A classical method for uncertainty analysis with multidimensional data

Abstract

A method of uncertainty analysis based on classical statistical principles is presented for a measurand that is a linear combination of multidimensional input quantities. The method assigns the measurand a combined standard uncertainty matrix and an effective degrees of freedom, which allows the measurand to be estimated by an ellipsoidal confidence region in the multidimensional space. Simulations for a 95 % nominal confidence level show the ellipsoids to contain the measurand with probability approximately 0.95, as required. The derivation of the method assumes all input uncertainties to be evaluated by the Type A method. So the method is analogous to the Welch-Satterthwaite formula for one-dimensional data, a derivation of which is given in an appendix.

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