Type B uncertainty of two-channel measurements

Abstract

The paper presents the problems of evaluating the standard uncertainty of measuring a quantity using the type B method, the result of which is the average value of the results obtained from two channels with the same parameters, for example, as the indications of two measuring instruments of the same type. It is shown that for given values of maximum permissible errors (MPE) of measuring instruments and their readings x1 and x2, the uncertainty of the result determined a posteriori is not equal to the uncertainty determined by the conventional method (GUM). It is shown that when the measurement result is determined as arithmetic mean y=(x1+x2)/2, additional information as the half distance of readings v=|x1-x2|/2 can be used to correctly determine the standard uncertainty of such measurement. Depending on the half distance of readings, the standard uncertainty can theoretically vary from its maximum value (the readings of both meters are equal) to zero (with maximum difference in readings). The analysis of the uncertainty was carried out for uniform distributions of possible deviations of the readings of measuring instruments within their MPE. The results of simulations by the modified Monte-Carlo method, which show good convergence with theoretical results, are given.