An Improvement on the Standard Linear Uncertainty Quantification Using a Least-Squares Method

Abstract

Linear uncertainty analysis based on a first order Taylor series expansion, described in ASME PTC (Performance Test Code) 19.1 “Test Uncertainty” and the ISO Guide for the “Expression of Uncertainty in Measurement,” has been the most widely technique used both in industry and academia. A common approach in linear uncertainty analysis is to use local derivative information as a measure of the sensitivity needed to calculate the uncertainty percentage contribution (UPC) and uncertainty magnification factors (UMF) due to each independent variable in the measurement/process being examined. The derivative information is typically obtained by either taking the symbolic partial derivative of an analytical expression or the numerical derivative based on central difference techniques. This paper demonstrates that linear multivariable regression is better suited to obtain sensitivity coefficients that are representative of the behavior of the data reduction equations over the region of interest. A main advantage of the proposed approach is the possibility of extending the range, within a fixed tolerance level, for which the linear approximation technique is valid. Three practical examples are presented in this paper to demonstrate the effectiveness of the proposed least-squares method.

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