Expanded uncertainty evaluation taking into account the correlation between estimates of input quantities

An expression for estimating the combined standard uncertainty taking into account the observed correlation between the estimates of the two input quantities is given. The Welch – Satterthwaite formula given in the GUM is analyzed. It is shown that the number of degrees of freedom calculated using this formula will vary over a wide range when the value of the correlation coefficient changes, and in some cases it may take an unacceptable zero value. An expression for calculating the combined standard uncertainty by the reduction method is given. It is shown that the number of degrees of freedom in this method does not depend on the value of the correlation coefficient. A formula for calculating the effective number of degrees of freedom taking into account the observed correlation is proposed. The existing expression for calculating the kurtosis of the measurand is analyzed and an expression is proposed for calculating the kurtosis of the measurand in the presence of a correlation between the input quantities. An example of estimation of expanded uncertainty when measuring the coefficient of a pressure transducer using a calibrator is considered. Estimates of the distribution of the measurand, obtained using Monte Carlo simulation, showed that they are closest to the estimates obtained by the kurtosis method. The considered example showed that taking into account the correlation in the processing of measurement results makes it possible to reduce the expanded measurement uncertainty of the converter coefficient by 1.22–1.27 times. Keywords: measurement uncertainty; correlation; effective number of degrees of freedom; method of kurtosis