CALIBRATION DESIGNS OF MASS STANDARDS FOR 2 COMPARATORS IN A DECADE SERIES

W. G. Lee, N. Y. Choi

Abstract

The decade series of 10-5-2-2’-1 and 10-5-3-2-1 for submultiples of the unit of mass have been studied to find designs where two comparators are used. The criterion used in finding the designs was to minimize, using the method of least squares, the sum of the absolute values of the elements in the inversion matrices of the normal equations. To date researchers only have reported that when more than one comparator is used in a decade using an orthogonal design for one comparator the orthogonality is lost to produce covariances. However this study has found several cases where orthogonal designs can be used for using two comparators in a decade. The designs could reduce both the nonorthogonality by 50 % and the overall variances by about 45 %. Even though the orthogonal designs are for the case where the ratio of the comparator’s standard deviation is 2, the combination of most comparators could be used with the orthogonal designs.

Keywords

mass standards, orthogonal, calibration design

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IMEKO TC

TC3 - Measurement of Force, Mass, Torque, and Gravity

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