Analysis of the truncated normal distribution applicability for selection of the multiple measurements optimal number
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Authors:
V.Ya Kopp, Dr. Sci. (Tech.), Prof., Sevastopol National Technical University, Head of the Automated Instrument Systems Department, Sevastopol, Crimea
A.I. Balakin, Cand. Sci. (Tech.), Sevastopol National Technical University, Senior Lecturer of the Automated Instrument Systems Department, Sevastopol, Crimea
M.V. Zamoryonov, Cand. Sci. (Tech.), Sevastopol National Technical University, Senior Lecturerof Information Technologies and Systems Department,Sevastopol, Crimea
Abstract:
Purpose. Ensuring the accuracy of measurement operations by estimating error when using the truncated normal distribution for determination of the optimal number of repeated measurements.
Methodology. On the basis of use of the principle of maximum of entropy and calculus of variations analytical expression for the form of appearances density of distribution of a random variable concentrated on a finite interval has been received provided that on borders of an interval the values of density are equal to zero. The resulting form of the density was subsequently used to estimate the error introduced by the use of the truncated normal distribution. An iterative procedure when determining the number of repeated measurements has been used.
Findings. The investigations have proved the applicability of the truncated normal distribution for estimating the number of repeated measurements. The discrepancy between the results of estimation of the required number of measurements using the truncated normal distribution and arbitration law, derived from investigations, was less than 0.5%.
Originality. We have formulated and proved the theorem which allows defining the type of density of the distribution, providing maximum of entropy of the sum of two random variables concentrated on final intervals given the set total dispersion.
Practical value. We have shown that it is possible to use the truncated normal distribution in order to simplify results processing considerably.
References:
1. Информационно-измерительная техника и технологии / [Калашников В.И., Нефедов С.В., Путилин А.Б. и др.]; под ред. Г.Г. Ранеева. – М.: Высшая школа, 2002. – 454 с.
Kalashnikov, V.I., Nefedov, S.V., Putilin, A.B. and Raneyev, G.G. (2002), Informatsyonno-izmeritelnaya tekhnika i tekhnologii [Information and Measuring Equipment and Technology], Vysshaya Shkola, Moscow, Russia.
2. Анализ дифференциальной энтропии при технических измерениях в машино- и приборостроении / В.Я. Копп, А.А. Скидан, А.И. Балакин, О.В. Филипович // Труды Одесского политехнического университета: Научный и производственно-практический сборник по техническим и естественным наукам. – 2007. – Вып.1(27). – С.214–219.
Kopp, V.Ya., Skidan, A.A., Balakin, A.I. and Filipovich, O.V. (2007), “The analysis of differential entropy at technical measurements in mechanical engineering and instrument making”, Trudy Odesskogo Politehnicheskogo Universiteta: Nauchnyy i Proizvodstvenno-Prakticheskiy Sbornik po Tehnicheskim i Estestvennym Naukam, issue 1 (27), pp. 214 – 219.
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