An accurate and consistent procedure for the evaluation of measurement uncertainty

Abstract

The statistical methodology described in the Guide to the Expression of Uncertainty in Measurement (GUM) is known to be flawed. Type A evaluation in the GUM appeals to the classical idea that probability represents the frequency-behaviour of errors in a measurement procedure, while Type B evaluation seems to make unknown constants the subjects of probability distributions, which is not permitted in the classical approach. This paper shows how Type B evaluation can be understood in terms of error distributions, so that the GUM methodology can be made coherent and hence extensible. Subsequently, a modification is described for better properties and performance.

Keywords

• Propagation of error
• Propagation of uncertainty
• Frequentist statistics
• Bayesian statistics
• Interpretation of probability