Use of uncertainty information for estimation of certified values. Comparison of four approaches using data from a recent certification exercise

Abstract

Four approaches for estimation of reference values and their respective uncertainties of characterisation were compared using data from the recently finalised certified reference materials ERM-EC680k and ERM-EC681k, elements in plastics. Reference values and uncertainties of characterisation were estimated as mean of laboratory means and their respective standard deviations, using equal weights and the weighting procedure of Mandel–Paule. In addition, two approaches taking into consideration uncertainty information reported by the participants, namely the consistency check and simulation procedure proposed by Cox for CCQM Key comparisons and an approach suggested by Pauwels et al. (Accred Qual Assur 3:180–184, 2000) were used. No difference between the equally-weighted and Mandel–Paule consensus means was observed and the reference value from the Cox approach was in all cases within ±2 uchar of each consensus mean. Uncertainties varied between the three approaches. Uncertainties derived from equally-weighted mean of means approach are on average 14% above uncertainties using the Mandel–Paule consensus mean, 36% above the uncertainties estimated by Pauwels et al., and 54% above the uncertainties from the Cox approach. Robustness of the uncertainty estimation against incorrect estimation of uncertainties was assessed. Assumption of a 50% uncertainty of the individual uncertainties resulted in an uncertainty of 30% of the uncertainty of characterisation. Differences between the four approaches are negligible for this dataset when combined with the uncertainty contribution from heterogeneity and stability as prescribed in ISO Guide 35.