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JJF 1059.1-2012: Evaluation and expression of uncertainty in measurement
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JJF 1059.1-2012
JJF
METEOROLOGICAL INDUSTRY STANDARD
OF THE PEOPLE’S REPUBLIC OF CHINA
Evaluation and expression of uncertainty in
measurement
[Including Amendment 2013XG1]
ISSUED ON: DECEMBER 03, 2012
IMPLEMENTED ON: JUNE 03, 2013
Issued by: General Administration of Quality Supervision, Inspection and
Quarantine
Table of Contents
Introduction ... 7 
1 Scope ... 10 
2 Normative references ... 11 
3 Terms and definitions ... 12 
3.1 Measured [JJF 1001,4.7]... 12 
3.2 Measurement results, result of measurement [JJF 1001,5.1] ... 13 
3.3 Measured quantity value [JJF 1001,5.2] ... 13 
3.4 Measurement precision [JJF 1001, 5.10] ... 14 
3.5 Measurement repeatability [JJF 1001, 5.13] ... 14 
3.6 Measurement repeatability condition of measurement [JJF 1001, 5.14] ... 14 
3.7 Measurement reproducibility [JJF 1001, 5.16] ... 15 
3.8 Measurement reproducibility condition of measurement [JJF 1001, 5.15] ... 15 
3.9 Intermediate precision condition of measurement [JJF 1001, 5.11] ... 15 
3.10 Experimental standard deviation [JJF 1001, 5.17] ... 16 
3.11 Measurement error, error of measurement [JJF 1001, 5.3] ... 17 
3.12 Measurement uncertainty, uncertainty of measurement [JJF 1001, 5.18] ... 17 
3.13 Standard uncertainty [JJF 1001, 5.19] ... 18 
3.14 Type A evaluation of measurement uncertainty [JJF 1001, 5.20] ... 18 
3.15 Type B evaluation of measurement uncertainty [JJF 1001, 5.21] ... 18 
3.16 Combined standard uncertainty [JJF 1001, 5.22] ... 19 
3.17 Relative standard uncertainty [JJF 1001, 5.23] ... 19 
3.18 Expanded Uncertainty [JJF 1001, 5.27] ... 19 
3.19 Coverage interval [JJF 1001, 5.28] ... 20 
3.20 Coverage probability [JJF 1001, 5.29]... 20 
3.21 Coverage factor [JJF 1001, 5.30] ... 20 
3.22 Measurement model, model of measurement [JJF 1001, 5.31] ... 21 
3.23 Measurement function [JJF 1001, 5.32] ... 21 
3.24 Input quantity in in a measurement model [JJF 1001, 5.33] ... 21 
3.25 Output quantity in the measurement model [JJF 1001, 5.34] ... 22 
3.26 Definitional uncertainty [JJF 1001, 5.24] ... 22 
3.27 Instrumental measurement uncertainty [JJF 1001, 7.24] ... 22 
3.28 Null measurement uncertainty [JJF 1001, 7.25] ... 23 
3.29 Uncertainty budget [JJF 1001, 5.25] ... 23 
3.30 Target uncertainty [JJF 1001, 5.26] ... 23 
3.31 Degrees of freedom... 23 
3.32 Covariance ... 24 
3.33 Correlation coefficient ... 25 
4 Evaluation method of measurement uncertainty ... 25 
4.1 Analysis of sources of measurement uncertainty ... 26 
4.2 Establishment of measurement model ... 27 
4.3 Evaluation of standard uncertainty ... 30 
4.4 Calculation of combined standard uncertainty ... 42 
4.5 Determination of extended uncertainty ... 50 
5 Report and expression of measurement uncertainty ... 51 
5.1 Report of measurement uncertainty ... 51 
5.2 Expression of measurement uncertainty ... 53 
5.3 Other requirements when reporting uncertainty ... 55 
6 Application of measurement uncertainty ... 56 
6.1 Requirements for reporting measurement uncertainty in calibration certificate
... 56 
6.2 Laboratory calibration and expression of measurement capability ... 57 
6.3 Application in other situations ... 58 
Appendix A Examples of evaluation methods of measurement uncertainty
(reference) ... 59 
Appendix B Table of tp(ν) values (t values) for t distributions with different
probabilities p and degrees of freedom ν (supplementary) ... 92 
Appendix C Summary of symbols related to quantities (supplementary) ... 94 
Appendix D English-Chinese contrast of terms (reference) ... 97 
Amendment No.1 to JJF 1059.1-2012 "Evaluation and expression of
uncertainty in measurement" ... 99 
Evaluation and expression of uncertainty in
measurement
1 Scope
a) The general method for evaluating and expressing measurement
uncertainty specified in this specification is applicable to measurement
fields of various accuracy levels, such as:
1) The establishment of national measurement standards and
measurement standards at all levels and the comparison of values;
2) The setting value of standard substance and the release of standard
reference data;
3) Preparation of technical documents such as measurement methods,
verification procedures, verification system tables, calibration
specifications, etc.;
4) Expression of measurement results and measurement capabilities in
measurement qualification recognition, measurement confirmation,
quality certification, laboratory accreditation;
5) Calibration, verification and other measurement services of measuring
instruments;
6) Measurement in the fields of scientific research, engineering, trade
settlement, medical and health care, safety protection, environmental
monitoring, resource protection.
b) This specification mainly concerns the measurement uncertainty of the
measured estimated value that is clearly defined and can be characterized
by a unique value. As for the measured quantity value that appears as a
distribution of a series of values or depends on one or more parameters
(for example, with time as the parameter variable), the description of the
measured quantity value shall be a set of values, the distribution and
relationship shall be given.
c) This specification is also applicable to the evaluation and expression of
uncertainties in the design and theoretical analysis of experiments,
measuring methods, measuring devices, complex components and
systems.
3 Terms and definitions
The metrology terminology in this specification adopts JJF 1001-2011, which is
based on the revision of international standard ISO/IEC GUIDE 99:2007 (the
third edition of VIM). The probability and statistical terms used in this
specification basically adopt the terms and definitions of the international
standard ISO 3534-1:2006.
3.1 Measured [JJF 1001,4.7]
The amount to be measured.
Note:
1 The description of the measured requires an understanding of the type of
quantity and the description of the phenomena containing the quantity,
objects or substance status, including relevant components and chemical
entities.
2 In the second edition of VIM and IEC 60050-300:2001, the measured is
defined as the measured quantity.
3 The measurement includes the measurement system and the conditions
under which the measurement is carried out. It may change the
phenomenon, object substance in the study, so that the measured quantity
may be different from the defined measured. In this case, it needs
necessary corrections to be made.
Example:
1 When measuring with a voltmeter with insufficient internal resistance, the
potential difference between the two ends of the battery will decrease; the
open circuit potential difference can be calculated based on the internal
resistance of the battery and the voltmeter.
2 The length of the steel bar when it is in equilibrium with the ambient
temperature of 23 °C is different from the length when the specified
temperature to be measured is 20 °C. In this case, it must be corrected.
3 In chemistry, the name of “analyte” or substance or compound is
sometimes called “measured”. This usage is wrong because these terms
do not involve quantity.
measurement is not too small compared with the measurement
uncertainty, the measured quantity value is usually an average or median
estimate of a set of true values.
4 In the Guide to Measurement Uncertainty (GUM), the terms used for the
measured quantity values are "measurement results" and "estimated
measured quantity value" or "estimated measured quantity value".
3.4 Measurement precision [JJF 1001, 5.10]
Referred to as precision
Under the specified conditions, the degree of agreement between the
measured indication value and the measured quantity value through
repeated measurement of the same or similar measured object.
Note:
1 Measurement precision is usually expressed in numerical form with
imprecision, such as standard deviation, variance or coefficient of variation
under specified measurement conditions.
2 The prescribed conditions may be repetitive measurement conditions,
intermediate precision measurement conditions or reproducible
measurement conditions.
3 Measurement precision is used to define measurement repeatability,
intermediate measurement precision or measurement repeatability.
4 The term "measurement precision" is sometimes used to refer to
"measurement accuracy", which is wrong.
3.5 Measurement repeatability [JJF 1001, 5.13]
Referred to as repeatability.
Measurement precision under a set of repeatable measurement conditions.
3.6 Measurement repeatability condition of measurement [JJF
1001, 5.14]
Referred to as repeatability condition.
A set of measurement conditions of repeated measurement on the same or
3.11 Measurement error, error of measurement [JJF 1001, 5.3]
Abbreviated as error.
The measured quantity value minus the reference value.
Note:
1 The concept of measurement error can be used in the following two
situations:
① When it involves the existence of a single reference value, such as
calibration with a measurement standard whose measurement
uncertainty of the measured quantity value is negligible, or when a
quantitative value is given, the measurement error is known;
② Assuming that the measured is characterized by a unique set of true
values or a set of true values with negligible range, the measurement
error is unknown.
2 Measurement errors shall not be confused with errors or faults.
3.12 Measurement uncertainty, uncertainty of measurement
[JJF 1001, 5.18]
Abbreviated as uncertainty
According to the information used, characterize the non-negative
parameters that give the measured quantity value dispersion.
Note:
1 Measurement uncertainty includes components caused by the influence of
the system, such as the component related to the correction value and the
assigned value of the measurement standard as well as the definitional
uncertainty. Sometimes the estimated system impact is not corrected, but
treated as an uncertainty component.
2 This parameter can be such as the standard deviation (or a specific
multiple of it) called the standard measurement uncertainty, or it can
specify the half width of the interval containing the probability.
3 The measurement uncertainty generally consists of several components.
Some of these components can be evaluated according to the statistical
different from the type A evaluation of measurement uncertainty.
Example: The evaluation is based on the following information:
- The value issued by the authority;
- The value of certified reference materials;
- Calibration certificate;
- Instrument drift;
- Accuracy level of certified measuring instruments;
- Inferred limit values based on personnel experience.
3.16 Combined standard uncertainty [JJF 1001, 5.22]
Full name is combined standard measurement uncertainty.
The standard measurement uncertainty of the output quantity obtained from
the standard measurement uncertainty of each input quantity in a
measurement model.
Note: In the case where the input in the measurement model is relevant, the
covariance must be considered when calculating the combined standard
uncertainty.
3.17 Relative standard uncertainty [JJF 1001, 5.23]
Full name is relative standard measurement uncertainty
The absolute value that is obtained by dividing the standard uncertainty by
the measured quantity value.
3.18 Expanded Uncertainty [JJF 1001, 5.27]
Full name is expanded measurement uncertainty.
The product of the combined standard uncertainty and a digital factor greater
than 1.
Note:
1 This factor depends on the type of probability distribution of the output in
3.22 Measurement model, model of measurement [JJF 1001,
5.31]
Referred to as model.
The mathematical relationship between all known quantities involved in the
measurement.
Note:
1 The general form of the measurement model is the formula: h(Y, X1,..., XN)
= 0, where the output Y in the measurement model is measured, whose
value is derived from the relevant information of the input quantity X1, ...,
XN in the measurement model.
2 In more complex situations with two or more outputs, the measurement
model contains more than one formula.
3.23 Measurement function [JJF 1001, 5.32]
In the measurement model, when the value calculated from the known
quantity of the input quantity is the measured quantity value of the output
quantity, the functional relationship between the input quantity and the output
quantity.
Note:
1 If the measurement model h (Y, X1, ..., XN) = 0 can be explicitly written as
Y = f(X1, ..., XN), where Y is the output in the measurement model, then
the function f is the measurement function. In more layman's terms, f is an
algorithm symbol, which is used to calculate the only output quantity y =
f(x1, ..., xN) corresponding to the input quantity x1, ..., xN.
2 The measurement function is also used to calculate the measurement
uncertainty of the measured quantity value Y.
3.24 Input quantity in in a measurement model [JJF 1001, 5.33]
Referred to as input quantity.
The quantity that must be measured in order to calculate the measured
quantity value being measured, or its value can be obtained in other ways.
B measurement uncertainty.
3 Information about the measurement uncertainty of the instrument can be
given in the instrument manual.
3.28 Null measurement uncertainty [JJF 1001, 7.25]
The measurement uncertainty when the measured quantity value is zero.
Note:
1 The null measurement uncertainty is related to the indication of zero or
close to zero. It contains the interval of the measurement being too small
to know whether it can be detected, or the indication interval of the
measuring instrument is caused only by noise.
2 The concept of null measurement uncertainty also applies when measuring
the difference between the sample and the blank.
3.29 Uncertai...