Uncertainty Estimation of the Subdivision Method of Calibration Results on an Automatic Mass Comparator

According to OIML R111, for determining the conventional mass, there are two methods: the subdivision, and the direct comparison. Comparing with the direct comparison method, the functional relationship in the subdivision/multiplication method is very complicated. Thirteen calculation equations are used to provide an appropriate adjustment calculation so as to avoid propagating errors. The effect of the correlations cannot be ignored during the uncertainty estimation. This manuscript took a set of mg weights as an example, and focused on the uncertainty estimation of the subdivision method of calibration. The uncertainty components were the reference weight uncertainty, the uncertainty of the weighing process, the air buoyancy uncertainty, and the uncertainty of mass comparators, etc. According to the OIML R111 Annex C and the EA-4/02, the uncertainty components were evaluated either by the Type A method or by the Type B method. With fully considering the covariance of the components, the uncertainty of mass calibration in subdivision method was properly estimated. Functional Relationships During the measurement, the uncertainty is a parameter which reasonably characterizes the dispersion of the measured result.With the functional relationship M = f(m1, m2, ..., mn ) in calibrations, output quantity M is related to a number of input quantities mi (i = 1, 2 ,..., n). The mathematical model represents the evaluation methods and the measurement procedure. It also reflects the relationship between input quantities mi and output quantity M. Routinely, there is only one analytical expression in the calibration, but in the subdivision method there are a group of equations with the corrections and the corresponding correction factors. The correlation between input components is also considered. Therefore, the relationships in the subdivision method are not explicitly written down as one function. In this manuscript the relationship in the subdivision method is given by two functions: i i j m m m m     (1) * ( , ) j j i m f m m   (2) Where, Δmi: the difference in conventional mass between a set of test weights and a reference weight with the same nominal value, i=(1~13); m∑mi: the sum of the conventional mass of the dissemination weights; mj : the conventional mass of the reference 1 g weight or the single test weight in every dissemination group; mj*: the conventional mass of the reference 1 g weigh or the single test weight in last dissemination group; Take 1 mg to 500 mg weight as an example. Table 1 shows the functional relationships in subdivision method. International Conference on Modeling, Analysis, Simulation Technologies and Applications (MASTA 2019) Copyright © 2019, the Authors. Published by Atlantis Press. This is an open access article under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/). Advances in Intelligent Systems Research, volume 168