On modelling of artefact instability in interlaboratory comparisons

Key comparisons are at the core of metrology and support the international equivalence of measurement standards. Typical key comparison setups involve travelling artefacts which are transferred between the participants of a study. After each participating laboratory performs its measurements of the artefacts, a subsequent analysis reveals the degree of equivalence between the participants. For this analysis stage, the stability of the artefacts plays a crucial role, and violations of the stability need to be taken into account to allow for a meaningful comparison. In this work, we present several mathematical models for a treatment of non-negligible artefact instability effects in bilateral comparisons. We highlight the underlying model assumptions and derive analytical formulae for the estimate and standard uncertainty of the instability effect. Moreover, we derive the bilateral degree of equivalence by applying the models in a treatment essentially based on the GUM (JCGM-100). Our considerations conclude with numerical experiments using data from a bilateral comparison on illuminance and from a recent CCM key comparison of kilogram realisations.