Analysis of key comparisons
The goal of the analysis of KC data is to assess the results reported by the participating laboratories. According to the MRA, a so-called key comparison reference value (KCRV) is usually calculated. The KCRV is then used to calculate the degrees of equivalence (DoEs) as the difference between the results reported by the laboratories and the KCRV, along with the uncertainties associated with these differences. The DoEs quantify the extent to which the laboratories are compatible, and they can also be viewed as a measure to judge whether the laboratories measure as good as they claim. When a DoE is significant different from zero, the (CMC of the) corresponding laboratory is seen to be not approved.
Figure 1 Example of a key comparison along with key comparison reference value (KCRV). The blue results indicate control measurements made by the so-called pilot laboratory.
Figure 2 Example posterior distributions for the degrees of equivalence (DoEs) obtained by a Bayesian inference of the data from Figure 1.
- M. Bergoglio, A. Malengo and D. Mari. Analysis of interlaboratory comparisons affected by correlations of the reference standards and drift of the travelling standards. Measurement 44, 1461-1467, 2011
- O. Bodnar, A. Link, K. Klauenberg, K. Jousten, and C. Elster. Application of Bayesian model averaging using a fixed effects model with linear drift for the analysis of key comparison CCM.P-K12. Meas. Tech. 56, 584-590, 2013
- O. Bodnar, A. Link and C. Elster. Bayesian treatment of a random effects model for the analysis of key comparisons. Talk at (MATHMET) International Workshop on Mathematics and Statistics for Metrology, March, 24-26, 2014, Berlin, 2014
Other interesting questions include the design of key comparisons in order to optimally benefit from a subsequent analysis. To this end, the power of a statistical test could be utilized, or other concepts optimal design of experiments.