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Title: Non-Linear Propagation Of Uncertainty
Author: Ricardo A. Nicholas
Source: 2001 Measurement Science Conference
Year Published: 2001
Abstract: In the vast majority of cases, even the best measurement uncertainty evaluations are based only on a first-order approximation of the uncertainty of a model of the measurement process output quantity as a function of the significant input quantities. That is perfectly adequate if the function is linear, however if it is not, an error will be present in the first-order approximation estimate of uncertainty. The magnitude of that error will be related to the degree of non-linearity. The Guide to the Expression of Uncertainty in Measurement (Guide) 1, 2 apparently considers a 6.5% error due to that cause in that estimate as significant, and implies that a higher-order approximation should be made. This paper presents some worked examples of secondorder approximations including example H.1 of Annex H of the Guide. A substantial working knowledge of this method can be obtained through practice by using the presented examples as models.

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