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EURACHEM / CITAC Guide CG 4

Quantifying Uncertainty in Analytical Measurement
Third Edition

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EURACHEM/CITAC Guide

Quantifying Uncertainty in Analytical Measurement
Third Edition

Editors
S L R Ellison (LGC, UK) A Williams (UK)

Composition of the Working Group*
EURACHEM members A Williams Chairman S Ellison Secretary R Bettencourt da Silva W Bremser A Brzyski PFodor R Kaarls R Kaus B Magnusson E Amico di Meane P Robouch M Rösslein A van der Veen M Walsh W Wegscheider R Wood P Yolci Omeroglu CITAC Representatives A Squirrell I Kuselman A Fajgelj
ILAC National Physical Laboratory of Israel IAEA Vienna UK LGC, Teddington, UK University of Lisbon, Portugal BAM, Germany Eurachem Poland Corvinus University of Budapest, Hungary Netherlands MeasurementInstitute, The Netherlands Eurachem Germany SP, Sweden Italy IRMM, EU EMPA St. Gallen, Switzerland Netherlands Measurement Institute, The Netherlands Eurachem IRE Montanuniversitaet, Leoben, Austria Food Standards Agency, UK Istanbul Technical University, Turkey

Acknowledgements
This document has been produced primarily by a joint EURACHEM/CITAC Working Group with the composition shown (right). Theeditors are grateful to all these individuals and organisations and to others who have contributed comments, advice and assistance. Production of this Guide was in part supported by the UK National Measurement System. CITAC Reference This Guide constitutes CITAC Guide number 4

Eurolab Representatives M Golze
BAM, Germany *Attending meetings or corresponding in the period 2009-2011Quantifying Uncertainty

Contents

CONTENTS
FOREWORD TO THE THIRD EDITION 1. SCOPE AND FIELD OF APPLICATION 2. UNCERTAINTY 2.1. 2.2. 2.3. 2.4. 2.5. DEFINITION OF UNCERTAINTY UNCERTAINTY SOURCES UNCERTAINTY COMPONENTS ERROR AND UNCERTAINTY THE VIM 3 DEFINITION OF UNCERTAINTY 1 3 4 4 4 4 5 6 7 7 8 9 10 12 14 16 16 16 17 17 17 17 18 20 21 22 22 22 23 23 24 25 26 26 26 28

3. ANALYTICAL MEASUREMENT ANDUNCERTAINTY 3.1. 3.2. 3.3. METHOD VALIDATION CONDUCT OF EXPERIMENTAL STUDIES OF METHOD PERFORMANCE TRACEABILITY

4. THE PROCESS OF MEASUREMENT UNCERTAINTY ESTIMATION 5. STEP 1. SPECIFICATION OF THE MEASURAND 6. STEP 2. IDENTIFYING UNCERTAINTY SOURCES 7. STEP 3. QUANTIFYING UNCERTAINTY 7.1. 7.2. 7.3. 7.4. 7.5. 7.6. 7.7. 7.8. 7.9. 7.10. 7.11. 7.12. 7.13. 7.14. 7.15. 7.16. INTRODUCTION UNCERTAINTYEVALUATION PROCEDURE RELEVANCE OF PRIOR STUDIES EVALUATING UNCERTAINTY BY QUANTIFICATION OF INDIVIDUAL COMPONENTS CLOSELY MATCHED CERTIFIED REFERENCE MATERIALS UNCERTAINTY ESTIMATION USING PRIOR COLLABORATIVE METHOD DEVELOPMENT
AND VALIDATION STUDY DATA UNCERTAINTY ESTIMATION USING IN-HOUSE DEVELOPMENT AND VALIDATION STUDIES USING DATA FROM PROFICIENCY TESTING EVALUATION OF UNCERTAINTY FOREMPIRICAL METHODS EVALUATION OF UNCERTAINTY FOR AD-HOC METHODS QUANTIFICATION OF INDIVIDUAL COMPONENTS EXPERIMENTAL ESTIMATION OF INDIVIDUAL UNCERTAINTY CONTRIBUTIONS ESTIMATION BASED ON OTHER RESULTS OR DATA MODELLING FROM THEORETICAL PRINCIPLES ESTIMATION BASED ON JUDGEMENT SIGNIFICANCE OF BIAS

8. STEP 4. CALCULATING THE COMBINED UNCERTAINTY 8.1. 8.2. 8.3. STANDARD UNCERTAINTIES COMBINED STANDARDUNCERTAINTY EXPANDED UNCERTAINTY

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Quantifying Uncertainty
9. REPORTING UNCERTAINTY 9.1. 9.2. 9.3. 9.4. 9.5. 9.6. 9.7. GENERAL INFORMATION REQUIRED REPORTING STANDARD UNCERTAINTY REPORTING EXPANDED UNCERTAINTY NUMERICAL EXPRESSION OF RESULTS ASYMMETRIC INTERVALS COMPLIANCE AGAINST LIMITS

Contents
30 30 30 30 30 31 31 31 33 35 41 51 60 72 81 89 97 101 102 104 104 106108 115 117

APPENDIX A. EXAMPLES EXAMPLE A1: PREPARATION OF A CALIBRATION STANDARD EXAMPLE A2: STANDARDISING A SODIUM HYDROXIDE SOLUTION EXAMPLE A3: AN ACID/BASE TITRATION EXAMPLE A4: UNCERTAINTY ESTIMATION FROM IN-HOUSE VALIDATION STUDIES. DETERMINATION OF ORGANOPHOSPHORUS PESTICIDES IN BREAD. EXAMPLE A5: DETERMINATION OF CADMIUM RELEASE FROM CERAMIC WARE BY ATOMIC ABSORPTION SPECTROMETRY...