The determination of an accepted reference value from proficiency data with stated uncertainties

Abstract

Proficiency data with stated uncertainties represent a unique opportunity for testing that the reported uncertainties are consistent with the Guide to the expression of uncertainty in measurement (GUM). In most proficiency tests, however, this opportunity is forfeited, because proficiency data are processed without regard to their uncertainties. In this paper we present alternative approaches for determining a reference value as the weighted mean of all mutually consistent results and their stated uncertainties. Using an accepted reference value each reported uncertainty estimate can be expressed as an E _n number, but a value of $|{E_n }| {<} 1$ confirms its validity only if the uncertainty of the reference value is negligible in comparison.

Reference values calculated for results from an International Measurement Evaluation Programme (IMEP-9) by “bottom up” as well as “top down” methods were practically identical, although the first strategy yielded the lowest uncertainty. A plot of individual coefficients of variation (CV) versus E _n numbers helps interpretation of the proficiency data, which could be used to validate relative uncertainties down to <1%.