Statistical procedures for comparing realizations of physical units using artefact standards, including an estimation of transportation effects

An artefact standard may be used in a comparison between two laboratories to measure the difference between their respective realizations of a physical unit. In the usual three-stage sequence, one laboratory, the "pilot" laboratory, measures the artefact before and after its measurement at the second laboratory. Three procedures are described for analysing the results of such a comparison: "deviation from fit to pilot" (DFP), "overall constant drift" (OCD, which yields similar results to DFP for any difference in the laboratories' realizations but which is statistically more rigorous and also gives quite different estimates of uncertainties), and "separately fitted lines" (SFL). If OCD is used, the uncertainty of the comparison is minimized if the measurements at the two laboratories have the same mean epoch. If SFL is used, the uncertainty is minimized if the intervals between successive epochs at the second laboratory are invariant under time-reversal. SFL allows transportation effects to be estimated as Type A uncertainties, separately from residual scatter, and can signal their presence through a sharp reduction in degrees of freedom. Computer simulations of comparisons indicate that SFL is at least as accurate as DFP and OCD, and is often more accurate. Two case studies of Zener-based voltage standard artefacts are given.