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BSI PD 6461-3:1995:2003 Edition

BSI PD 6461-3:1995:2003 Edition

$215.11

General metrology – Guide to the expression of uncertainty in measurement (GUM)

Published By Publication Date Number of Pages
BSI 2003 114
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PDF Catalog

PDF Pages PDF Title
1 PUBLISHED DOCUMENT
2 Committees responsible for this Published�Document
3 Contents
9 0 Introduction
10 Recommendation INC-1 (1980)
11 1 Scope
2 Definitions
2.1 General metrological terms
12 2.2 The term “uncertainty”
2.3 Terms specific to this
2.3.1 standard uncertainty
2.3.2 type A evaluation (of uncertainty)
2.3.3 type B evaluation (of uncertainty)
13 2.3.4 combined standard uncertainty
2.3.5 expanded uncertainty
2.3.6 coverage factor
3 Basic concepts
3.1 Measurement
14 3.2 Errors, effects, and corrections
15 3.3 Uncertainty
16 3.4 Practical considerations
17 4 Evaluating standard uncertainty
4.1 Modelling the measurement
18 4.2 Type A evaluation of standard uncertainty
20 4.3 Type uncertainty B evaluation of standard�uncertainty
23 Figure 1 – Graphical illustration of evaluating the standard uncertainty of an input quantity from repeated …
24 4.4 Graphical illustration of evaluating standard uncertainty
Table 1 – Twenty repeated observations of the temperature
25 Figure 2 – Graphical illustration of evaluating the standard uncertainty of an input quantity from an a prio…
26 5 Determining combined standard uncertainty
5.1 Uncorrelated input quantities
28 5.2 Correlated input quantities
30 6 Determining expanded uncertainty
6.1 Introduction
31 6.2 Expanded uncertainty
6.3 Choosing a coverage factor
32 7 Reporting uncertainty
7.1 General guidance
33 7.2 Specific guidance
35 8 Summary of procedure for evaluating and expressing uncertainty
36 Annex A Recommendations of Working Group and CIPM
A.1 Recommendation INC-1 (1980)
37 A.2 Recommendation 1 (CI-1981)
A.3 Recommendation 1 (CI-1986)
38 Annex B General metrological terms
B.1 Source of definitions
B.2 Definitions
B.2.1 (measurable) quantity
B.2.2 value (of a quantity)
39 B.2.3 true value (of a quantity)
B.2.4 conventional true value (of a quantity)
B.2.5 measurement
B.2.6 principle of measurement
B.2.7 method of measurement
B.2.8 measurement procedure
B.2.9 measurand
40 B.2.10 influence quantity
B.2.11 result of a measurement
B.2.12 uncorrected result
B.2.13 corrected result
B.2.14 accuracy of measurement
B.2.15 repeatability (of results of measurements)
41 B.2.16 reproducibility (of results of measurements)
B.2.17 experimental standard deviation
B.2.18 uncertainty (of measurement)
42 B.2.19 error (of measurement)
B.2.20 relative error
B.2.21 random error
B.2.22 systematic error
B.2.23 correction
B.2.24 correction factor
43 Annex C Basic statistical terms and concepts
C.1 Source of definitions
C.2 Definitions
46 C.3 Elaboration of terms and concepts
C.3.1 Expectation
47 C.3.2 Variance
C.3.3 Standard deviation
C.3.4 Covariance
48 C.3.5 Covariance matrix
C.3.6 Correlation coefficient
C.3.7 Independence
C.3.8 The t-distribution; Student’s distribution
49 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
50 D.4 Error
D.5 Uncertainty
51 D.6 Graphical representation
52 Figure D.1 – Graphical illustration of value, error, and uncertainty
53 Figure D.2 – Graphical illustration of values, error, and uncertainty
54 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
57 E.4 Standard deviations as measures of uncertainty
59 E.5 A comparison of two views of uncertainty
60 Annex F Practical guidance on evaluating uncertainty components
F.1 Components evaluated from repeated observations: Type A evaluation of standard uncertainty
F.1.1 Randomness and repeated observations
F.1.2 Correlations
62 F.2 Components evaluated by other means: Type B evaluation of standard uncertainty
F.2.1 The need for Type B evaluations
63 F.2.2 Mathematically determinate distributions
F.2.3 Imported input values
64 F.2.4 Measured input values
68 F.2.5 Uncertainty of the method of measurement
F.2.6 Uncertainty of the sample
69 Annex G Degrees of freedom and levels of confidence
G.1 Introduction
Table G.1 – Value of the coverage factor
70 G.2 Central Limit Theorem
G.3
72 G.4 Effective degrees of freedom
73 G.5 Other considerations
74 G.6 Summary and conclusions
76 Table G.2
77 Annex H Examples
H.1 End-gauge calibration
H.1.1 The measurement problem
H.1.2 Mathematical model
78 H.1.3 Contributory variances
80 Table H.1 – Summary of standard uncertainty components
81 H.1.4 Combined standard uncertainty
H.1.5 Final result
H.1.6 Expanded uncertainty
82 H.1.7 Second-order terms
83 H.2 Simultaneous resistance and reactance measurement
H.2.1 The measurement problem
H.2.2 Mathematical model and data
84 H.2.3 Results: approach 1
85 Table H.2 – Values of the input quantities
H.2.4 Results: approach 2
86 Table H.3 – Calculated values of the output quantities
Table H.4 – Calculated values of the output quantities
87 H.3 Calibration of a thermometer
H.3.1 The measurement problem
88 H.3.2 Least-squares fitting
H.3.3 Calculation of results
89 H.3.4 Uncertainty of a predicted value
90 H.3.5 Elimination of the correlation between the slope and intercept
91 H.3.6 Other considerations
H.4 Measurement of Activity
H.4.1 The measurement problem
92 Table H.7 – Counting data for determining the activity concentration of an unknown sample
93 H.4.2 Analysis of data
H.4.3 Calculation of final results
94 Table H.8 – Calculation of decay-corrected and background-corrected counting rates
96 H.5 Analysis of variance
H.5.1 The measurement problem
97 Table 9 – Summary of voltage standard calibration data obtained on
H.5.2 A numerical example
100 H.5.3 The role of ANOVA in measurement
101 H.6 Measurements on a reference scale: hardness
H.6.1 The measurement problem
102 H.6.2 Mathematical model
H.6.3 Contributory variances
103 H.6.4 The combined standard uncertainty,
104 Table 10 – Summary of data for determining the hardness of a sample block on the scale Rockwell C
H.6.5 Numerical example
105 Annex J Glossary of principal symbols
108 Annex K Bibliography
109 Alphabetical index

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