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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.


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


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.


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.


Wisniewski M.,Central Office of Measures | Ramotows Z.,Central Office of Measures
Metrologia | Year: 2014

EUROMET TC Length decided to carry out a comparison of laser distance measuring instruments (EDMs), with the Central Office of Measures (GUM), Poland as the pilot laboratory. The comparison was carried out in the form of a circulation. The pilot laboratory performed measurements with the EDMs at the beginning, in the middle and at the end of the circulation in order to monitor their stability. Before calibration, the EDMs were inspected for damage. It was checked if their batteries had been discharged. The participants were asked to report detailed measurements uncertainty budgets evaluated according to the ISO Guide. Two additional experiments were conducted in order to determine which factors have the greatest impact on the results For the calibration the desired positions are programmed. After the carriage reaches a measurement position, the operator waits for another 30s for the carriage to settle. In control experiments the remaining movement between positioning and measurement remained smaller than 2 μ m.


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.


Fotowicz P.,Central Office of Measures
Measurement: Journal of the International Measurement Confederation | Year: 2014

The paper presents numerical and analytical methods for calculating the measurement uncertainty. The methods are based on the Flatten-Gaussian distribution, which is a convolution of rectangular and normal distributions. This distribution represents the possible values associated with the measurand. The methods maybe used when model of the measurand is a linear or a linearized mathematical function, and the input quantities of the model characterizes by the Student's, normal, rectangular, triangular and trapezoidal distributions. The article presents the numerical examples of a use of proposed method. © 2014 Elsevier Ltd. All rights reserved.


Chyla W.T.,Central Office of Measures
Acta Physica Polonica A | Year: 2011

Once the New SI is approved by the General Conference on Weights and Measures (CGPM), all base units of the international metric system of units (SI) will be defined in terms of physical constants and atomic properties. In this paper, we consider the rationale and the direction of the possible further evolution of the SI. The idea is to define all base units exclusively in terms of fundamental physical constants, with no reference to specific phenomena, physical theories or properties of material entities (including properties of atoms and elementary particles), so that those definitions would not have to be altered or amended following advancement in our understanding of the structure of matter, emergence of new physical theories or due to the technological progress. New developments in science and technology would then affect only the mise en pratique (realization) of base units, rather than their definitions. Furthermore, we point out the need for including base units for the weak interaction and the strong interaction into the SI and propose a way to do it. The structure of the fundamental-constants-based system of units (the FC SI) is discussed and prerequisites for the implementation of the FC SI are considered.


Fotowicz P.,Central Office of Measures
Metrology and Measurement Systems | Year: 2015

The paper deals with the problem of bias randomization in evaluation of the measuring instrument capability. The bias plays a significant role in assessment of the measuring instrument quality. Because the measurement uncertainty is a comfortable parameter for evaluation in metrology, the bias may be treated as a component of the uncertainty associated with the measuring instrument. The basic method for calculation of the uncertainty in modern metrology is propagation of distributions. Any component of the uncertainty budget should be expressed as a distribution. Usually, in the case of a systematic effect being a bias, the rectangular distribution is assumed. In the paper an alternative randomization method using the Flatten-Gaussian distribution is proposed. © 2015 Polish Academy of Sciences. All rights reserved.


Bozydar Knyziak A.,Central Office of Measures | Rzodkiewicz W.,Central Office of Measures
Nuclear Instruments and Methods in Physics Research, Section A: Accelerators, Spectrometers, Detectors and Associated Equipment | Year: 2016

This paper deals with the problem of measurement of very low direct currents and electrical charges in dosimetric application. It describes the known and used methods of measurement: the current method, the charge method, and the null method. A new method, which is presented here, is a combination of the two latter methods. The new method is compared with the known methods of measurement and the results of this comparison are summarized and discussed. The new method allows achieving relative standard uncertainty of 0.003% for current measurements around 3 pA and a long term stability of about 0.01%. Apart from this, preliminary measurements by using a built in comparator were also performed. Therefore, the uncertainty budget of the measurements for the system without an external comparator was also taken into account in the paper. The combined measurement uncertainties for current measurements obtained for the above-mentioned two methods (the new method and the method with the comparator built in the 6517A Keithley electrometer used in our experiments) were similar. © 2016 Elsevier B.V. All rights reserved.

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