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[Including 2013XG] Evaluation and Expression of Uncertainty in Measurement

JJF 1059.12012
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JJF 1059.12012

Standard ID  JJF 1059.12012 (JJF1059.12012)  Description (Translated English)  Evaluation and Expression of Uncertainty in Measurement  Sector / Industry  Metrology & Measurement Industry Standard  Classification of Chinese Standard  A50  Classification of International Standard  17.020  Word Count Estimation  61,697  Older Standard (superseded by this standard)  JJF 10591999  Quoted Standard  JJF 10012011; GB/T 702008; GB 31011993; ISO/IEC GUIDE 9832008; ISO 353412006; GB/T 48832008  Drafting Organization  Jiangsu Province Institute of Metrology  Administrative Organization  National Technical Committee of Legal Metrology management  Regulation (derived from)  New version of " Evaluation and Expression of Uncertainty in Measurement Technical specifications" released; AQSIQ Announcement No. 199 of 2012  Issuing agency(ies)  State Administration of Quality Supervision, Inspection and Quarantine  Summary  This standard applies to the level of accuracy of measurement of various fields. Required by this specification Evaluation and Expression of Uncertainty in Measurement general method, for example: a) Basis of measurement and at all levels of national meas 
JJF 1059.12012
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 EnglishChinese contrast of terms (reference) ... 97
Amendment No.1 to JJF 1059.12012 "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 10012011, 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 35341:2006.
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 60050300:2001, 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 nonnegative
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 Uncertainty budget [JJF 1001, 5.25]
Statement of measurement uncertainty, including the components of
measurement uncertainty and their calculation and synthesis.
Note: The uncertainty report shall include the measurement model, the
estimated value, the measurement uncertainty associated with each quantity
in the measurement model, the covariance, the type of probability density
distribution function used, the degrees of freedom, the evaluation type of the
measurement uncertainty, the coverage factors.
3.30 Target uncertainty [JJF 1001, 5.26]
Full name is target measurement uncertainty.
According to the intended use of the measurement results, the measurement
uncertainty which is specified as the upper limit.
3.31 Degrees of freedom
In the calculation of variance, the number of sums minus the limit of sums.
Note:
1 Under repeatability conditions, when n independent measurements are
uncertainty of the instrument;
g) The inaccuracy of the standard value provided by the measurement
standard or reference material;
h) Inaccurate values of quoted constants or other parameters;
i) Approximations and assumptions in measurement methods and
measurement procedures;
j) Under the same conditions, the changes of measured repeated
observations.
The source of measurement uncertainty must be specifically analyzed
according to the actual measurement situation. In the analysis, in addition to
the definitional uncertainty, it can be comprehensively considered from the
aspects of measuring instruments, measuring environment, measuring
personnel, measuring methods. In particular, pay attention to the sources of
uncertainty that have a greater impact on the measurement results; try to avoid
missing or repetition.
4.1.3 The correction is only to compensate the system error; the correction
value is uncertain. When evaluating the measurement uncertainty of the
corrected measured estimated value, it shall consider the uncertainty
introduced by the correction. Only when the uncertainty of the correction value
is small and the contribution to the combined standard uncertainty is negligible,
it may not be considered.
4.1.4 Errors or sudden factors in the measurement are not a source of
measurement uncertainty. In the evaluation of measurement uncertainty, the
outliers in the measured quantity values shall be eliminated. The elimination of
outliers shall be carried out after proper inspection of the data.
Note: The judgment and processing method of outliers can be found in GB/T
48832008 "Statistical interpretation of data  Detection and treatment of outliers
in the normal sample".
4.2 Establishment of measurement model
4.2.1 In the measurement, when the measured (i.e. output quantity) Y is
determined by N other quantities X1, X2, ..., XN (i.e. input quantity) through the
function f, the formula (1) is called the measurement model:
Where the capital letters represent the symbol of quantity, f is the measurement
is helpful to establish the measurement model when using the verification
standard and control chart method to indicate that the measurement process is
always in the state of statistical control.
4.2.5 If the data indicates that the measurement function fails to model the
measurement process to the accuracy required for measurement, additional
input must be added to the measurement model to reflect the lack of knowledge
of the amount of influence.
4.2.6 The input quantity in the measurement model can be:
a) The quantity directly measured by the current. These quantities and their
uncertainties can be obtained by single observation, repeated observation
or empirical estimation; it can include correction values for readings of
measuring instruments and correction values for influence quantities such
as ambient temperature, atmospheric pressure, humidity, etc.
b) Quantity introduced by external sources. Such as the quantity of calibrated
measurement standards or certified reference materials, as well as the
reference data found in the manual.
4.2.7 When analyzing measurement uncertainty, the uncertainty of each input
quantity in the measurement model is the source of the uncertainty of the output
quantity.
4.2.8 This specification is mainly applicable when the measurement model is a
linear function. If it is a nonlinear function, Taylor series expansion shall be
adopted and its highorder terms shall be ignored; the measured quantity value
shall be approximated as a linear function of the input value, so as to evaluate
the measurement uncertainty. If the measurement function is obviously non
linear, the evaluation of the combined standard uncertainty must include the
main higherorder terms in the Taylor series expansion.
4.2.9 When the best estimated value y of the measured Y is obtained through
the estimated value x1, x2, ..., xN of the input quantities X1, X2, ..., XN, there are
two calculation methods: formula (5) and formula (6):
a) Calculation method I:
Where, y is the arithmetic average of the measured quantity values yk
obtained by n independent measurements of Y; the uncertainty of each
measured quantity value yk is the same; each yk is obtained by a complete
set of measured quantity value based on the N input quantities Xi as
obtained at the same time.
This method can increase the degree of freedom of the standard uncertainty of
the evaluation, thus improve the credibility.
4.3.2.6 Preevaluation of repeatability
In the routine verification, calibration or detection work of the same type of the
test piece, if the measurement system is stable and there is no obvious change
in the measurement repeatability, the measurement system can be used, using
the same procedure, operator, at the same location with the test piece under
measurement, to make n premeasurements on the typical measured quantity
value of the typical test piece (generally n is not less than 10), to calculate the
experimental standard deviation s(xk) of the single measured quantity value
from the Bessel formula, that is, the measurement repeatability. When actually
measuring a certain test piece, it can only measure n’ times (1 ≤ n’ < n), take
the arithmetic average value of n’ independent measurements as the estimated
value of the measured, then the type A standard uncertainty of this measured
estimate value due to repeatability is calculated according to formula (20):
The degree of freedom of standard uncertainty as evaluated by this method is
still ν = n  1. It shall be noted that when the repeatability of the measurement
is suspected to be changed, the experimental standard deviation s(xk) shall be
remeasured and calculated in time.
4.3.2.7 When the estimated value xi of the input quantity Xi is obtained from the
curve fitted by the experimental data by the method of least squares, any point
on the curve and the standard uncertainty characterizing the curve fitting
parameters can be evaluated by the relevant statistical procedures. If the
measured estimated value xi presents a timedependent random change in
multiple observations, a special statistical analysis method shall be used. For
example, in frequency measurement, the Allen standard deviation (Allen
variance) is used.
4.3.2.8 Type A evaluation methods are usually more objective than those
obtained by other evaluation methods, meanwhile are statistically rigorous, but
require a sufficient number of repetitions. In addition, the measured quantity
values as obtained by repeated measurements in this measurement procedure
shall be independent of each other.
4.3.2.9 The source of random effects shall be considered as much as possible
in the type A evaluation, so that it can be reflected in the measured quantity
value.
Note: For example:
u(xi) and u(xj)  The standard uncertainty of xi and xj.
4.4.4.3 Use appropriate methods to remove correlations
a) Introduce the correlationinduced quantity into the measurement model as
an independent additional input quantity
For example, if the measurement model of the measured estimated value
is y = f(xi, xj), when determining the measured Y, use a thermometer to
determine the temperature correction value xi of the estimated value of
the input Xi, meanwhile use the same thermometer to determine the
temperature correction value xj of the estimated value of the other input
quantity Xj, the two temperature correction values xi and xj are obviously
correlated. xi = F(T), xj = G(T), that is, both xi and xj are related to the
temperature; because the same thermometer is used for measurement,
if the thermometer shows a large value, the correction values of both are
affected at the same time, so the two input quantities xi and xj in y = f[xi(T),
xj(T)] are correlated. However, as long as the temperature T is used as
an independent additional input in the measurement model, that is, y =
f(xi, xj, T), wherein xi, xj are the estimated values of the input quantities Xi,
Xj, the input quantity T has the standard uncertainty which is not related
to the above two quantities, so there is no need to introduce the
covariance or correlation coefficient of xi and xj when calculating the
combined standard uncertainty.
b) Take effective measures to transform the input quantity
For example, the uncertainty component of the calibration value in the
calibration of the gauge block includes two input quantities: the
temperature θs of the standard gauge block and the temperature θ of the
calibrated gauge block, that is, L = f(θs, θ, ...). Since the two gauge blocks
are on the same measuring device in the laboratory, the temperatures θs
and θ are related. But as long as θ is transformed into θ = θs + δθ, the
temperature difference δθ of the calibrated block and the standard block
and the temperature θs of the standard block are used as two input
quantities, at this time the two input quantities are not related, that is, the
θs in L = f(θs, δθ, ...) is not related to δθ.
4.4.5 Effective degrees of freedom of combined standard uncertainty
4.4.5.1 The degree of freedom of the combined standard uncertainty uc(y) is
called the effective degree of freedom, which is represented by the symbol νeff.
It indicates the reliability of the evaluated uc(y). The greater the νeff, the more
reliable the evaluated uc(y).
4.4.5.2 Effective degrees of freedom νeff need to be calculated in the following
shall be as detailed as possible, so that users can correctly use the
measurement results. Only for certain uses, if the measurement uncertainty is
considered to be negligible, the measurement result can be expressed as a
single measured quantity value, without reporting its measurement uncertainty.
5.1.2 Generally, when reporting the following measurement results, the
combined standard uncertainty uc(y) is used; if necessary, its effective degree
of freedom νeff is given:
a) Basic metrology research;
b) Measurement of basic physical constants;
c) International comparison reproducing the units of international units
(according to relevant international provisions, it may also use the
extended uncertainty of k = 2).
5.1.3 In addition to the above provisions or the parties concerned agreed to the
use of combined standard uncertainty, usually when reporting measurement
results, they are expressed as extended uncertainty.
When it comes to the measurement of industry, commerce, health and safety,
if there are no special requirements, the extended uncertainty U will be reported,
which is generally taken as k = 2.
5.1.4 The measurement uncertainty report generally includes the following:
a) The measurement model being measured;
b) Sources of uncertainty;
c) The value of the standard uncertainty u(xi) of the input quantity as well as
its evaluation method and evaluation process;
d) Sensitivity coefficient ;
e) Uncertainty component of output quantity ui(y) = ci u(xi), if necessary, give
the degrees of freedom of each component νi;
f) Give the covariance or correlation coefficient for all relevant input quantities;
g) The combined standard uncertainty uc and its calculation process, if
necessary, give the effective degree of freedom νeff;
h) Extended uncertainty U or Up and its determination method;
i) Report the measurement results, including the estimated value being
U or Up, including the unit of measurement;
c) If necessary, it may also give the relative expanded uncertainty Urel;
d) It shall give the value of k for U; give p and νeff for Up.
5.2.2.1 U = kuc(y) report can be in one of the following four forms.
For example, the mass of the standard weight is ms, the estimated value being
measured is 100.02147 g, uc(y) = 0.35 mg, the coverage factor k = 2, U = 2 ×
0.35 mg = 0.70 mg, then it is reported as follows:
a) ms = 100.02147 g, U = 0.70 mg; k = 2.
b) ms = (100.02147 ± 0.00070) g; k = 2.
c) ms = 100.02147 (70) g; for the U value of k = 2 in parentheses, the last
digit is aligned with the last digit in the previous result.
d) ms = 100.02147 (0.00070) g; the U value when k = 2 in parentheses has
the same measurement unit as the previous result.
5.2.2.2 Up = kpuc(y) can be reported in one of the following four forms.
For example, the mass of the standard weight is ms, the estimated value
measured is 100.02147 g, uc(y) = 0.35 mg, νeff = 9, according to p = 95%, check
Appendix B to get kp = t95(9) = 2.26, U95 = 2.26 × 0.35 mg = 0.79 mg, then:
a) ms = 100.02147 g, U95 = 0.79 mg, νeff = 9.
b) ms = (100.02147 ± 0.00079) g, νeff = 9, the second item in brackets is the
value of U95.
c) ms = 100.02147 (79) g, νeff = 9, for the value of U95 in parentheses, the
last digit is aligned with the last digit in the previous result.
d) ms = 100.02147 (0.00079) g, νeff = 9, the value of U95 in parentheses has
the same unit of measurement as the previous results.
Note: When the extended uncertainty Up is given, for clarity, the following
description is recommended, for example: ms = (100.02147 ± 0.00079) g, where
the value after the positive/negative sign is the extended uncertainty U95 = k95uc,
wherein the combined standard uncertainty uc(ms) = 0.35 g, the degree of
freedom νeff = 9, the coverage factor kp = t95(9) = 2.26, so it has an coverage
interval with an coverage probability of 95%.
Note: When the first digit of the effective digits of uc(y) and U is 1 or 2, it shall
generally give two significant digits.
For each uncertainty component u(xi) or ui(y) in the evaluation process, in order
to avoid the uncertainty due to rounding off error, it may appropriately reserve
some more digits.
5.3.8.2 When the calculated uc(y) and U have too many digits, the routine
rounding rule is generally used to round off the data to the required valid number.
For the rounding rule, see GB/T 81702008 “Numerical rounding rules and
expression and judgment of limit values”. Sometimes the numbers after the last
digit of the uncertainty can be rounded up instead of rounded down.
Note: For example: U = 28.05 kHz and it needs to take two significant digits,
write it as 28 kHz after rounding off according to the regular rounding off rules.
Another example: U = 10.47 mΩ, sometimes it can be rounded up to 11 mΩ; U
= 28.05 kHz can also be written as 29 kHz.
5.3.8.3 In general, under the same measurement unit, the estimated value to
be measured shall be rounded off to the digit where its last digit is consistent to
the last digit of the uncertainty.
Note: For example: if y = 10.05762 Ω, U = 27 mΩ, because U = 0.027 Ω at the
time of reporting, y shall be rounded off to 10.058 Ω.
6 Application of measurement uncertainty
6.1 Requirements for reporting measurement uncertainty in
calibration certificate
6.1.1 In the calibration certificate, the uncertainty of the calibration value or
correction value shall generally be evaluated according to the actual situation
at each calibration.
Note:
1 The uncertainty of the calibration value or correction value...
