Estimation of Uncertainties in Indirect Multivariable Measurements: Part 1. Case of Correlated Quantities

This two-part paper presents an improved version of the method of evaluation uncertainties in the multiparameter indirect measurements stated in the Supplement 2 to GUM guide. In this part 1 it was done for the case of correlated quantities on the example of two-parameter (2D) jointed measurements. It consists the correlation of individual components of deviations from the estimator of result with the type A and/or type B uncertainty of measurands. The general formulas for the covariance matrix, final uncertainties and correlation coefficient were determined as well as formulas for several specific cases. The graphs show the correlation coefficients of the output quantities as a function of the type B contribution in the uncertainty of the input quantities. The inclusion of correlations of uncertainty components makes the uncertainty evaluations of output quantities more reliable and accurate.