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Project of the Slovak Research and Development Agency (APVV) APVV-0096-10
Duration of the project: 5/2011- 10/2014
Project Summary
Developed countries pay special attention to development of methods and analysis of measurement results. Measurements have a significant impact on economic growth (up to 7% of GDP is dedicated to various aspects of measurement and analysis of measurement results). Analysis of measurement uncertainty is an important part of data processing, which gives an answer to the question how to trust the result of measurement. This is one of the basic objectives of metrology. As estimation of unknown parameters and prediction of random variables is typically considered, the probability and mathematical-statistical methods are used for such analysis primarily. Their accuracy and appropriateness of use for specific situations in metrological practice should be verified theoretically as well as by computer simulations and real examples.
Many new problems aimed at processing of measurement results, calibration of measuring instruments and devices, as well as problems connected with estimation of the value of the measured variable (measurand), arise in connection with wider spreading use of the analysis of measurement uncertainties. The expected results of the project include new knowledge in the theory of statistical methods for metrology, focusing primarily on new methods, models and algorithmic solutions for analysis and evaluation of calibration and interlaboratory comparisons.
Results
The research was focused on the calibration problem in the case that the calibrated and the calibration device are measured with comparable uncertainties. Following the model suggested by Kubáček we have developed a parametric model approach with a quadratic calibration function.
We have suggested an algorithm to determine the distance of two micro / nano structures and uncertainty of this determination. Standard procedure with international standards in this case is inappropriate.
Detection limits LOD (limit of detection) and LOQ (limit of quantification) have been derived for measurements using PTR-MS mass spectrometer (Proton Transfer Reaction Mass Spectrometer).
The results of this research were published in peer-reviewed journals Acta Univ. Palacky. Olomouc, Fac. Rer. Nat. Mathematica and successfully presented at international konfenciách MEASUREMENT 2011, 27-30.IV.2011 in Smolenice (Slovakia), PROBASTAT 2011, 4-8.VII.2011 in Smolenice (Slovakia) and Breath Analysis Summit 2011, 11-14.IX. 2011 in Parma (Italy).
Publications
- BARTOŠOVÁ, K.: Classification of breath gas compounds for detection of severe diseases. Tatra Mountains Mathematical Publications, 2011, Submitted.
- CHVOSTEKOVÁ, M.: Simultánne obojstranné tolerančné intervaly v lineárnom regresnom modeli. Fakulta elektrotechniky a informatiky STU a Ústav merania SAV Dizertačná práca v študijnom odbore 5-2-54 Meracia technika, 2011, 78
- CHVOSTEKOVÁ, M.: A comparison of the simultaneous two-sided tolerance intervals for a linear regression model. In: R. Harman, J. Somorčík, V. Witkovský, editors, PROBASTAT 2011 - The sixth international conference on Mathematical Statistics. Abstracts. Smolenice Castle, Slovak Republic, July 4-8, 2011, 2011, 23
- CHVOSTEKOVÁ, M.: Simultaneous two-sided tolerance intervals for a univariate linear regression model. Communications in Statistics - Theory and Methods, 2011, Submitted.
- CHVOSTEKOVÁ, M.: Simultaneous two-sided tolerance intervals for a linear regression model. In: P.C. Rodrigues, M. de Carvalho, editors, 17th European Young Statisticians Meeting. Lisbon, Portugal, September 5-9, 2011, 63-67. Faculdade de Ciencias e Tecnologia, Universidade Nova de Lisboa.
- HORNIŠOVÁ, K.: Properties of data depth calibration set. In: R. Harman, J. Somorčík, V. Witkovský, editors, PROBASTAT 2011 - The sixth international conference on Mathematical Statistics. Abstracts. Smolenice Castle, Slovak Republic, July 4-8, 2011, 2011, 28.
- KÖNING, R. - KAROVIČ, K. - WIMMER, G. - WITKOVSKÝ, V.: Estimating the standard uncertainty contribution of the straight-line fit algorithm used to determine the position and the width of a graduation line. Metrologia, 2011, Accepted.
- WIMMER, G. - KAROVIČ, K. - WITKOVSKÝ, V. - KÖNING, R.: Confidence interval for the distance of two micro/nano structures and its applications in dimensional metrology. In: M. Tyšler, J. Maňka, V. Witkovský, editors, MEASUREMENT 2011, Proceedings of the 8th International Conference on Measurement Smolenice, Slovakia, April 27-30, 2011, 2011, 80-83. Institute of Measurement Science, Slovak Academy of Sciences, Bratislava.
- WIMMER, G. - MAČUTEK, J.: Partial-sums distributions from a new point of view. In: R. Harman, J. Somorčík, V. Witkovský, editors, PROBASTAT 2011 - The sixth international conference on Mathematical Statistics. Abstracts. Smolenice Castle, Slovak Republic, July 4-8, 2011, 2011, 41-42.
- WIMMER, G. - WITKOVSKÝ, V.: Note on a calibration problem: Selected results and extensions of professor Kubáček's research. Acta Universitatis Palackianae Olomucensis, Facultas Rerum Naturalium, Mathematica 50 (2), 2011, 123-130.
- WITKOVSKÝ, V.: O niektorých exaktných simultánnych konfidenčných oblastiach založených na funkcii vierohodnosti pre parametre normálneho LRM (On some exact simultaneous likelihood-based confidence regions for the parameters of normal LRM). In: D. Hampel, J. Hartmann, J. Michálek, editors, Biometric Methods and Models in Current Science and Research. Proceedings of the XIX. Summer School of Biometrics. Lednice, Czech Republic, September 6-10, 2010, Faculty of Horticulture of Mendel University, 2011, 347-357. Central Institute of Supervising and Testing in Agriculture, Brno.
- WITKOVSKÝ, V.: Generalized likelihood inference for Gaussian linear regression with quantized observations. In: D. Hlubinka, editor Nonparametrics and Geometry. Book of Abstracts. Prague, Czech Republic, August 15-19, 2011, 31. Univerzita Karlova v Praze a Česká matematická společnost, sekce Jednoty českých matematiků a fyziků.
- WITKOVSKÝ, V.: On generalized likelihood approach and its applications. In: XLI International Biometrical Colloquium and Czech-Slovakian-Polish Workshops on Biometry. Lublin, Poland, September 5-8, 2011, 16. University of Life Sciences, Lublin.
- WITKOVSKÝ, V.: On some exact simultaneous likelihood-based confidence regions for two variance components. In: R. Harman, J. Somorčík, V. Witkovský, editors, PROBASTAT 2011 - The sixth international conference on Mathematical Statistics. Abstracts. Smolenice Castle, Slovak Republic, July 4-8, 2011, 2011, 42.
- WITKOVSKÝ, V. - WIMMER, G.: Methodology for determination of detection limits for Proton Transfer Reaction Mass Spectrometer measurements. In: Breath Analysis Summit 2011. International Conference on Breath Research. Abstract Book. Parma, Italy, September 11-14, 2011, 227. Nuova Editrice Berti.
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