Informative Bayesian type A evaluation of standard uncertainty

Abstract

The non-informative (improper priors) Bayesian type A evaluation of standard uncertainty consistent with the Supplement 1 and Supplement 2 of the Guide to the expression of Uncertainty in Measurement (GUM) leads to a result that cannot be applied in case of small sample size <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$n$</tex> , namely when <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$n=2,3$</tex> . An ad hoc and non-rigorous solution to this issue, based on the use of the quantiles of the Student's <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$t$</tex> probability PDF, is provided in the IEC/TR 61000-1-6 (Guide to the assessment of measurement uncertainty), a basic electromagnetic compatibility (EMC) publication. A novel informative Bayesian type A evaluation of standard uncertainty is proposed here that can be easily implemented through a spreadsheet and it is applicable also in the case of small sample size. The aim and the approach are like those in a recent paper published in Metrologia by Cox and Shirono. The apparent limitation that the variance has an upper bound, as assumed by Cox and Shirono, is here removed at the expense of introducing a best guess and a value of the variance that is unlikely to (but it can) be exceeded. In addition to a step-by-step derivation numerical examples are offered to support the viability the proposed type A evaluation. The imminent start of the maintenance of the IEC/TR 61000-1-6 stimulates a critical review and update of the type A evaluation of standard uncertainty in EMC.