Quantifying Uncertainty in Analytical Measurement
Second Edition
EURACHEM/CITAC Guide
Editors
S L R Ellison (LGC, UK)
M Rosslein (EMPA, Switzerland)
A Williams (UK)

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CONTENTS
FOREWORD TO THE SECOND EDITION 1
1. SCOPE AND FIELD OF APPLICATION 3
2. UNCERTAINTY 4
2.1. DEFINITION OF UNCERTAINTY 4
2.2. UNCERTAINTY SOURCES 4
2.3. UNCERTAINTY COMPONENTS 4
2.4. ERROR AND UNCERTAINTY 5
3. ANALYTICAL MEASUREMENT AND UNCERTAINTY 7
3.1. METHOD VALIDATION 7
3.2. CONDUCT OF EXPERIMENTAL STUDIES OF METHOD PERFORMANCE 8
3.3. TRACEABILITY 9
4. THE PROCESS OF MEASUREMENT UNCERTAINTY ESTIMATION 11
5. STEP 1. SPECIFICATION OF THE MEASURAND 13
6. STEP 2. IDENTIFYING UNCERTAINTY SOURCES 14
7. STEP 3. QUANTIFYING UNCERTAINTY 16
7.1. INTRODUCTION 16
7.2. UNCERTAINTY EVALUATION PROCEDURE 16
7.3. RELEVANCE OF PRIOR STUDIES 17
7.4. EVALUATING UNCERTAINTY BY QUANTIFICATION OF INDIVIDUAL COMPONENTS 17
7.5. CLOSELY MATCHED CERTIFIED REFERENCE MATERIALS 17
7.6. USING PRIOR COLLABORATIVE METHOD DEVELOPMENT AND VALIDATION STUDY DATA 17
7.7. USING IN-HOUSE DEVELOPMENT AND VALIDATION STUDIES 18
7.8. EVALUATION OF UNCERTAINTY FOR EMPIRICAL METHODS 20
7.9. EVALUATION OF UNCERTAINTY FOR AD-HOC METHODS 20
7.10. QUANTIFICATION OF INDIVIDUAL COMPONENTS 21
7.11. EXPERIMENTAL ESTIMATION OF INDIVIDUAL UNCERTAINTY CONTRIBUTIONS 21
7.12. ESTIMATION BASED ON OTHER RESULTS OR DATA 22
7.13. MODELLING FROM THEORETICAL PRINCIPLES 22
7.14. ESTIMATION BASED ON JUDGEMENT 22
7.15. SIGNIFICANCE OF BIAS 24
8. STEP 4. CALCULATING THE COMBINED UNCERTAINTY 25
8.1. STANDARD UNCERTAINTIES 25
8.2. COMBINED STANDARD UNCERTAINTY 25
8.3. EXPANDED UNCERTAINTY 27
9. REPORTING UNCERTAINTY 29
9.1. GENERAL 29
9.2. INFORMATION REQUIRED 29
9.3. REPORTING STANDARD UNCERTAINTY 29
9.4. REPORTING EXPANDED UNCERTAINTY 29
9.5. NUMERICAL EXPRESSION OF RESULTS 30
9.6. COMPLIANCE AGAINST LIMITS 30
APPENDIX A. EXAMPLES 32
INTRODUCTION 32
EXAMPLE A1: PREPARATION OF A CALIBRATION STANDARD 34
EXAMPLE A2: STANDARDISING A SODIUM HYDROXIDE SOLUTION 40
EXAMPLE A3: AN ACID/BASE TITRATION 50
EXAMPLE A4: UNCERTAINTY ESTIMATION FROM IN-HOUSE VALIDATION STUDIES.
DETERMINATION OF ORGANOPHOSPHORUS PESTICIDES IN BREAD. 59
EXAMPLE A5: DETERMINATION OF CADMIUM RELEASE FROM CERAMIC WARE BY
ATOMIC ABSORPTION SPECTROMETRY 70
EXAMPLE A6: THE DETERMINATION OF CRUDE FIBRE IN ANIMAL FEEDING STUFFS 79
EXAMPLE A7: DETERMINATION OF THE AMOUNT OF LEAD IN WATER USING DOUBLE
ISOTOPE DILUTION AND INDUCTIVELY COUPLED PLASMA MASS SPECTROMETRY 87
APPENDIX B. DEFINITIONS 95
APPENDIX C. UNCERTAINTIES IN ANALYTICAL PROCESSES 99
APPENDIX D. ANALYSING UNCERTAINTY SOURCES 100
D.1 INTRODUCTION 100
D.2 PRINCIPLES OF APPROACH 100
D.3 CAUSE AND EFFECT ANALYSIS 100
D.4 EXAMPLE 101
APPENDIX E. USEFUL STATISTICAL PROCEDURES 102
E.1 DISTRIBUTION FUNCTIONS 102
E.2 SPREADSHEET METHOD FOR UNCERTAINTY CALCULATION 104
E.3 UNCERTAINTIES FROM LINEAR LEAST SQUARES CALIBRATION 106
E.4: DOCUMENTING UNCERTAINTY DEPENDENT ON ANALYTE LEVEL 108
APPENDIX F. MEASUREMENT UNCERTAINTY AT THE LIMIT OF DETECTION/
LIMIT OF DETERMINATION 112
F1. INTRODUCTION 112
F2. OBSERVATIONS AND ESTIMATES 112
F3. INTERPRETED RESULTS AND COMPLIANCE STATEMENTS 113
APPENDIX G. COMMON SOURCES AND VALUES OF UNCERTAINTY 114
APPENDIX H. BIBLIOGRAPHY 120

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