ISO 29473:2010
(Main)Fire tests — Uncertainty of measurements in fire tests
Fire tests — Uncertainty of measurements in fire tests
ISO 29473:2010 gives guidance on the evaluation and expression of uncertainty of fire test method measurements. Application of ISO 29473:2010 is limited to tests that provide quantitative results in engineering units. This includes, for example, methods for measuring the heat release rate of burning specimens based on oxygen consumption calorimetry, as in ISO 5660-1:2002 ISO 29473:2010 does not apply to tests that provide results in the form of indices or binary results (e.g. pass/fail).
Essais au feu — Incertitude de mesures dans les essais au feu
General Information
Standards Content (Sample)
INTERNATIONAL ISO
STANDARD 29473
First edition
2010-12-01
Fire tests — Uncertainty
of measurements in fire tests
Essais au feu — Incertitude de mesures dans les essais au feu
Reference number
ISO 29473:2010(E)
©
ISO 2010
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ISO 29473:2010(E)
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ISO 29473:2010(E)
Contents Page
Foreword .iv
Introduction.v
1 Scope.1
2 Normative references.1
3 Terms, definitions and symbols .2
3.1 Terms and definitions .2
3.2 Symbols.3
4 Principles .4
5 Evaluating standard uncertainty.5
5.1 General .5
5.2 Type A evaluation of standard uncertainty.6
5.3 Type B evaluation of standard uncertainty.6
5.4 Accounting for multiple sources of error .7
6 Determining combined standard uncertainty.7
7 Determining expanded uncertainty .8
8 Reporting uncertainty .9
9 Summary of procedure for evaluating and expressing uncertainty .10
Annex A (informative) Basic concepts of measurement uncertainty.11
Annex B (informative) Uncertainty of fire test results.13
Annex C (informative) Example of estimating the uncertainty in heat release measurements in the
cone calorimeter.14
Bibliography.23
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ISO 29473:2010(E)
Foreword
ISO (the International Organization for Standardization) is a worldwide federation of national standards bodies
(ISO member bodies). The work of preparing International Standards is normally carried out through ISO
technical committees. Each member body interested in a subject for which a technical committee has been
established has the right to be represented on that committee. International organizations, governmental and
non-governmental, in liaison with ISO, also take part in the work. ISO collaborates closely with the
International Electrotechnical Commission (IEC) on all matters of electrotechnical standardization.
International Standards are drafted in accordance with the rules given in the ISO/IEC Directives, Part 2.
The main task of technical committees is to prepare International Standards. Draft International Standards
adopted by the technical committees are circulated to the member bodies for voting. Publication as an
International Standard requires approval by at least 75 % of the member bodies casting a vote.
Attention is drawn to the possibility that some of the elements of this document may be the subject of patent
rights. ISO shall not be held responsible for identifying any or all such patent rights.
ISO 29473 was prepared by Technical Committee ISO/TC 92, Fire safety, Subcommittee SC 1, Fire initiation
and growth. ISO 29473 is based, with the permission of ASTM International, on ASTM E 2536 Standard
Guide for Assessment of Measurement Uncertainty in Fire Tests, copyright ASTM International.
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ISO 29473:2010(E)
Introduction
Users of fire test data often need a quantitative indication of the quality of the data presented in a test report.
This quantitative indication is referred to as the “measurement uncertainty”. There are two primary reasons for
estimating the uncertainty of fire test results:
⎯ ISO/IEC 17025 requires that competent testing and calibration laboratories include uncertainty estimates
for the results that are presented in a report.
⎯ Fire safety engineers need to know the quality of the input data used in an analysis to determine the
uncertainty of the outcome of the analysis.
General principles for evaluating and reporting measurement uncertainties are described in
ISO/IEC Guide 98-3:2008. Application of ISO/IEC Guide 98-3:2008 to fire test data presents some unique
challenges. This International Standard shows how these challenges can be overcome.
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INTERNATIONAL STANDARD ISO 29473:2010(E)
Fire tests — Uncertainty of measurements in fire tests
1 Scope
This International Standard gives guidance on the evaluation and expression of uncertainty of fire test method
measurements developed and maintained by ISO/TC 92, based on the approach presented in
ISO/IEC Guide 98-3.
Application of this International Standard is limited to tests that provide quantitative results in engineering units.
This includes, for example, methods for measuring the heat release rate of burning specimens based on
oxygen consumption calorimetry, as in ISO 5660-1:2002.
This International Standard does not apply to tests that provide results in the form of indices or binary results
(e.g. pass/fail).
In some cases, additional guidance will be required to supplement this International Standard. For example,
the expression and use of uncertainty at low levels may require additional guidance and uncertainties
associated with sampling are not explicitly addressed.
NOTE 1 The procedures described in this International Standard involve some complex mathematics. Basic concepts
of measurement uncertainty are provided in Annex A.
NOTE 2 The guidelines presented in this International Standard may also be used to evaluate and express the
uncertainty associated with fire test results. However, it is not always possible to quantify the uncertainty of fire test results
as some sources of uncertainty cannot be accounted for.
2 Normative references
The following referenced documents are indispensable for the application of this document. For dated
references, only the edition cited applies. For undated references, the latest edition of the referenced
document (including any amendments) applies.
ISO 5660-1:2002, Reaction-to-fire tests — Heat release, smoke production and mass loss rate — Part 1: Heat
release rate (cone calorimeter method)
ISO 5725-2:1994, Accuracy (trueness and precision) of measurement methods and results — Part 2: Basic
method for the determination of repeatability and reproducibility of a standard measurement method
ISO 13943, Fire safety — Vocabulary
ISO/IEC 17025:2005, General requirements for the competence of testing and calibration laboratories
ISO/IEC Guide 98-3:2008, Uncertainty of measurement — Part 3: Guide to the expression of uncertainty in
measurement (GUM:1995)
ISO/IEC Guide 99:2007, International vocabulary of metrology — Basic and general concepts and associated
terms (VIM)
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ISO 29473:2010(E)
3 Terms, definitions and symbols
For the purposes of this document, the following terms, definitions and symbols apply.
3.1 Terms and definitions
3.1.1
measurement uncertainty
uncertainty of measurement
uncertainty
non-negative parameter characterizing the dispersion of the quantity values being attributed to a measurand,
based on the information used
NOTE Adapted from ISO/IEC Guide 99:2007: the Notes are not included here.
3.1.2
standard measurement uncertainty
standard uncertainty of measurement
standard uncertainty
measurement uncertainty expressed as a standard deviation
[ISO/IEC Guide 99:2007, definition 2.30]
3.1.3
Type A evaluation of measurement uncertainty
Type A evaluation
evaluation of a component of measurement uncertainty by a statistical analysis of measured quantity values
obtained under defined measurement conditions
NOTE Adapted from ISO/IEC Guide 99:2007: the Notes are not included here.
3.1.4
Type B evaluation of measurement uncertainty
Type B evaluation
evaluation of a component of measurement uncertainty determined by means other than a Type A evaluation
of measurement uncertainty
NOTE Modified from ISO/IEC Guide 99:2007: the Example and Note are not included here.
3.1.5
combined standard measurement uncertainty
combined standard uncertainty
standard measurement uncertainty that is obtained using the individual standard measurement uncertainties
associated with the input quantities in a measurement model
[ISO/IEC Guide 99:2007, definition 2.31]
3.1.6
expanded measurement uncertainty
expanded uncertainty
product of a combined standard measurement uncertainty and a coverage factor one
NOTE Adapted from ISO/IEC Guide 99:2007: the Notes are not included here and the definition is slighty modified.
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ISO 29473:2010(E)
3.1.7
coverage factor
number larger than one by which a combined standard measurement uncertainty is multiplied to expand the
coverage probability to a specified value
NOTE 1 A coverage factor is usually symbolized k (see also ISO/IEC Guide 98-3:2008, 2.3.6).
NOTE 2 Adapted from ISO/IEC Guide 99:2007.
3.2 Symbols
1/2 1/2 1/2
C cone calorimeter orifice coefficient (m ·kg ·K )
c sensitivity coefficient of X
i i
f functional relationship between the measurand and the input quantities (Equation 2)
k coverage factor
m number of sources of error affecting the uncertainty of X (Equation 8)
i
N number of input quantities
n number of observations or measurements
&
Q heat release rate (kW)
&
Q burner heat release rate (kW)
b
r stoichiometric oxygen to fuel ratio (kg/kg)
o
r(x , x) estimated correlation coefficient between X and X
i j i j
s experimental standard deviation
T exhaust stack temperature at the cone calorimeter orifice plate flow meter (K)
e
t t-distribution statistic for the specified level of confidence and effective degrees of freedom
U expanded uncertainty
u standard uncertainty
u combined standard uncertainty
c
th
u standard uncertainty due to j source of error
j
th
X i input quantity
i
X measured oxygen mole fraction in the exhaust duct
O
2
o
X ambient oxygen mole fraction in dry air (0,209 5)
O
2
x mean of n measurements
i
th
x k measured value of X
i,k i
Y true value of the measurand
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ISO 29473:2010(E)
y measured value of the measurand
y mean of n measurements
th
y k measured value
k
β number of moles of gaseous combustion products generated per mole of O consumed
2
Δh net heat of combustion (kJ/kg)
c
ΔP pressure drop across the cone calorimeter orifice plate (Pa)
ΔX half-width of the interval [Equation 7)]
i
ε measurement error
ε contribution to the total measurement error from the error associated with the input estimate x
i
i
ν effective degrees of freedom
eff
ν degrees of freedom assigned to the standard uncertainty of input estimate x
i i
4 Principles
The objective of a measurement is to determine the value of the measurand, i.e. the physical quantity that
needs to be measured. Every measurement is subject to error, no matter how carefully it is conducted. The
(absolute) error of a measurement is defined as follows:
ε≡−y Y (1)
where
ε is the measurement error;
y is the measured value of the measurand;
Y is the true value of the measurand.
All terms in Equation (1) have the units of the physical quantity that is measured. This equation cannot be
used to determine the error of a measurement because the true value is unknown, otherwise a measurement
would not be needed. In fact, the true value of a measurand is unknown because it cannot be measured
without error. However, it is possible to estimate, with some confidence, the expected limits of error. This
estimate is referred to as the “uncertainty of measurement” and provides a quantitative indication of its quality.
Errors of measurement may have two components, a random component and a systematic component. The
former is due to a number of sources that affect a measurement in a random and uncontrolled manner.
Random errors cannot be eliminated, but their effect on uncertainty may be reduced by increasing the number
of repeat measurements and by applying a statistical analysis to the results. Systematic errors remain
unchanged when a measurement is repeated under the same conditions. Their effect on uncertainty cannot
be completely eliminated either, but it can be reduced by applying corrections to account for the error
contribution due to recognized systematic effects. The residual systematic error is unknown and may be
treated as a random error for the purpose of this International Standard.
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ISO 29473:2010(E)
5 Evaluating standard uncertainty
5.1 General
A quantitative result of a fire test Y is not normally obtained from a direct measurement, but is determined as a
function (f) from N input quantities X , X , …, X :
1 2 N
Yf= (,X X,L,X ) (2)
12 N
where
Y is measurand;
f is the functional relationship between the measurand;
X is input quantities (i = 1 … N).
i
The input quantities may be categorized as quantities whose values and uncertainties are:
⎯ directly determined from single observation, repeated observation or judgment based on experience; or
⎯ brought into the measurement from external sources such as reference data obtained from handbooks.
An estimate of the output, y, is obtained from Equation (2) using input estimates x , x , …, x for the values of
1 2 N
the N input quantities:
yf= (,xx,L,x ) (3)
12 N
Substituting Equations (2) and (3) into Equation (1) leads to:
yY=+ε=Y+εε+ +L+ε (4)
12 N
where
ε is the contribution to the total measurement error from the error associated with the input estimate x .
i i
A possible approach to determine the uncertainty of y involves a large number (n) of repeat measurements.
The mean value of the resulting distribution ()y is the best estimate of the measurand. The experimental
standard deviation of the mean is the best estimate of the standard uncertainty of y, denoted by u(y):
n
2
()yy−
∑ k
2
sy()
2
k=1
uy()≈=s (y) = (5)
nn(1n−)
where
u is standard uncertainty;
s is the experimental standard deviation;
n is the number of observations;
th
y is the k measured value;
k
y is the mean of n measurements.
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ISO 29473:2010(E)
The number of observations n should be large enough to ensure that y provides a reliable estimate of the
2
expectation μ of the random variable y, and that s ()y provides a reliable estimate of the variance
y
22
σσ()yy= ( )/n.
NOTE If the probability distribution of y is normal, then the standard deviation of s ()y relative to σ ()y is approximately
–1 –1/2
[2(n )] . Thus, for n = 10 the relative uncertainty of s()y is 24 percent, while for n = 50 it is 10 percent. Additional
values are given in Table E.1 in ISO/IEC Guide 98-3:2008.
Unfortunately, it is often not feasible or even possible to perform a sufficiently large number of repeat
measurements. In those cases, the uncertainty of the measurement can be determined by combining the
standard uncertainties of the input estimates. The standard uncertainty of an input estimate x is obtained from
i
the distribution of possible values of the input quantity X . There are two types of evaluations depending on
i
how the distribution of possible values is obtained.
5.2 Type A evaluation of standard uncertainty
A Type A evaluation of standard uncertainty of x is based on the frequency distribution, which is estimated
i
from a series of n repeated observations x (k = 1 … n). The resulting equation is similar to Equation (5):
i,k
n
2
()xx−
∑ ik, i
2
sx()
2 ik=1
ux()≈=s (x) = (6)
ii
nn(1n−)
where
th
x is the k measured value;
i,k
x is the mean of n measurements.
i
NOTE Type A evaluations of standard uncertainty are rare in fire tests as repeated measurements are not common.
5.3 Type B evaluation of standard uncertainty
A Type B evaluation of standard uncertainty of x is not based on repeated measurements but on an a priori
i
frequency distribution. In this case the uncertainty is determined from previous measurement data, experience
or general knowledge, manufacturer's specifications, data provided in calibration certificates, uncertainties
assigned to reference data taken from handbooks, etc.
If the quoted uncertainty from a manufacturer specification, handbook or other source is stated to be a
particular multiple of a standard deviation, the standard uncertainty u(x ) is simply the quoted value divided by
i
the multiplier. For example, the quoted uncertainty is often at the 95 % level of confidence. Assuming a normal
distribution, this corresponds to a multiplier of two, i.e. the standard uncertainty is half the quoted value.
Often the uncertainty is expressed in the form of upper and lower limits. Usually there is no specific knowledge
about the possible values of X within the interval and one can only assume that it is equally probable for X to
i i
lie anywhere in it. Figure 1 shows the most common example where the corresponding rectangular distribution
is symmetric with respect to its best estimate x . The standard uncertainty in this case is given by:
i
ΔX
i
ux()= (7)
i
3
where
ΔX is the half-width of the interval.
i
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ISO 29473:2010(E)
ΔX ΔX
i i
μ
μ ΔX μ μ μ +ΔX
-- +
i i
3
3
Figure 1 — Rectangular distribution
If some information is known about the distribution of the possible values of X within the interval, that
i
knowledge is used to better estimate the standard deviation.
5.4 Accounting for multiple sources of error
The uncertainty of an input quantity is sometimes due to multiple sources error. In this case, the standard
uncertainty associated with each source of error has to be estimated separately and the standard uncertainty
of the input quantity is then determined in accordance with the following equation:
m
2
⎡⎤
ux()= u()x (8)
ij∑ i
⎣⎦
j=1
where
m is the number of sources of error affecting the uncertainty of x ;
i
th
u is the standard uncertainty due to j source of error.
j
6 Determining combined standard uncertainty
The standard uncertainty of y is obtained by appropriately combining the standard uncertainties of the input
estimates x x ,…, x . If all input quantities are independent, the combined standard uncertainty of y is given
,
1 2 N
by:
2
2
NN⎡⎤
∂f
2
⎢⎥
uy()=≡u (x) cu(x) (9)
⎡ ⎤
c∑∑iii
⎣ ⎦
⎢⎥∂X
i
ii==11x
i
⎣⎦
where
u is a combined standard uncertainty;
c
c are sensitivity coefficients.
i
Equation (9) is referred to as the law of propagation of uncertainty and based on a first-order Taylor series
approximation of Y = f (X X , …, X ). When the non-linearity of f is significant, higher-order terms shall be
,
1 2 N
included (see 5.1.2 in ISO/IEC Guide 98-3 for details).
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ISO 29473:2010(E)
When the input quantities are correlated, Equation (9) shall be revised to include the covariance terms. The
combined standard uncertainty of y is then calculated from:
2
NN−1N
uy()=+⎡⎤cu(x) 2 ccu(x)u(x )r(x,x ) (10)
c∑∑⎣⎦ii ∑ ij i j i j
ii==11j=i+1
where
r(x , x ) is the estimated correlation coefficient between X and X .
i j i j
Since the values of the input quantities are not known, the correlation coefficient is estimated on the basis of
the measured values of the input quantities.
7 Determining expanded uncertainty
It is often necessary to give a measure of uncertainty that defines an interval about the measurement result
that may be expected to encompass a large fraction of the distribution of values that could be attributed to the
measurand. This measure is termed expanded uncertainty and is denoted by U. The expanded uncertainty is
obtained by multiplying the combined standard uncertainty by a coverage factor k:
Uy()=ku ()y (11)
c
where
U is expanded uncertainty;
k is the coverage factor.
The value of the coverage factor k is chosen on the basis of the level of confidence required of the interval
y − U to y + U. In general, k will be in the range 2 to 3. Because of the central limit theorem (CLT), k can
usually be determined from:
k = t(v , α/2) (12)
eff
where
t is the t-distribution statistic for the specified level of confidence and effective degrees of freedom;
ν is effective degrees of freedom.
eff
(confidence level: 100 (1-α) %)
Table 1 gives values of the t-distribution statistic for different levels of confidence and degrees of freedom.
A more complete table can be found in Annex G of ISO/IEC Guide 98-3:2008.
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ISO 29473:2010(E)
Table 1 — Selected values of the t-distribution statistic
Confidence level Confidence level Confidence level
Degrees Degrees Degrees
of freedom of freedom of freedom
95 % 99 % 95 % 99 % 95 % 99 %
1 12,71 63,66 6 2,45 3,71 20 2,09 2,85
2 4,30 9,92 7 2,36 3,50 30 2,04 2,75
3 3,18 5,84 8 2,31 3,36 40 2,02 2,70
4 2,78 4,60 9 2,26 3,25 50 2,01 2,68
5 2,57 4,03 10 2,23 3,17 ∞ 1,96 2,58
The effective degrees of freedom can be computed from the Welch-Satterthwaite formula:
4
⎡⎤uy()
⎣⎦c
ν (13)
=
eff
4
N
ux()
⎡⎤
⎣⎦i
∑
ν
i
i=1
where
ν is the degree of freedom assigned to the standard uncertainty of input estimate x .
i i
The degrees of freedom ν is equal to n −1 if x is estimated as the arithmetic mean of n independent
i i
observations (Type A standard uncertainty evaluation). If u(x ) is obtained from a Type B evaluation and it can
i
be treated as exactly known, which is often the case in practice, ν → ∞. If u(x ) is not exactly known, ν can be
i i i
estimated from:
2 −2
⎡⎤ux() ⎡⎤
11 Δux()
⎣⎦c i
i
ν≈≈ (14)
i ⎢⎥
2
22 ux()
⎣⎦i
σ ux()
⎡⎤
{}
i
⎣⎦
The quantity in large brackets in Equation (14) is the relative uncertainty of u(x ), which is a subjective quantity
i
whose value is obtained by scientific judgement based on the pool of available information.
The probability distribution of u (y) is often approximately normal and the effective degrees of freedom of u (y)
c c
is of significant size. When this is the case, one can assume that taking k = 2 produces an interval having a
level of confidence of approximately 95,5 percent, and that taking k = 3 produces an interval having a level of
confidence of approximately 99,7 percent.
8 Reporting uncertainty
The result of a measurement and the corresponding uncertainty should be reported in the form of Y = y + U
followed by the units of y and U. Alternatively, the relative expanded uncertainty U/| y| in percent can be
specified instead of the absolute expanded uncertainty. In either case the report should describe how the
measurand Y is defined, specify the approximate confidence level and explain how the corresponding
coverage factor was determined. The former can be done by reference to the appropriate fire test standard.
The report should also include a discussion of sources of uncertainty that are not addressed by the analysis.
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ISO 29473:2010(E)
9 Summary of procedure for evaluating and expressing uncertainty
The procedure for evaluating and expressing uncertainty of fire test results involves the following steps:
1) Express mathematically the relationship between the measurand Y and the input quantities X upon
i
which Y depends: Y = f (X , X , …, X ).
1 2 N
2) Determine x , the estimated value for each input quantity X .
i i
3) Identify all sources of error for each input quantity and evaluate the standard uncertainty u (x ) for
i
each input estimate x .
i
4) Evaluate the correlation coefficient for estimates of input quantities that are dependent.
5) Calculate the result of the measurement, i.e. the estimate y of the measurand Y from the functional
relationship f using the estimates x of the input quantities X obtained in step 2.
i
i
6) Determine the combined standard uncertainty u (y) of the measurement result y from the standard
c
uncertainties and correlation coefficients associated with the input estimates as described in
Clause 6.
7) Select a coverage factor k on the basis of the desired level of confidence as described in Clause 7
and multiply u (y) by this value to obtain the expanded uncertainty U.
c
8) Report the result of the measurement y together with its expanded uncertainty U as discussed in
Clause 8.
An example from heat release measurements in the cone calorimeter illustrating the application of this
procedure can be found in Annex C.
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ISO 29473:2010(E)
Annex A
(informative)
Basic concepts of measurement uncertainty
The objective of a measurement is to determine the value of the measurand, i.e. the quantity being measured.
Measurements are not perfect and give rise to errors. The true value of a measurand can therefore never be
determined because measurement errors cannot be eliminated.
The purpose of measurement uncertainty analysis is to quantify the quality of a measurement by establishing
limits of the measurement errors at a specified level of confidence. Sometimes the term accuracy is used to
describe the quality of a measurement. However, this term is ambiguous. For example, what is twice the
accuracy of ± 2 %? Is it ± 1 % or ± 4 %? To avoid this ambiguity, the term uncertainty is preferred and used in
ISO/IEC Guide 98-3 and in this International Standard.
Measurement errors can be random or systematic. A series of measurements of a measurand performed
under the same conditions results in values that are randomly scattered around a mean value. The scatter is
due to the effects of sources of random error. Random errors cannot be eliminated, but the corresponding
uncertainty can be reduced by increasing the number of measurements and applying a statistical analysis.
Systematic errors remain unchanged when measurements are repeated. Systematic errors should be
eliminated as much as possible, for example through calibration of the measuring equipmen
...
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