A Bayesian approach to the linking of key comparisons

TL;DR

This paper introduces a Bayesian statistical method for linking key comparison results in measurement science, providing a robust way to determine reference values and equivalence without assuming a comparison priority.

Contribution

It develops a novel Bayesian approach for linking key comparisons, including formulas and examples, enhancing the robustness and flexibility of measurement result linking.

Findings

Provides formulas for key comparison reference value and degree of equivalence

Demonstrates the method with synthetic and real data examples

Offers a new linking procedure applicable without comparison priority assumptions

Abstract

This contribution presents a Bayesian approach to the issue of linking of the results from key comparison measurements. A mathematical treatment based on Bayesian statistics for the analysis of the results from two comparisons with some joint participants is described. This robust statistical analysis provides expressions and standard uncertainties for the key comparison reference value (KCRV) and the degree of equivalence (DOE) as well as a conformity check without any assumption on a priority of one of the comparisons. In addition to the derivation of the mathematical formulae to be used for this type of "distributed linking", we also present one synthetic and one real linking example and discuss possible applications of this new linking procedure.