1. bookVolume 14 (2014): Issue 6 (December 2014)
Journal Details
License
Format
Journal
eISSN
1335-8871
First Published
07 Mar 2008
Publication timeframe
6 times per year
Languages
English
access type Open Access

Measurement Uncertainty Evaluation Method Considering Correlation and its Application to Precision Centrifuge

Published Online: 15 Dec 2014
Volume & Issue: Volume 14 (2014) - Issue 6 (December 2014)
Page range: 308 - 316
Received: 19 May 2014
Accepted: 24 Oct 2014
Journal Details
License
Format
Journal
eISSN
1335-8871
First Published
07 Mar 2008
Publication timeframe
6 times per year
Languages
English
Abstract

Measurement uncertainty evaluation based on the Monte Carlo method (MCM) with the assumption that all uncertainty sources are independent is common. For some measure problems, however, the correlation between input quantities is of great importance and even essential. The purpose of this paper is to provide an uncertainty evaluation method based on MCM that can handle correlated cases, especially for measurement in which uncertainty sources are correlated and submit to non-Gaussian distribution. In this method, a linear-nonlinear transformation technique was developed to generate correlated random variables sampling sequences with target prescribed marginal probability distribution and correlation coefficients. Measurement of the arm stretch of a precision centrifuge of 10-6 order was implemented by a high precision approach and associated uncertainty evaluation was carried out using the mentioned method and the method proposed in the Guide to the Expression of Uncertainty in Measurement (GUM). The obtained results were compared and discussed at last.

Keywords

[1] Joint Committee for Guides in Metrology. (2008). Evaluation of measurement data — Guide to the expression of uncertainty in measurement, 1st edition. JCGM 100:2008.Search in Google Scholar

[2] Martins, M.A.F., Requiao, R., Kalid, R.A. (2011). Generalized expressions of second and third order for the evaluation of standard measurement uncertainty. Measurement, 44, 1526-1530.10.1016/j.measurement.2011.06.008Search in Google Scholar

[3] Joint Committee for Guides in Metrology. (2008). Evaluation of measurement data — Supplement 1 to the “Guide to the expression of uncertainty in measurement” — Propagation of distributions using Monte Carlo method, 1st edition. JCGM 101:2008.Search in Google Scholar

[4] Eichstad, S., Link, A., Harris, P., et al. (2012). Efficient implementation of a Monte Carlo method for uncertainty evaluation in dynamic measurement. Metrologia, 49, 401-410.10.1088/0026-1394/49/3/401Search in Google Scholar

[5] Wen, X., Zhao, Y., Wang, D., Pan, J. (2013). Adaptive Monte Carlo and GUM methods for the evaluation of measurement uncertainty of cylindricity error. Precision Engineering, 37, 856-864.10.1016/j.precisioneng.2013.05.002Search in Google Scholar

[6] Theodorou, D., Meligotsidou, L., Karavoltsos, S., et al. (2011). Comparison of ISO-GUM and Monte Carlo methods for evaluation of measurement uncertainty: Application to direct cadmium measurement in water by GFAAS. Talanta, 83, 1568-1574.10.1016/j.talanta.2010.11.05921238753Search in Google Scholar

[7] Matus, M. (2012). Uncertainty of the variation in length of gauge blocks by mechanical comparison: A worked example. Measurement Science and Technology, 23, 1-6.10.1088/0957-0233/23/9/094003Search in Google Scholar

[8] Decker, J.E., Eves, B.J., Pekelsky, J.R. (2011). Evaluation of uncertainty in grating pitch measurement by optical diffraction using Monte Carlo methods. Measurement Science and Technology, 22, 1-6.10.1088/0957-0233/22/2/027001Search in Google Scholar

[9] Moschioni, G., Saggin, B., Tarabini, M., et al. (2013). Use of design of experiments and Monte Carlo method for instruments optimal design. Measurement, 46, 976- 984.10.1016/j.measurement.2012.10.024Search in Google Scholar

[10] Chew, G., Walczyk, T. (2012). A Monte Carlo approach for estimating measurement uncertainty using standard spreadsheet software. Analytical and Bioanalytical Chemistry, 402, 2463-2469.10.1007/s00216-011-5698-422287047Search in Google Scholar

[11] Theodorou, D., Zannikou, Y., Zannikos, F. (2012). Estimation of the standard uncertainty of a calibration curve: Application to sulfur mass concentration determination in fuels. Accreditation and Quality Assurance, 17, 275–281.10.1007/s00769-011-0852-4Search in Google Scholar

[12] Gonzalez, A.G., Herrador, M.A., Asuero, A.G. (2005). Uncertainty evaluation from Monte-Carlo simulations. Accreditation and Quality Assurance, 10, 149-154.10.1007/s00769-004-0896-9Search in Google Scholar

[13] Cox, M.G., Siebert, B.R. (2006). The use of a Monte Carlo method for evaluating uncertainty and expanded uncertainty. Metrologia, 43, S178-188.10.1088/0026-1394/43/4/S03Search in Google Scholar

[14] Cox, M., Harris, P., Siebert, B.R. (2003). Evaluation of measurement uncertainty based on the propagation of distributions using Monte Carlo simulation. Measurement Techniques, 46, 824-833.10.1023/B:METE.0000008439.82231.adSearch in Google Scholar

[15] Herrador, M.A., Gonzalez, A.G. (2004). Evaluation of measurement uncertainty in analytical assays by means of Monte-Carlo simulation. Talanta, 64, 415-422.10.1016/j.talanta.2004.03.01118969620Search in Google Scholar

[16] Pertile, M., De Cecco, M. (2008). Uncertainty evaluation for complex propagation models by means of the theory of evidence. Measurement Science and Technology, 19, 1-10.10.1088/0957-0233/19/5/055103Search in Google Scholar

[17] Wubbeler, G., Harris, P.M., Cox, M.G., et al. (2010). A two-stage procedure for determining the number of trials in the application of a Monte Carlo method for uncertainty evaluation. Metrologia, 47, 317-324.10.1088/0026-1394/47/3/023Search in Google Scholar

[18] Li, S.T., Hammond, J.L. (1975). Generation of pseudo random numbers with specified univariate distributions and correlation coefficients. IEEE Systems, Man, and Cybernetics, 5, 557-561.10.1109/TSMC.1975.5408380Search in Google Scholar

[19] Marida, K.V. (1970). A translation family of bivariate distributions and Frechet’s bounds. Sankhya, 32, 119- 122.Search in Google Scholar

[20] Cairo, M.C., Nelson, B.L. (1997). Modeling and generating random vectors with arbitrary marginal distributions and correlation matrix. Technical Report. Department of Industrial Engineering and Management Science, Northwestern University, Evanston, IL.Search in Google Scholar

[21] Yen, J.C. (2001). NORTA initialization for random vector generation by numerical methods. Masters of Industrial Engineering Thesis. Chung Yaun Chiristian University, Taiwan.Search in Google Scholar

[22] Niaki, S., Abbasi, B. (2008). Generating correlation matrices for normal random vectors in NORTA algorithm using artificial neural networks. Journal of Uncertain Systems, 12 (3), 192-201.Search in Google Scholar

[23] IEEE Standards. (2009). IEEE recommended practice for precision centrifuge testing of linear accelerometers. 836-2009.Search in Google Scholar

[24] Theodorou, D., Zannikou, Y., Anastopoulos, G., et al. (2008). Coverage interval estimation of the measurement of Gross Heat of Combustion of fuel by bomb calorimetry: Comparison of ISO GUM and adaptive Monte Carlo method. Thermochimica Acta, 526, 122-129.10.1016/j.tca.2011.09.004Search in Google Scholar

[25] Solaguren-Beascoa Fernandez, M., Alegre Calderon, J.M., Bravo Diez, P.M. (2009). Implementation in MATLAB of the adaptive Monte Carlo method for the evaluation of measurement uncertainties. Accreditation and Quality Assurance, 14, 95–106.10.1007/s00769-008-0475-6Search in Google Scholar

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