Comparison of GUM and Monte Carlo methods for the uncertainty estimation in hardness measurements

Abstract

Abstract. Monte Carlo Simulation (MCS) and Expression of Uncertainty in Measurement (GUM) are the most common approaches for uncertainty estimation. In this work MCS and GUM were used to estimate the uncertainty of hardness measurements. It was observed that the resultant uncertainties obtained with the GUM and MCS without correlated inputs for Brinell hardness (HB) were ±0.69 HB, ±0.67 HB and for Vickers hardness (HV) were ±6.7 HV, ±6.5 HV, respectively. The estimated uncertainties with correlated inputs by GUM and MCS were ±0.6 HB, ±0.59 HB and ±6 HV, ±5.8 HV, respectively. GUM overestimate a little bit the MCS estimated uncertainty. This difference is due to the approximation used by the GUM in estimating the uncertainty of the calibration curve obtained by least squares regression. Also the correlations between inputs have significant effects on the estimated uncertainties. Thus the correlation between inputs decreases the contribution of these inputs in the budget uncertainty and hence decreases the resultant uncertainty by about 10%. It was observed that MCS has features to avoid the limitations of GUM. The result analysis showed that MCS has advantages over the traditional method (GUM) in the uncertainty estimation, especially that of complex systems of measurement. MCS is relatively simple to be implemented.

An investigation on using measurement uncertainty as decision rule for statement of conformity

“…During this investigation the contribution of each parameter has been identified and the expanded uncertainty has been estimated. To evaluate the contribution of each uncertainty component the following formulas were used [12].…”

Information entropy theory for steam turbine system monitoring study

“…In the figure, indexes calculated by ∣ E 0 − E i ∣ with the proposed method in the article have been shown in the form of histogram, as well as those by GUM 16 and MC 17 . Moreover, Table 3 has listed the indexes values by GUM and MC methods in the reference.…”

Estimating CO2 emissions from emergency-supply transport: The case of COVID-19 vaccine global air transport

“…The GUM (“Guide to the Expression of Uncertainty in Measurement”) gives general criteria for evaluating and expressing uncertainty in measurement ( Farrance and Frenkel, 2012 ). The most widely used methods for estimating uncertainty are the “Expression of Uncertainty in Measurement” (GUM, as defined by the “Joint Committee on Guides in Metrology” ( Joint Committee for Guides in Metrology, 2008a )) and Monte Carlo Simulation (MCM, as defined in GUM supplements 1 ( Joint Committee for Guides in Metrology, 2008b ) and 2 ( Joint Committee for Guides in Metrology, 2011 )) ( Mahmoud and Hegazy, 2017 ). Therefore, we have also used the GUM and MCM, the two most accepted methods, to estimate the uncertainty related to the results of our study.…”