Exact Propagation of Variance and Confidence Interval Calculations

The standard approach to uncertainty propagation used by the no ndestructive assay community in the case of analytical measurement models is commonly referred to as p ropagation of variance (PoV). It is based on the first - order Taylor expansion of the measurement model function . It is routinely applied without quantifying the quality of the approximation. Thi s is understandable because popular textbooks used to teach measurement uncertainty for the physical sciences often also ignore th e issue of approximation quality . The purpose of this paper is to show the nature of the first - order Taylor approximation in the case of a measurand with quadratic dependence on a single observed predictor variate drawn from a Normal distribution. We show how the average value and the most probable values computed by the standard PoV method are shifted compared to the exact cal culation , and how the variance estimate is also change d.