Combined result and associated uncertainty from interlaboratory evaluations based on the ISO Guide

Abstract

We address the problem of determining the combined result and its associated uncertainty in the measurement of a common measurand by a group of competent laboratories. Most data analyses of interlaboratory evaluations are based on the assumption that the expected values of the individual laboratory results are all equal to the value of the common measurand. This means that the laboratory results are subject to random effects only with respect to the value of the measurand. This assumption is frequently unjustified. We use the more realistic assumption that the laboratory results are subject to both random and systematic effects with respect to the value of the measurand. In this case, the value of the measurand may fall anywhere within the range of results. Therefore, a combined result and its associated standard uncertainty that place a non-negligible fraction of the results outside the 2-standard-uncertainty interval are unsatisfactory representations of the value of the common measurand provided by the set of laboratory results. The more realistic assumption requires us to deal with the uncertainty arising from possible systematic effects in the laboratory results. Following the approach of the ISO Guide to deal with systematic effects, we propose a three-step method to determine a combined result and its associated standard uncertainty such that the 2-standard-uncertainty interval would include a sufficiently large fraction of the results. When the interlaboratory evaluation is an International Committee for Weights and Measures (CIPM) key comparison, we suggest that the combined result and its associated standard uncertainty determined by the three-step method be identified with the key comparison reference value and its associated standard uncertainty. These quantities can then be used to specify the degree of equivalence of the individual laboratory results. We illustrate the three-step method by applying it to the results of an international comparison of cryogenic radiometers recently organized by the Consultative Committee for Photometry and Radiometry (CCPR).