Incertidumbre

EURACHEM / CITAC Guide CG 4

Quantifying Uncertainty in Analytical Measurement
Second Edition

QUAM:2000.1

EURACHEM/CITAC Guide*

Quantifying Uncertainty in Analytical Measurement

Second Edition

Editors
S L R Ellison (LGC, UK) M Rosslein (EMPA, Switzerland) A Williams (UK)

Composition of the Working Group
EURACHEM members A Williams Chairman S EllisonSecretary M Berglund WHaesselbarth K Hedegaard R Kaarls M Månsson M Rösslein R Stephany A van der Veen W Wegscheider H van de Wiel R Wood CITAC Members
UK LGC, Teddington, UK Institute for Reference Materials and Measurements, Belgium Bundesanstalt fur Materialforschung und Prufung, Germany EUROM II Netherlands Measurement Institute, The Netherlands SP Swedish National Testing and Research Institute, Sweden EMPA St.Gallen, Switzerland National Institute of Public Health and the Environment, The Netherlands Netherlands Measurement Institute, The Netherlands University of Mining and Metallurgy, Leoben, Austria National Institute of Public Health and the Environment, The Netherlands Food Standards Agency, UK

Acknowledgements
This document has been produced primarily by a joint EURACHEM/CITAC Working Groupwith the composition shown (right). The editors 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 under contract with the UK Department of Trade and Industry as part of the National Measurement System Valid Analytical Measurement (VAM) Programme. *CITAC Reference This Guideconstitutes CITAC Guide number 4

Pan Xiu Rong M Salit A Squirrell K Yasuda AOAC Representatives R Johnson Jung-Keun Lee D Mowrey IAEA Representatives P De Regge A Fajgelj EA Representative D Galsworthy,

Director, NRCCRM,. China National Institute of Science and Technology USA NATA, Australia Hitachi Ltd, Japan

Agricultural Analytical Services, Texas State Chemist, USA U.S. F.D.A. Washington EliLilly & Co., Greenfield, USA

IAEA Vienna IAEA Vienna

UKAS, UK

Quantifying Uncertainty in Analytical Measurement English edition

Second edition 2000 ISBN 0 948926 15 5 Copyright  2000 Copyright in this document is vested in the contributing members of the working group.

Quantifying Uncertainty

Contents

CONTENTS
FOREWORD TO THE SECOND EDITION 1. SCOPE AND FIELD OFAPPLICATION 2. UNCERTAINTY 2.1. 2.2. 2.3. 2.4. DEFINITION OF UNCERTAINTY UNCERTAINTY SOURCES UNCERTAINTY COMPONENTS ERROR AND UNCERTAINTY 1 3 4 4 4 4 5 7 7 8 9 11 13 14 16 16 16 17 17 17 17 18 20 20 21 21 22 22 22 24 25 25 25 27

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

4. THE PROCESS OF MEASUREMENTUNCERTAINTY 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. INTRODUCTION UNCERTAINTY EVALUATION PROCEDURE RELEVANCE OF PRIOR STUDIES EVALUATING UNCERTAINTY BY QUANTIFICATION OF INDIVIDUAL COMPONENTS CLOSELY MATCHED CERTIFIED REFERENCEMATERIALS USING PRIOR COLLABORATIVE METHOD DEVELOPMENT AND VALIDATION STUDY DATA USING IN-HOUSE DEVELOPMENT AND VALIDATION STUDIES EVALUATION OF UNCERTAINTY FOR EMPIRICAL 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 THEORETICALPRINCIPLES ESTIMATION BASED ON JUDGEMENT SIGNIFICANCE OF BIAS

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

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Quantifying Uncertainty
9. REPORTING UNCERTAINTY 9.1. 9.2. 9.3. 9.4. 9.5. 9.6. GENERAL INFORMATION REQUIRED REPORTING STANDARD UNCERTAINTY REPORTING EXPANDED UNCERTAINTY...