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Uncertainty estmation approach based on validation and Quality Control Data “the Nordtest approach" Single-laboratory validation approach Effects contributing to uncertainty Random Systematic The two groups of uncertainty contributions are quantified separately and then combined: Ivo Leito University of Tartu Institute of Chemistry uc u1 u 2 2 2013 Uncertainty arising from random effects Nordtest Technical Report 537, 3rd ed (2011) http://www.nordtest.info/ Single lab validation approach: in practice (1) 2 uc u ( Rw ) u (bias ) 2 Absolute vs relative uncertainties: Rules of Thumb • At low concentrations (near detection limit, trace level) use absolute uncertainties 2 – Uncertainty is not much dependent on analyte level Within-laboratory reproducibility Uncertainty of the estimate of the laboratory and the method bias This component accounts for the random effects This component accounts for the systematic effects This and subsequent equations work with absolute and relative values Nordtest Technical Report 537, 3rd ed (2011) http://www.nordtest.info/ Uncertainty accounting for possible bias at „long term“ level! 1 The main equation: 2 3 Single lab validation approach: in practice Steps of the process: • At medium and higher concentrations use relative uncertainties – Uncertainty is roughly proportional to analyte level • In general: whichever is more constant Appendix E.4 from Quantifying Uncertainty in Analytical Measurement, EURACHEM/CITAC Guide, Second Edition (2000) Available from : http://www.eurachem.org/ 4 • u(Rw) is the uncertainty component that u(Rw) takes into account long-term variation of results within lab, that means: within-lab reproducibility (sRw) Include sample • Ideally: preparation! – The same sample 1. Specify measurand • Sample similar to test samples – matrix, concentration, homogeneity 2. Quantify Rw component u(Rw) 3. Quantify bias component u(bias) 4. Convert components to standard uncertainties u(x) 5. Calculate combined standard uncertainty uc 6. Calculate expanded uncertainty U 5 – – – – – – The same lab The same procedure Different days (preferably over 1 year) Different persons Different reagent batches … 6 1 u(bias) u(Rw) • The possible bias of lab’s results from the best estimate of true value is taken into account u(Rw) = sRw Include sample preparation! • u(bias) can be found: – From repeated analysis of the same samples with a reference procedure – From repeated analysis of certified reference materials (CRMs) – From repeated interlaboratory comparison measurements – From repeated spiking experiments The control sample analysis has to cover the whole analytical process Ideally: separately for different matrices and different concentration levels! 7 Ideally: several reference materials, several PTs because the bias will in most cases vary with matrix and concentration range 8 u(bias) u(bias) • The averaging is done using the root mean square: u (bias ) RMS bias u (Cref ) 2 (biasi ) 2 2 This component accounts for the average bias of the laboratory results from the Cref biasi Clabi Cref i This component accounts for the average uncertainty of the reference values Cref u (Cref i ) si ni RMSbias u (Cref ) n u(Cref ) 2 i n • n: the number of bias estimates used – If n is too small then the bias component will include a large share of random effects and may be overestimated 9 u(bias): only one CRM 10 Uncertainty due to possible bias • If only one single CRM is used: Evaluation of uncertainty due to bias, ideally: 2 u (bias ) RMS bias sbias / n u (Cref ) 2 2 – Separately for different sample matrices – Separately for different concentration levels 11 12 2 Roadmap: Possible bias u (Cref i ) from certificates u (Cref i ) biasi Clabi Cref i RMSbias si u (Cref ) ni u(Cref ) 2 i n (biasi ) 2 n u (bias ) RMS bias u (Cref ) 2 2 Uncertainty due to random effects Combined standard uncertainty u ( Rw ) sRW uc u ( Rw ) 2 u (bias ) 2 13 3