Uncertainty Evaluation for a System of Weighing Equations for the Determination of Microgram Weights

Abstract

Subdivision comparisons of mass measurement are usually used in the mass dissemination for class $E_{1}$ mass standards from 1 kg to 1 mg or from 1 to 50 kg. Many equations of mass measurement are included in the subdivision comparisons. Therefore, matrix calculations for mass measurement are very convenient to get the true or conventional mass value of every weight compared. In conventional matrix equations, the important air buoyancy corrections are completely neglected, and uncertainties are normally calculated using the variance–covariance matrix. In this paper, we propose a new matrix calculation for both the system of weighing equations as well as the corresponding uncertainty budget using directly partial derivations of the weighting equations. The method is applied to a set of weights from 500 to $50~\mu $ g. An alternative method for evaluating uncertainties of matrix equations is by Monte Carlo simulation, introduced in this paper, to validate the calculation of uncertainty budget by means of the matrix method. (Some figures in this paper are in color only in the electronic version.)