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On Higher Order Corrections for Propagating Uncertainties



Chih-Ming Wang, Hariharan K. Iyer


The ISO Guide to the Expression of Uncertainty in Measurement (GUM) recommends the use of a first-order Taylor series expansion for propagating errors and uncertainties. The GUM also suggests the use of a second-order Taylor series approximation for calculating uncertainties when the first-order approximation alone is not adequate. In this paper we derive the formulas for evaluating measurement uncertainty based on a second-order Taylor series approximation. We provide a computer program that uses symbolic derivatives to calculate the second-order approximations of the uncertainty in measurement results.


GUM, propagation of error, software, Taylor series expansion
Created January 1, 2005, Updated January 27, 2020