Estimation of Uncertainties in Indirect Multivariable Measurements: Part 2. Influence of the Processing Function Accuracy

Abstract

This two-part paper presents an improved version of the method of evaluation uncertainties in the multivariable indirect measurements. It has an extended scope of application compared to the method given in Supplement 2 of the international guide with the acronym GUM [1], which assumes a perfectly accurate parameters multidimensional function of processing input measurement data. Part 1 discussed the cases of various correlations of measured values. The law of variance propagation is described in the form of dependencies between input and output covariance matrices. General formulas for uncertainty and correlation coefficients at the output are given as well as formulas for several characteristic cases. It has been shown that for pairs of all measured quantities, the effect of correlation between sets of deviations with uncertainty for each of types A and B should be considered separately. Proposed is to calculate output covariance matrices of correlated variables separately for uncertainties type A and type B An example of associated two-parameter (2D) measurements is also discussed. In this Part 2, the effect of uncertainties of the processing function parameters on the elements of output multimeasurand covariance matrix has been determined. General formulas for full correlation and its absence are given. An example of the evaluation uncertainties of indirect current and voltage measurements on the inaccessible input of the T-type impedance twoport network based on measurements at its output is considered in detail. Final conclusions are given. The proposed upgraded method is versatile, because it allows both the estimation of the accuracy of indirect multivariable measurements as well a description of the accuracy of instruments and measuring systems performing such measurements.