This paper deals with the problem of establishing degrees of equivalence for national measurement standards participating in regional key comparisons (RMO KC), with respect to a key comparison reference value (KCRV), using measurement results obtained by linking national metrology institutes (NMIs). Two types of key comparisons are considered, which differ in applying either a material measure or a measuring instrument as a travelling measurement standard.The results obtained by linking NMIs are used to determine transformation procedures for measurement results of the RMO KC so that the transformed results can be compared directly with CIPM KC results.Formulae are given for evaluating the degrees of equivalence of the national measurement standards of laboratories participating in the RMO KC, with respect to the KCRV, taking into account possible correlations between measurement results.

The analysis of key comparison data is at the focus of metrology-related research and many papers have been published on this issue in recent years. Typically, the approaches make use of quoted combined uncertainties. We propose an approach which is based on more detailed uncertainty information. We assume that each of the participating laboratories has knowledge about the precision of its measurements and, in addition, provides a probability density function (PDF) which encodes its assessment on the size of its bias. Only the case of a single stable travelling standard is considered.The analysis starts with a consistency test of the data and the PDFs provided by the participating laboratories. If this test is passed, a probabilistic approach based on a bias model is applied in order to merge the information of all participants. PDFs for the value of the travelling standard and, in particular, for the biases of the participating laboratories are derived. Explicit results are given for Gaussian PDFs. It is shown that the proposed use of detailed uncertainty information results in improved estimates of the biases. In particular for those laboratories expecting to have a large bias, the uncertainty about their biases can thereby be reduced significantly.

A procedure is proposed for linking the results of a RMO key comparison to those of a related CIPM key comparison when different travelling standards are used. The approach is based on a relationship between unilateral and bilateral degrees of equivalence (DOEs) as defined in the MRA, and it assumes that the quantities being estimated by the unilateral DOEs for the linking laboratories are the same in the CIPM and the RMO key comparisons.We show that in the particular situation of single stable travelling standards in the two key comparisons the assumptions and the results of the approach are in line with previously proposed linking procedures which employ an additive shift to the RMO data prior to their comparison with the CIPM key comparison reference value. However, the procedure put forward here yields (slightly) smaller linking uncertainties compared with these methods and, more important, it is generally applicable also in situations when several travelling standards are used or when the travelling standard shows a drift.

No abstract

The International Vocabulary of Metrology (VIM) is a foundational document of measurement science, with the ambition of providing a system of “basic and general concepts and associated terms” of metrology. Such a system has evolved with the evolution of measurement science, and this is particularly manifest in the case of the cluster of concepts around ‘quantity’. The present paper presents some aspects of this development, by first remarking on the importance of terminology for measurement science and then introducing the basic problem what is a quantity? as a way to provide a well-grounded explanation to the usual claims that two quantities can be equal, or two values of quantities can be equal, or a quantity of an object can be equal to a value of a quantity. The analysis develops along three questions: (1) what is the relation between general properties and individual properties? (2) what is the relation between properties and quantities? (3) what is the relation between quantities of objects and values of quantities?