stability of characteristics. Interval methods for constructing the feasible parameter set do not require information on the probabilistic distribution of errors, they only rely on the process of instability model and two-sided error bounds. The resulting set of feasible parameter values is called information set. We use it to calculate the predicted values for the characteristic of the standard sample and, accordingly, the predicted errors of this value.
[full text]
Keywords: standard sample, certified value, certified value error, instability model, feasible parameter values, information set, feasible dependency tube
Author(s):
Kumkov Sergei Ivanovich
PhD. , Senior Scientist
Position: Senior Research Scientist
Office: N.N. Krasovskii Institute of Mathematics and Mechanics UrB RAS
Address: 620990, Russia, Ekaterinburg, S. Kvalevskaya str., 16
Phone Office: (343) 374 83 32
E-mail: kumkov@imm.uran.ru
SPIN-code: 3469-2439Ignatenkova Larisa Arkadievna
Position: Director
Office: Sertimet Center, Ural Branch, Russian Academy of Sciences
Address: 6200990, Russia, Ekaterinburg, Pervomayskaya str., 91
Phone Office: (343) 362 33 97
E-mail: sertimet@prm.uran.ru
SPIN-code: 1572-0269 References:
[1] R 50.2.031-2003. Standartnye obraztsy sostava i svoystv veshchestv i materialov. Metodika otsenivaniya kharakteristik [Standard samples for compound and properties of substances and materials. Methodic for estimation of characteristics. Gosstandart of Russia. Official edition]. Moscow: IPK Izdatel'stvo standartov; 2004: 10. (In Russ.)
[2] GÎÑÒ 8.207-76. Gosudarstvennaya sistema obespecheniya edinstva izmereniy. Pryamye izmereniya s mnogokratnymi nablyudeniyami. Metody obrabotki rezul'tatov nablyudeniy [Direct measurements with multiple observations. Methods for processing the observation results]. Moscow: Standartinform; 2006: 9. (In Russ.)
[3] R 50.2.028–2003. Gosudarstvennaya sistema obespecheniya edinstva izmereniy. Rekomendatsii po postroeniyu graduirovochnykh kharakteristik. Otsenivanie pogreshnostey (neopredelennosti) lineynykh graduirovochnykh kharakteristik pri ispol'zovanii metoda naimen'shikh Interval'nyy podkhod k otsenivaniyu stabil'nosti 13 kvadratov [Estimation of errors (uncertainty) for linear calibration characteristics by application of the least squares method]. Moscow: IPK Izdatel'stvo standartov; 2003: 9. ( In Russ.)
[4] Otchet po razrabotke i attestatsii standartnogo obraztsa predpriyatiya sostava rudy titano-magnetitovoy SOP-16352-002-2013 [Report on elaboration and certification of the industrial enterprise standard for sample of titanium–magnetite ore SOP ÑÎÏ-16352-002-2013]. Ekaterinburg: Tsentr metrologii i sertifikatsii «SERTIMET» UrO RAN; 2013: 63.
[5] Kearfott, R.B., Nakao, R.B., Neumaier, A., Rump, S.M., Shary, S.M., van Hentenryck, P. Standardized notation in interval analysis. Computational Technologies. 2010; 15(1):7–13.
[6] Kantorovich, L.V. O nekotorykh novykh podkhodakh k vychislitel'nym metodam i obrabotke nablyudeniy [On some new approaches to numerical methods and processing the observations]. Siberian Mathematical Journal. 1962; 3(5):701–709.
[7] Jaulin, L., Kieffer, M., Didrit, O., Walter, E. Applied interval analysis. London: Springer; 2001: 395.
[8] Hansen, E., Walster, G.W. Global optimization using interval analysis. New York: Marcel Dekker; 2004: 492.
[9] Shary, S.P. Finite-dimensional interval analysis. Novosibirsk: Institute of Computational Technologies SB RAS; 2016: 617. Available at: http://www.nsc.ru/interval/Library/InteBooks/SharyBook.pdf ( In Russ.)
[10] Zhilin, S.I. Simple method for outlier detection in fitting experimental data under interval error. Chemometrics and Intelligent Laboratory Systems. 2007; 88(1):6–68.
[11] Kumkov, S.I. An estimation problem of chemical process with confluent parameters: an interval approach. Reliable Computing. 2016; (22):15–25.
[12] Redkin, A.A., Zaikov, Yu.P., O. Tkacheva, O., Kumkov, S.I. Molar thermal conductivity of molten salts. Ionics. 2016; 22(1):143–149.
[13] Redkin, A.A., Zaikov, Yu.P., Korzun, I. V., Reznitskikh, O.G., Yaroslavtseva, T.V., Kumkov, S.I. Heat capacity of molten halides. Journal of Physical Chemistry B. 2015; 119(2):509–512.
[14] Kumkov, S.I., Mikushina, Yu.V. Interval Approach to identification of catalytic process parameters. Reliable Computing. 2013; 19(2):197–214.
[15] Kumkov, S.I. Procession of experimental data on conductivity of molten electrolyte by methods of interval analysis. Journal Melts. 2010; (3):86–96.
Bibliography link:
Kumkov S.I., Ignatenkova L.A. Interval approach to estimation of stability for characteristics of standard samples // Computational technologies. 2017. V. 22. ¹ 2. P. 85-98
|
