University of Minnesota
School of Physics & Astronomy
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Chad Geppert

An Alternative Approach to Standard Decade Series Linear Regression Dissemination of the Mass Unit by using a Weighted Least Squares Analysis
D. Dikken, C. Geppert, S. M. Lee, NCSLI Measure, Sep. 2008, p. 40 - 55

Abstract

A brief review of current practices in dissemination of the unit of mass is discussed focusing on the strengths and weakness of current practice. Based on improved mass comparators and advances in data collection/analysis systems, an opportunity exists to employ an alternative method of calculation which uses a Weighted Least Squares Regression on measured observations to better predict a solution to the selected mass comparison design matrix. Mathematical equations employing a Weighted Least Squares Regression approach are derived as a generalized solution for any valid mass calibration design. While this approach may be employed with demonstrated benefit over a traditional decade series approach, it also opens up an alternative for eliminating the necessity for single restraints to be passed from decade series to decade series. The critical component in the validity of this method is to weight each mass difference measurement in the design matrix according to an accurate estimate of each difference's uncertainty. Analysis from 1 kg to 1 mg, using both the current practice and the proposed practice, are compared. Key elements of improvement are shown to be the optimization of available mass comparators and the increased redundancy within the weighing design.