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Analysis of key comparisons

Working Group 8.42


Key comparisons are interlaboratory comparisons carried out regularly between National Metrology Institutes (NMIs) within the framework of the CIPM Mutual Recognition Arrangement (Opens external link in new windowMRA). Key comparisons enable the mutual recognition of calibrations, measurements, and test certificates of the NMIs and mark a major step in supporting international trade, commerce and regulatory affairs. The final report and the supporting technical data of each key comparison are stored and made publicly available at the key comparison data base  Opens external link in new windowKCDB of the Bureau International des Poids et Mesures (Opens external link in new windowBIPM). Fig. 1 shows a typical example of key comparison data.

Fig.1 Example data of a key comparison along with the key comparison reference value (KCRV). The blue results indicate control measurements made by the so-called pilot laboratory.


The analysis of key comparisons can be seen as a Opens external link in new windowMeta-Analysis in which the results reported by the participating laboratories are assessed. Fixed effects or random effects models are popular models applied in meta-analysis. One focus of research of PTB’s Working Group 8.42 is the development of Bayesian methods for the estimation of fixed and random effects models. This includes the assignment of vaguely informative or appropriate non-informative priors and the exploration of the properties of the resulting inference. Other topics of research are situations in which the common measurand shows a drift, or where the explanatory power of key comparisons is assessed in dependence on the stability of the common measurand and the uncertainties reported by the participating laboratories.



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Title: Analysis of Key Comparisons Incorporating Knowledge About Bias
Author(s): I. Lira, A. G. Chunovkina, C. Elster and W. Wöger
Journal: IEEE Transactions on Instrumentation and Measurement
Year: 2012
Volume: 61
Issue: 8
Pages: 2079--2084
DOI: 10.1109/TIM.2012.2193690
ISSN: 0018-9456
Web URL: http://ieeexplore.ieee.org/lpdocs/epic03/wrapper.htm?arnumber=6189781
Keywords: Atmospheric measurements,Bayesian methods,Bismuth,Gaussian distribution,Laboratories,Measurement uncertainty,Particle measurements,Systematics,Uncertainty,laboratory bias estimation,measurement errors,measurement uncertainty,performance evaluation,statistical analysis,systematic effect,vanishing bias estimation
Tags: 8.42,KC
Abstract: A method is proposed for analyzing key comparison data. It is based on the assumption that each laboratory participating in the comparison exercise obtains independent and consistent estimates of the measurand and that, in addition, each laboratory provides an estimate of the quantity that collects all systematic effects that the laboratory took into account. The unknown value of the latter quantity, subtracted from its estimate, is defined as the laboratory's bias. The uncertainties associated with the estimates of the measurand and with the vanishing biases' estimates are also assumed to be reported. In this paper, we show that the information provided in this way may be of help for judging the performances of the laboratories in their correction of systematic effects. This is done by developing formulas for the final (consensus) estimates and uncertainties of the measurand and of the biases. Formulas for the final estimates and uncertainties of the pairwise differences between the biases are also developed. An example involving simulated key comparison data makes apparent the benefits of the proposed approach.

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