Linking the results of CIPM and RMO key comparisons with linear trends

Abstract

A statistical approach to link the results of interlaboratory comparisons with linear trends is proposed. This approach can be applied to the case that the comparison artifacts have the same nominal values or the measured quantities have the same magnitudes. The degrees of equivalence between the pairs of National Metrology Institutes that have not participated in the same comparisons, and their corresponding uncertainties are established. The approach is applied to link the CCEM-K2 and SIM.EM-K2 comparisons for resistance at 1 G Ω level.

Statistical analysis for interlaboratory comparisons with linear trends in multiple loops

“…If the j th non-pilot laboratory is in the pth loop and the mth non-pilot laboratory is in the qth loop (p = q), we treat the case as the linkage of two laboratories in two interlaboratory comparisons, as discussed in [9]. As in [9,10], treating the pilot laboratory as the only linking laboratory of the two loops, the difference between the pth loop and the qth loop is given by…”

“…In this case, the results can be extended by replacing D(p, q) in (18) by an average or a weighted mean of the differences on the right-hand side of (18) for multiple linking laboratories. The details can be found in [9]. The difference for the degree of equivalence between the j th laboratory in the pth loop and the mth laboratory in the qth loop when p = q can be obtained by the first equality of (19).…”

“…However, the calculation of the corresponding standard uncertainty (comparing (20)) will involve the covariances between the difference of one laboratory with respect to the CRV in the same loop and that of a linking laboratory with respect to the same CRV. This covariance calculation can be found in the appendix of [9].…”