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Fotowicz P.,Central Office of Measures
Advances in Intelligent Systems and Computing | Year: 2016

Basic methods for calculating a measurement uncertainty are presented. One method is based on the approach called the propagation of distributions, and the second method is based on the approach called the law of uncertainty propagation. The methods give not the same calculation result in evaluation of standard uncertainty associated with the measurand. The reasons for these discrepancies are explained. © Springer International Publishing Switzerland 2016. Source


Fotowicz P.,Central Office of Measures
Measurement Science and Technology | Year: 2010

This article presents a practical application of an analytical method for the calculation of the measurement uncertainty. The proposed method enables the determination of uncertainty in accordance with the new probabilistic definition of the coverage interval for a measurand. The proposed method ensures that the expanded uncertainty is calculated with the recommended number of significant digits at the recommended coverage probability. The method was used for the uncertainty evaluation of measurement of small outer diameters with a laser scanning instrument. © 2010 IOP Publishing Ltd. Source


Fotowicz P.,Central Office of Measures
Metrology and Measurement Systems | Year: 2010

The paper concerns the problem of treatment of the systematic effect as a part of the coverage interval associated with the measurement result. In this case the known systematic effect is not corrected for but instead is treated as an uncertainty component. This effect is characterized by two components: systematic and random. The systematic component is estimated by the bias and the random component is estimated by the uncertainty associated with the bias. Taking into consideration these two components, a random variable can be created with zero expectation and standard deviation calculated by randomizing the systematic effect. The method of randomization of the systematic effect is based on a flatten-Gaussian distribution. The standard uncertainty, being the basic parameter of the systematic effect, may be calculated with a simple mathematical formula. The presented evaluation of uncertainty is more rational than those with the use of other methods. It is useful in practical metrological applications. © 2010 Polish Academy of Sciences. Source


Moszczynski L.,Warsaw University of Technology | Bielski T.,Central Office of Measures
Measurement: Journal of the International Measurement Confederation | Year: 2013

The paper presents the new method for calculating a coverage factor. In this case the calculation is done in a linear combination of the both the Gaussian and the rectangular distribution. Its exact analytical form is difficult to find because the rectangular distribution is not in an analytical form at the borders, although a form can be built using multiplicative law of probabilities as the product of conditional probability. This approach was checked in MS Excel 2007, and achieved very high accuracy of calculations. Such accuracy is hard to be achieved using other known methods, e.g. Monte Carlo method. In the Appendices are a formal reasoning of the algorithm, an exemplary macro for MS Excel, as well as the R and MATLAB codes for the MC simulation used for comparing its performance with the new method. The paper presents an example of calculating the uncertainty for the case of investigating precise voltage measurement of a transducer using the method being discussed. © 2013 Elsevier Ltd.All rights reserved. Source


Fotowicz P.,Central Office of Measures
Advances in Intelligent Systems and Computing | Year: 2015

A modified Monte Carlo method for calculating the measurement uncertainty is presented. The method is based on a random number generator for drawing the possible values associated with the output quantity. The set of the random values are represented by the Flatten-Gaussian distribution, which is a convolution of rectangular and normal distributions. The model of measurand must be defined a linear or linearized mathematical function. The numerical and practical examples of the use of the proposed method are also presented. © Springer International Publishing Switzerland 2015 Source

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