Use of Measurement Uncertainty Information in Compliance Assessment of Chemical Results

1. Use of Measurement Uncertainty Information in Compliance Assessment of Chemical Results D. Theodorou Athens, October 2008

2. idealized concepts What is not uncertainty ! • Error: result of a measurement minus the • true value of the measurand Accuracy: accuracy is not aquantifiable term

3. What is uncertainty Result: 20 ± 3 mg The true amount is between 17 and 23 mg Uncertainty = tolerance interval a parameter associated with the result of a measurement, that characterizes the dispersion of the values that could reasonably be attributed to the measurand (ISO Guide to the Expression of Uncertainty in Measurement)

4. Uncertainty of Chemical Measurements There is always experimental variations when we make ameasurement • Typical Sources of Uncertainty in Chemical Analyses • Sampling • Storage Conditions • Instrument effects (e.g. calibration, accuracy, carry over effects) • Reagent purity • Assumed stoichiometry (e.g. incomplete or side reactions) • Measurement conditions (e.g temperature, humidity) • Sample effects (e.g. recovery - matrix effects) • Computational effects (e.g calibration model, truncation / round off) • Blank correction • Operator effects • Random effects Type A &Type B contributions Combined Uncertainty coverage factor, k Overall Estimate of Uncertainty or Expanded Uncertainty Eurachem/CITAC Guide

5. Expanded Uncertainty U, coverage factor k k=3 99,73% U U U=k∙uC k=2 95,45% U U

6. Typical Uncertainty Statement Total cadmium content (Cd): 328 μg·kg-1 Measurement Uncertainty: 27 μg·kg-1 (8,2%) The stated uncertainty is an expanded measurement uncertainty (U). It was obtained by multiplying the combined standard uncertainty uc with a coverage factor k equal to 2. This corresponds approximately to a 95 % confidence interval.

7. Procedures for the Estimation of Measurement Uncertainty • ISO Guide to the expression of measurement uncertainty (ISO GUM) • EURACHEM Guide to quantifying uncertainty in analytical measurement • Use of collaborative trial data – ISO 5725 critical differences • ISO/TS 21748 – Guide to the Use of Repeatability, Reproducibility • andTrueness Estimates in Measurement Uncertainty Estimation • Concept established by Commission Decision 2002/657/EC implementing • CouncilDirective 96/23/EC concerning the performance of analytical • methods and theinterpretation of results • AOAC INTERNATIONAL approach • Internal quality control approach • NMKL (Nordic Committee on Food Analysis) approach • Microbiological Analyses (ISO/TS 19036, Niemelä Guide) • Monte Carlo Simulation (ISO GUM Supplement 1)

8. Why is it important? repeatability uncertainty Uncertainty = Confidence Informed Decision

9. Uncertainty and limiting values Many analyses are made to assure that limiting values are not exceeded (e.g. for drinking water quality) Without information about the measurement uncertainty it may appear to be very easy to make decisions, but these decisions may be incorrect

10. Uncertainty and limiting values AN EXAMPLE Drinking water -> Pb content Parametric value: 10 μg/l(COUNCIL DIRECTIVE 98/83/EC) Laboratory uncertainty at that level: ± 0,8μg/l (Expanded uncertainty, 95% confidence interval)

11. Uncertainty and limiting values

12. Uncertainty and limiting values Straightforward Approach • If possible use a methodproducing more accurate results • Report the result and uncertainty with a statement that compliance (or non-compliance) could not be demonstrated (for a suggested statement see UKAS Guide, M3003, The Expression of Uncertainty and Confidence in Measurement)

13. Uncertainty and limiting values Decision Limit Upper limit guard band Acceptance zone Rejection zone Upper limit Decision Limit guard band Acceptance zone Rejection zone Detailed Approach • Set up probability based decision rules • Select a decision limit (critical value) taking into account what the end user expects: • low probability of false rejection, α • low probability offalse acceptance, β

14. Uncertainty and limiting values Upper Limit DL guard band, g = 2∙uc= U95% U95% 2,5% of the values under the curve are inside the specification limit High confidence of correct rejection DecisionlimitDL is chosensothatthe risk of false rejection (α) is less than2,5%. Rejection Zone Acceptance Zone

15. Uncertainty and limiting values Upper Limit DL guard band, g = 2∙uc= U95% U95% 2,5% of the values under the curve are outside the specification limit Rejection Zone Acceptance Zone High confidence of correct acceptance DecisionlimitDL is chosensothatthe risk of false acceptance (β) is less than2,5%.

16. EURACHEM / CITAC Guide • USE OF UNCERTAINTY INFORMATION IN COMPIANCE ASSESSMENT, Edition 1(2007) • The Guide describes many aspects of the matter. • It covers cases of: • Simultaneous upper and lower limits • Uncertainties depending on the value of the measurand • Asymmetric distributions of the measurand • Standard uncertainties with effective degrees of freedom • Different decision rules are compared.

17. Conclusions • Need for consistent way of reporting test results • Uncertainty: quantitative measure of the reliability of a result • Decisions for compliance or non-compliance with a specification should take into account uncertainty • When the state of compliance is not clear, appropriate judgments should be based on probability-based decision criteria • Decision criteria should be based on risks associated with making wrong decision i.e. false rejection or false acceptance

18. Dimitris Theodorou, MSc, MBAdtheodorou@priority.com.grPRIORITY S.A. Business ConsultantLaboratory Accreditation Dept. Thank you for your attention !!!