Analysis of key comparison data and laboratory biases

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.

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