Propagation of the Measurement Error and the Measured Mean of a Physical Quantity for Elementary Functions ax and loga x
DOI:
https://doi.org/10.15407/ujpe64.5.371Keywords:
propagation of an error, propagation of an uncertaintyAbstract
Rules have been obtained for the propagation of the error and the mean value for a measured physical quantity onto another one with a functional relation of the type ax or loga x between them. In essence, these rules are inherently based on the Gaussian weight scheme. Therefore, they should be valid in the framework of a real Gaussian weight scheme applied to discrete data of a real physical experiment (a sample). An analytical form that was used to present the rules concerned (“analytical propagation rules”) and their character allow the processing and the analysis of experimental data to be simplified and accelerated.
References
D.J. Hudson, Statistics. Lectures on Elementary Statistics and Probability (CERN, 1964).
G.G. Rode. Propagation of measurement errors and measured means of a physical quantity for the elementary functions cos x and arccos x. Ukr. J. Phys. 61, 345 (2016). https://doi.org/10.15407/ujpe61.04.0345
G.G. Rode. Propagation of the measurement errors and measured means of physical quantities for the elementary functions x^2 and vx. Ukr. J. Phys. 62, 148 (2017). https://doi.org/10.15407/ujpe62.02.0184
I.S. Gradshtein, I.M. Ryzhik. Table of Integrals, Series, and Products (Academic Press, 1980).
Propagation of uncertainty [https://en.wikipedia.org/wiki/Propagation of uncertainty].
H.H. Ku. Notes on the use of propagation of error formulas. J. Res. Nat. Bur. Stand. C 70, 263 (1966). https://doi.org/10.6028/jres.070C.025
Ph.R. Bevington, D.K. Robinson. Data Reduction and Error Analysis for the Physical Sciences (McGraw-Hill, 2002).
J.R. Taylor. An Introduction to Error Analysis: The Study of Uncertainties in Physical Measurements (University Sci. Books, 1997).
B.N. Taylor, C.E. Kuyatt. Guidelines for Evaluating and Expressing the Uncertainty of NIST Measurement Results, NIST Technical Note 1297 (National Institute of Standards and Technology, 1994). https://doi.org/10.6028/NIST.TN.1297
P.K. Sinervo. Denition and treatment of systematic uncertainties in high energy physics and astrophysics. In: Proceedings of the PHYSTAT2003 Conference, SLAC, Stanford, Ca, September 8-11 (2003), p. 122.
J. Denker. Nonlinear least squares [http://www.av8n.com/physics/nonlinear-least-squares.htm].
E.W. Weisstein. Standard Deviation Entry at Math World [http://mathworld.wolfram.com/StandardDeviation.html.]
Evaluation of measurement data - An introduction to the "Guide to the expression of uncertainty in measurement" and related documents [http://www.bipm.org/utils/ common/documents/jcgm/JCGM 104 2009 E.pdf].
Downloads
Published
How to Cite
Issue
Section
License
Copyright Agreement
License to Publish the Paper
Kyiv, Ukraine
The corresponding author and the co-authors (hereon referred to as the Author(s)) of the paper being submitted to the Ukrainian Journal of Physics (hereon referred to as the Paper) from one side and the Bogolyubov Institute for Theoretical Physics, National Academy of Sciences of Ukraine, represented by its Director (hereon referred to as the Publisher) from the other side have come to the following Agreement:
1. Subject of the Agreement.
The Author(s) grant(s) the Publisher the free non-exclusive right to use the Paper (of scientific, technical, or any other content) according to the terms and conditions defined by this Agreement.
2. The ways of using the Paper.
2.1. The Author(s) grant(s) the Publisher the right to use the Paper as follows.
2.1.1. To publish the Paper in the Ukrainian Journal of Physics (hereon referred to as the Journal) in original language and translated into English (the copy of the Paper approved by the Author(s) and the Publisher and accepted for publication is a constitutive part of this License Agreement).
2.1.2. To edit, adapt, and correct the Paper by approval of the Author(s).
2.1.3. To translate the Paper in the case when the Paper is written in a language different from that adopted in the Journal.
2.2. If the Author(s) has(ve) an intent to use the Paper in any other way, e.g., to publish the translated version of the Paper (except for the case defined by Section 2.1.3 of this Agreement), to post the full Paper or any its part on the web, to publish the Paper in any other editions, to include the Paper or any its part in other collections, anthologies, encyclopaedias, etc., the Author(s) should get a written permission from the Publisher.
3. License territory.
The Author(s) grant(s) the Publisher the right to use the Paper as regulated by sections 2.1.1–2.1.3 of this Agreement on the territory of Ukraine and to distribute the Paper as indispensable part of the Journal on the territory of Ukraine and other countries by means of subscription, sales, and free transfer to a third party.
4. Duration.
4.1. This Agreement is valid starting from the date of signature and acts for the entire period of the existence of the Journal.
5. Loyalty.
5.1. The Author(s) warrant(s) the Publisher that:
– he/she is the true author (co-author) of the Paper;
– copyright on the Paper was not transferred to any other party;
– the Paper has never been published before and will not be published in any other media before it is published by the Publisher (see also section 2.2);
– the Author(s) do(es) not violate any intellectual property right of other parties. If the Paper includes some materials of other parties, except for citations whose length is regulated by the scientific, informational, or critical character of the Paper, the use of such materials is in compliance with the regulations of the international law and the law of Ukraine.
6. Requisites and signatures of the Parties.
Publisher: Bogolyubov Institute for Theoretical Physics, National Academy of Sciences of Ukraine.
Address: Ukraine, Kyiv, Metrolohichna Str. 14-b.
Author: Electronic signature on behalf and with endorsement of all co-authors.
.png){kind=small}
