ISO/IEC Guide 98-3:2008
Uncertainty of measurement — Part 3: Guide to the expression of uncertainty in measurement (GUM:1995)
ISO/IEC Guide 98-3:2008 is a reissue of the 1995 version of the Guide to the Expression of Uncertainty in Measurement (GUM), with minor corrections. This Guide establishes general rules for evaluating and expressing uncertainty in measurement that can be followed at various levels of accuracy and in many fields — from the shop floor to fundamental research. The principles of this Guide are intended to be applicable to a broad spectrum of measurements, including those required for:
- maintaining quality control and quality assurance in production;
- complying with and enforcing laws and regulations;
- conducting basic research, and applied research and development, in science and engineering;
- calibrating standards and instruments and performing tests throughout a national measurement system in order to achieve traceability to national standards;
- developing, maintaining, and comparing international and national physical reference standards, including reference materials.
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Guide 98-3 - Uncertainty of measurement - Part 3: Guide to the expression of uncertainty in measurement (GUM 1995)
Copyright
Contents
Preliminary
Foreword
0 Introduction
1 Scope
2 Definitions
2.1 General metrological terms
2.2 The term “uncertainty”
2.3 Terms specific to this Guide
3 Basic concepts
3.1 Measurement
3.2 Errors, effects, and corrections
3.3 Uncertainty
3.4 Practical considerations
4 Evaluating standard uncertainty
4.1 Modelling the measurement
4.2 Type A evaluation of standard uncertainty
4.3 Type B evaluation of standard uncertainty
4.4 Graphical illustration of evaluating standard uncertainty
5 Determining combined standard uncertainty
5.1 Uncorrelated input quantities
5.2 Correlated input quantities
6 Determining expanded uncertainty
6.1 Introduction
6.2 Expanded uncertainty
6.3 Choosing a coverage factor
7 Reporting uncertainty
7.1 General guidance
7.2 Specific guidance
8 Summary of procedure for evaluating and expressing uncertain
Annex A - Recommendations of Working Group and CIPM
A.1 Recommendation INC-1 (1980)
A.2 Recommendation 1 (CI-1981)
A.3 Recommendation 1 (CI-1986)
Annex B - General metrological terms
B.1 Source of definitions
B.2 Definitions
Annex C - Basic statistical terms and concepts
C.1 Source of definitions
C.2 Definitions
C.3 Elaboration of terms and concepts
C.3.1 Expectation
C.3.2 Variance
C.3.3 Standard deviation
C.3.4 Covariance
C.3.5 Covariance matrix
C.3.6 Correlation coefficient
C.3.7 Independence
C.3.8 The t-distribution; Student's distribution
Annex D - "True" value, error, and uncertainty
D.1 The measurand
D.2 The realized quantity
D.3 The "true" value and the corrected value
D.4 Error
D.5 Uncertainty
D.6 Graphical representation
Annex E - Motivation and basis for Recommendation INC-1 (1980)
E.1 "Safe", "random", and "systematic"
E.2 Justification for realistic uncertainty evaluations
E.3 Justification for treating all uncertainty components identically
E.4 Standard deviations as measures of uncertainy
E.5 A comparison of two views of uncertainty
Annex F - Practical guidance on evaluating uncertainty components
F.1 Components evaluated from repeated observations: Type A
F.1.1 Randomness and repeated observations
F.1.2 Correlations
F.2 Components evaluated from repeated observations: Type B
F.2.1 The need for Type B evaluations
F.2.2 Mathematically determinate distributions
F.2.3 Imported input values
F.2.4 Measured input values
F.2.5 Uncertainty of the method of measurement
F.2.6 Uncertainty of the sample
Annex G - Degrees of freedom and levels of confidence
G.1 Introduction
G.2 Central Limit Theorem
G.3 The t-distribution and degrees of freedom
G.4 Effective degrees of freedom
G.5 Other considerations
G.6 Summary and conclusions
Annex H - Examples
H.1 End-gauge calibration
H.1.1 The measurement problem
H.1.2 Mathematical model
H.1.3 Contributory variances
H.1.4 Combined standard uncertainty
H.1.5 Final result
H.1.6 Expanded uncertainty
H.1.7 Second-order terms
H.2 Simultaneous resistance and reactance measurement
H.2.1 The measurement problem
H.2.2 Mathematical model and data
H.2.3 Results: approach 1
H.2.4 Results: approach 2
H.3 Calibration of a thermometer
H.3.1 The measurement problem
H.3.2 Least-squares fitting
H.3.3 Calculation of results
H.3.4 Uncertainty of a predicted value
H.3.5 Elimination of the correlation between the slope and intercept
H.3.6 Other considerations
H.4 Measurement of activity
H.4.1 The measurement problem
H.4.2 Analysis of data
H.4.3 Calculation of final results
H.5 Analysis of variance
H.5.1 The measurement problem
H.5.2 A numerical example
H.5.3 The role of ANOVA in measurement
H.6 Measurements on a reference scale: hardness
H.6.1 The measurement problem
H.6.2 Mathematical model
H.6.3 Contributory variances
H.6.4 The combined standard uncertainty
H.6.5 Numerical example
Annex J - Glossary of principal symbols
Bibliography
Alphabetical index
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Guide 98-3 - Uncertainty of measurement - Part 3: Guide to the expression of uncertainty in measurement (GUM 1995)
Copyright
Contents
Preliminary
Foreword
0 Introduction
1 Scope
2 Definitions
2.1 General metrological terms
2.2 The term “uncertainty”
2.3 Terms specific to this Guide
3 Basic concepts
3.1 Measurement
3.2 Errors, effects, and corrections
3.3 Uncertainty
3.4 Practical considerations
4 Evaluating standard uncertainty
4.1 Modelling the measurement
4.2 Type A evaluation of standard uncertainty
4.3 Type B evaluation of standard uncertainty
4.4 Graphical illustration of evaluating standard uncertainty
5 Determining combined standard uncertainty
5.1 Uncorrelated input quantities
5.2 Correlated input quantities
6 Determining expanded uncertainty
6.1 Introduction
6.2 Expanded uncertainty
6.3 Choosing a coverage factor
7 Reporting uncertainty
7.1 General guidance
7.2 Specific guidance
8 Summary of procedure for evaluating and expressing uncertain
Annex A - Recommendations of Working Group and CIPM
A.1 Recommendation INC-1 (1980)
A.2 Recommendation 1 (CI-1981)
A.3 Recommendation 1 (CI-1986)
Annex B - General metrological terms
B.1 Source of definitions
B.2 Definitions
Annex C - Basic statistical terms and concepts
C.1 Source of definitions
C.2 Definitions
C.3 Elaboration of terms and concepts
C.3.1 Expectation
C.3.2 Variance
C.3.3 Standard deviation
C.3.4 Covariance
C.3.5 Covariance matrix
C.3.6 Correlation coefficient
C.3.7 Independence
C.3.8 The t-distribution; Student's distribution
Annex D - "True" value, error, and uncertainty
D.1 The measurand
D.2 The realized quantity
D.3 The "true" value and the corrected value
D.4 Error
D.5 Uncertainty
D.6 Graphical representation
Annex E - Motivation and basis for Recommendation INC-1 (1980)
E.1 "Safe", "random", and "systematic"
E.2 Justification for realistic uncertainty evaluations
E.3 Justification for treating all uncertainty components identically
E.4 Standard deviations as measures of uncertainy
E.5 A comparison of two views of uncertainty
Annex F - Practical guidance on evaluating uncertainty components
F.1 Components evaluated from repeated observations: Type A
F.1.1 Randomness and repeated observations
F.1.2 Correlations
F.2 Components evaluated from repeated observations: Type B
F.2.1 The need for Type B evaluations
F.2.2 Mathematically determinate distributions
F.2.3 Imported input values
F.2.4 Measured input values
F.2.5 Uncertainty of the method of measurement
F.2.6 Uncertainty of the sample
Annex G - Degrees of freedom and levels of confidence
G.1 Introduction
G.2 Central Limit Theorem
G.3 The t-distribution and degrees of freedom
G.4 Effective degrees of freedom
G.5 Other considerations
G.6 Summary and conclusions
Annex H - Examples
H.1 End-gauge calibration
H.1.1 The measurement problem
H.1.2 Mathematical model
H.1.3 Contributory variances
H.1.4 Combined standard uncertainty
H.1.5 Final result
H.1.6 Expanded uncertainty
H.1.7 Second-order terms
H.2 Simultaneous resistance and reactance measurement
H.2.1 The measurement problem
H.2.2 Mathematical model and data
H.2.3 Results: approach 1
H.2.4 Results: approach 2
H.3 Calibration of a thermometer
H.3.1 The measurement problem
H.3.2 Least-squares fitting
H.3.3 Calculation of results
H.3.4 Uncertainty of a predicted value
H.3.5 Elimination of the correlation between the slope and intercept
H.3.6 Other considerations
H.4 Measurement of activity
H.4.1 The measurement problem
H.4.2 Analysis of data
H.4.3 Calculation of final results
H.5 Analysis of variance
H.5.1 The measurement problem
H.5.2 A numerical example
H.5.3 The role of ANOVA in measurement
H.6 Measurements on a reference scale: hardness
H.6.1 The measurement problem
H.6.2 Mathematical model
H.6.3 Contributory variances
H.6.4 The combined standard uncertainty
H.6.5 Numerical example
Annex J - Glossary of principal symbols
Bibliography
Alphabetical index