EN ISO 20988:2007

SLOVENSKI STANDARD
01-januar-2008
Kakovost zraka - Smernice za ocenjevanje merilne negotovosti (ISO 20988:2007)
Air quality - Guidelines for estimating measurement uncertainty (ISO 20988:2007)
Luftbeschaffenheit - Leitlinien zur Schätzung der Messunsicherheit (ISO 20988:2007)
Qualité de l'air - Lignes directrices pour estimer l'incertitude de mesure (ISO 20988:2007)
Ta slovenski standard je istoveten z: EN ISO 20988:2007
ICS:
13.040.01 Kakovost zraka na splošno Air quality in general
2003-01.Slovenski inštitut za standardizacijo. Razmnoževanje celote ali delov tega standarda ni dovoljeno.

EUROPEAN STANDARD
EN ISO 20988
NORME EUROPÉENNE
EUROPÄISCHE NORM
June 2007
ICS 13.040.01
English Version
Air quality - Guidelines for estimating measurement uncertainty
(ISO 20988:2007)
Qualité de l'air - Lignes directrices pour estimer l'incertitude Luftbeschaffenheit - Leitlinien zur Schätzung der
de mesure (ISO 20988:2007) Messunsicherheit (ISO 20988:2007)
This European Standard was approved by CEN on 9 June 2007.
CEN members are bound to comply with the CEN/CENELEC Internal Regulations which stipulate the conditions for giving this European
Standard the status of a national standard without any alteration. Up-to-date lists and bibliographical references concerning such national
standards may be obtained on application to the CEN Management Centre or to any CEN member.
This European Standard exists in three official versions (English, French, German). A version in any other language made by translation
under the responsibility of a CEN member into its own language and notified to the CEN Management Centre has the same status as the
official versions.
CEN members are the national standards bodies of Austria, Belgium, Bulgaria, Cyprus, Czech Republic, Denmark, Estonia, Finland,
France, Germany, Greece, Hungary, Iceland, Ireland, Italy, Latvia, Lithuania, Luxembourg, Malta, Netherlands, Norway, Poland, Portugal,
Romania, Slovakia, Slovenia, Spain, Sweden, Switzerland and United Kingdom.
EUROPEAN COMMITTEE FOR STANDARDIZATION
COMITÉ EUROPÉEN DE NORMALISATION
EUROPÄISCHES KOMITEE FÜR NORMUNG
Management Centre: rue de Stassart, 36  B-1050 Brussels
© 2007 CEN All rights of exploitation in any form and by any means reserved Ref. No. EN ISO 20988:2007: E
worldwide for CEN national Members.

Foreword
This document (EN ISO 20988:2007) has been prepared by Technical Committee ISO/TC 146
"Air quality" in collaboration with Technical Committee CEN/TC 264 "Air quality", the secretariat
of which is held by DIN.
This European Standard shall be given the status of a national standard, either by publication of
an identical text or by endorsement, at the latest by December 2007, and conflicting national
standards shall be withdrawn at the latest by December 2007.

According to the CEN/CENELEC Internal Regulations, the national standards organizations of
the following countries are bound to implement this European Standard: Austria, Belgium,
Bulgaria, Cyprus, Czech Republic, Denmark, Estonia, Finland, France, Germany, Greece,
Hungary, Iceland, Ireland, Italy, Latvia, Lithuania, Luxembourg, Malta, Netherlands, Norway,
Poland, Portugal, Romania, Slovakia, Slovenia, Spain, Sweden, Switzerland and United
Kingdom.
Endorsement notice
The text of ISO 20988:2007 has been approved by CEN as EN ISO 20988:2007 without any
modifications.
INTERNATIONAL ISO
STANDARD 20988
First edition
2007-06-15
Air quality — Guidelines for estimating
measurement uncertainty
Qualité de l'air — Lignes directrices pour estimer l'incertitude de mesure

Reference number
ISO 20988:2007(E)
©
ISO 2007
ISO 20988:2007(E)
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ii © ISO 2007 – All rights reserved

ISO 20988:2007(E)
Contents Page
Foreword. iv
Introduction . v
1 Scope . 1
2 Normative references . 1
3 Terms and definitions. 1
4 Symbols and abbreviated terms . 5
5 Basic concepts. 6
5.1 Outline. 6
5.2 Measurement uncertainty . 9
5.3 Correction for systematic effects. 10
5.4 Provision of input data. 11
6 Problem specification. 13
6.1 Objectives. 13
6.2 Measurement. 13
6.3 Uncertainty parameters. 15
6.4 Input data. 15
6.4.1 General. 15
6.4.2 Assessment of representativeness . 16
6.5 Effects not described by series of observations. 17
7 Statistical analysis. 18
7.1 Objectives. 18
7.2 Indirect approach. 19
7.3 Direct approach. 21
7.4 Statistical validity. 22
8 Estimation of variances and covariances . 23
8.1 General. 23
8.2 Variance estimates of Type A. 23
8.3 Variance estimates of Type B. 23
8.4 Estimation of covariances . 24
9 Evaluation of uncertainty parameters . 25
9.1 Objective. 25
9.2 Combined standard uncertainty. 25
9.3 Expanded uncertainty . 26
9.3.1 General. 26
9.3.2 Expanded uncertainty of results exhibiting a Gaussian distribution. 27
10 Reporting . 28
Annex A (informative) Testing a coverage probability . 30
Annex B (informative) Type A evaluation methods for experimental designs A1 to A8. 34
Annex C (informative) Examples . 49
Bibliography . 81

ISO 20988:2007(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 20988 was prepared by Technical Committee ISO/TC 146, Air quality, Subcommittee SC 4, General
aspects.
iv © ISO 2007 – All rights reserved

ISO 20988:2007(E)
Introduction
The general concept of uncertainty estimation is described in the Guide to the Expression of Uncertainty in
Measurement (GUM). Practical considerations of the GUM are focussed on evaluation of series of unbiased
observations. In air quality measurements, series of observations may rarely be considered unbiased due to
the presence of random effects not varying throughout a series of observations.
This International Standard supports evaluation of random effects causing variation or bias in series of
observations for the purpose of uncertainty estimation. Appropriate data may be collected in experimental
designs providing comparison with reference material, or with reference instruments, or with independent
measurements of the same type. In provision of experimental data for uncertainty estimation, it is important to
ensure representativeness for variations and bias occurring in intended use of the method of measurement.
Generic guidance and statistical procedures presented by this International Standard are addressed to
technical experts of air quality measurement, acting, e.g. in standardization, validation or documentation of
methods of measurement in ambient air, indoor air, stationary source emissions, workplace atmospheres or
meteorology.
This International Standard does not provide comprehensive information on planning and execution of
experimental designs to be evaluated for the purpose of uncertainty estimation.
Uncertainties of results of measurement caused by incomplete time-coverage of measurement data are not
[2]
considered in this document, but in ISO 11222 . Uncertainties of results of measurement induced by
incomplete spatial coverage by measurement data are not considered in this document.

INTERNATIONAL STANDARD ISO 20988:2007(E)

Air quality — Guidelines for estimating measurement
uncertainty
1 Scope
This International Standard provides comprehensive guidance and specific statistical procedures for
uncertainty estimation in air quality measurements including measurements of ambient air, stationary source
emissions, indoor air, workplace atmospheres and meteorology. It applies the general recommendations of
the Guide to the Expression of Uncertainty in Measurement (GUM) to boundary conditions met in air quality
measurement. The boundary conditions considered include measurands varying rapidly in time, as well as the
presence of bias in a series of observations obtained under conditions of intended use of methods of air
quality measurement.
The methods of measurement considered comprise
⎯ methods corrected for systematic effects by repeated observation of reference materials,
⎯ methods calibrated by paired measurement with a reference method,
⎯ methods not corrected for systematic effects because they are unbiased by design, and
⎯ methods not corrected for systematic effects in intended use deliberately taking into account a bias.
Experimental data for uncertainty estimation can be provided either by a single experimental design in a direct
approach or by a combination of different experimental designs in an indirect approach.
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/IEC Guide 98:1995, Guide to the expression of uncertainty in measurement (GUM)
3 Terms and definitions
3.1
uncertainty (of measurement)
measurement uncertainty
parameter, associated with the result of a measurement, that characterizes the dispersion of the values that
could reasonably be attributed to the measurand
[ISO/IEC Guide 98:1995, B.2.18; VIM:1993, 3.9]
3.2
standard uncertainty
uncertainty of the result of measurement expressed as a standard deviation
[ISO/IEC Guide 98:1995, 2.3.1]
ISO 20988:2007(E)
NOTE The standard uncertainty of a result of measurement is an estimate of the standard deviation of the population
of all possible results of measurement which can be obtained by means of the same method of measurement for the
measurand exhibiting a unique value.
3.3
combined standard uncertainty
standard uncertainty of the result of measurement when that result is obtained from the values of a number of
other input quantities, equal to the positive square root of a sum of terms, the terms being the variances or
covariance of these other quantities weighted according to how the measurement result varies with changes
in these quantities
[ISO/IEC Guide 98:1995, 2.3.4]
NOTE The adjective “combined” can be omitted often without loss of generality.
3.4
expanded uncertainty
quantity defining an interval [y − U (y); y + U (y)] about the result of a measurement y that may be expected to
p p
encompass a large fraction p of the distribution of values that could reasonably be attributed to the measurand
NOTE 1 Adapted from ISO/IEC Guide 98:1995, 2.3.5.
NOTE 2 If the uncertainty has been obtained mainly by Type A evaluation, the interval [y − U (y); y + U (y)] can be
p p
understood as confidence interval for the true value of the measurand on a level of confidence p.
NOTE 3 The interval [y − U (y); y + U (y)] characterizes the range of values within which the true value of the
p p
measurand is confidently expected to lie (see ISO/IEC Guide 98:1995, 2.2.4).
3.5
coverage factor
numerical factor used as multiplier of the combined standard uncertainty in order to obtain an expanded
uncertainty
[ISO/IEC Guide 98:1995, 2.3.6]
3.6
coverage probability
fraction of results of measurement expected to be encompassed by a specified interval
3.7
Type A evaluation (of uncertainty)
method of evaluation of uncertainty by the statistical analysis of series of observations
[ISO/IEC Guide 98:1995, 2.3.2]
3.8
Type B evaluation (of uncertainty)
method of evaluation of uncertainty by means other than the statistical analysis of series of observations
[ISO/IEC Guide 98:1995, 2.3.3]
3.9
standard deviation
positive square root of the variance
[ISO/IEC Guide 98:1995, C.2.12]
NOTE In general, the standard deviation of the population of a random variable X is estimated by the positive square
root of an estimate of the variance of the population of X.
2 © ISO 2007 – All rights reserved

ISO 20988:2007(E)
3.10
experimental standard deviation
for a series of N measurements of the same measurand, the quantity s(x) characterizing the dispersion of the
results is given by the formula
N
()xj()−x
sx()=
∑
N−1
j=1
x(j) being the result of the jth measurement and x being the arithmetic mean of the N results considered
NOTE 1 Adapted from ISO/IEC Guide 98:1995, B.2.17.
2 2
NOTE 2 s (x) is an unbiased estimate of the variance σ (X) of the investigated random variable X, if the series of
observations x(j) with j = 1 to N is unbiased.
3.11
variance
the expectation of the square of the centred random variable:
⎡⎤
σ XE=−X EX
() ()
{⎢⎥ }
⎣⎦
[ISO/IEC Guide 98:1995, C.2.11]
NOTE The population variance σ (X) of a random variable X can be estimated by the square of the experimental
standard deviation s (x) of a simple random sample of unbiased observations x(j) with j = 1 to N of the random variable X.
Otherwise, s (x) underestimates the population variance.
3.12
covariance
mean of the product of two centred random variables in their joint probability distribution
NOTE 1 Adapted from ISO 3534-1: 2006, 2.43.
NOTE 2 The covariance cov(x, y) is a sample statistic used to estimate the covariance of the populations of x and y.
3.13
expectation
expected value
1) For a discrete random variable X taking the values x with probabilities p , the expectation, if it exists, is
i i
E(X) = Σ p x , the sum being extended over all values x which may be taken by X.
i i i
2) For a continuous random variable X having the probability density function f(x), the expectation, if it exists,
is E(X ) = x ⋅ f (x)⋅dx , the integral being extended over the interval(s) of variation of X.
∫
[ISO/IEC Guide 98:1995, C.2.9]
3.14
degrees of freedom
in general, the number of terms in a sum minus the number of constraints on the terms of the sum
[ISO/IEC Guide 98:1995, C.2.31]
NOTE For a variance estimate, the (effective) number of degrees of freedom can be understood as the number of
independent pieces of information used to obtain that variance estimate.
3.15
measurement
set of operations having the object of determining the value of a quantity
[VIM:1993, 2.1]
ISO 20988:2007(E)
3.16
result of measurement
value attributed to the measurand, obtained by measurement
[VIM:1993, 3.1]
3.17
sensitivity coefficient
deviation of the result of measurement divided by the deviation of an influence quantity causing the change, if
all other influence quantities are kept constant
3.18
measurand
particular quantity subject to measurement
[VIM:1993, 2.6]
NOTE The measurand is considered to exhibit a unique value at least for the time period needed for a single
measurement.
3.19
measuring system
complete set of measuring instruments and other equipment with operating procedures to carry out specified
air quality measurements
[ISO 11222:2002, 3.9]
NOTE A measuring system is a technical realization of a method of measurement. Method documentation is
considered part of a measuring system.
3.20
reference material
RM
material or substance for which one or more properties are sufficiently homogeneous and well established to
be used for the calibration and/or the validation of a measuring system
NOTE 1 Adapted from VIM:1993, 6.13.
NOTE 2 A reference material may be in the form of a pure or mixed gas, liquid or solid.
3.21
systematic effect
Influence causing a bias that is expected to occur consistently in each series of observations obtained in
repeated or parallel execution of the measurement
3.22
random effect
influence causing either random variation or a bias of random value (inconsistent bias) in a series of
observation obtained in repeated execution of the measurement
NOTE An effect exhibiting a fixed, but random value while executing the measurement repeatedly causes a bias of
random value.
3.23
bias
systematic error of the indication of a measuring instrument
[VIM:1993, 5.25]
NOTE A bias of a series of observations about an accepted reference value can be caused either by systematic
effects, or by random effects exhibiting (unknown) fixed values in the series of observations.
4 © ISO 2007 – All rights reserved

ISO 20988:2007(E)
3.24
representativeness
ability of a series of observations to provide an unbiased estimate of a parameter of a specified statistical
population
3.25
population
totality of items under consideration
[ISO 3534-1:2006, 1.1]
NOTE Ensemble of possible results of measurement which can be obtained for a unique measurand by all possible
technical realizations of a specified method of measurement.
4 Symbols and abbreviated terms
a parameter (constant)
b parameter (constant)
c parameter (constant)
c sensitivity coefficient
i
cov(x , x ) estimate of covariance between input quantities x and x
i k i k
E(X) expectation of random variable X
i index
j index
k index
k coverage factor
p
K number
L number of laboratories
M number
N number
p coverage probability; level of confidence
σ(x) standard deviation of the population of a random variable X
s(x) experimental standard deviation of data set x(j) with j = 1 to N
t(p,ν) (1 − p)-quantile of Student's t-distribution of ν degrees of freedom
u uncertainty caused by bias
B
u(x ) standard uncertainty of input value x
i i
ISO 20988:2007(E)
u(x ) (combined) standard uncertainty of reference value x
R R
u(y ) (combined) standard uncertainty of reference value y
R R
u(y (j)) (combined) standard uncertainty of reference value y (j)
R R
U (y) expanded uncertainty of result of measurement y on level of coverage p
p
var(x ) estimate of the variance of input quantity x
i i
var(Y) estimate of the variance of possible results of measurement Y
var(y) estimate of the variance of results of measurement y(j) with j = 1 to N observed in a direct
approach
w(y) relative standard uncertainty of a result of measurement y
W (y) relative expanded uncertainty of a result of measurement y on level of coverage p
p
x input quantity of the method model equation y = f (x ,., x )
1 K
i
x reference value for input quantity x
R
δX potential deviation of influence quantity x
Y possible result of measurement that could reasonably be attributed to the same measurand by
independent replication of the measurement which was executed to obtain the result of
measurement y
y result of measurement
y accepted value of reference material of the measurand
R
y (i) result of measurement obtained by a reference method of measurement
R
δY potential deviation of result of measurement y about the (unknown) true value of the measurand,
which is not described implicitly by the experimental data to be evaluated
γ level of confidence
µ (unknown) true value of the measurand
ν number of degrees of freedom
ν effective number of degrees of freedom
eff
χ (γ, ν) γ−percentile of chi-square distribution of ν degrees of freedom
5 Basic concepts
5.1 Outline
The general objective of this International Standard is to support application of the Guide to the Expression of
Uncertainty in Measurement (GUM) in the various fields of air quality measurement including ambient air,
6 © ISO 2007 – All rights reserved

ISO 20988:2007(E)
indoor air, meteorology, stationary source emissions and workplace atmospheres. Standard methods of air
quality measurement are considered to be fully documented, e.g. in method standards, standard operating
procedures, validation reports or in other technical documents.
Documentation for a given method should comprise
⎯ instructions on intended use (standard operating procedure),
⎯ instructions on correction for systematic effects, if appropriate,
⎯ method model equation y = f(x ,., x ), if results of measurement y are calculated from observed or
1 K
otherwise known input quantities x ,
i
⎯ results of method-validation, if appropriate, and
⎯ instructions on how to assign uncertainty parameters to results of measurement y.
The focus of this International Standard is on how to assign appropriate uncertainty parameters to results of
measurement obtained by air quality measurement methods. To this end, uncertainty estimation is considered
to be a five-step procedure consisting of
⎯ problem specification (see Clause 6),
⎯ statistical analysis (see Clause 7),
⎯ estimation of variances and covariances (see Clause 8),
⎯ evaluation of uncertainty parameters (see Clause 9), and
⎯ reporting (see Clause 10).
Figure 1 relates this five-step procedure to the eight steps recommended by the GUM.
ISO 20988:2007(E)
Figure 1 — Comparison of the 5-step ISO 20988 procedure (left side) with the 8-step procedure of the
GUM (right side)
8 © ISO 2007 – All rights reserved

ISO 20988:2007(E)
The main objectives of problem specification as a separate first step are
⎯ to identify the questions to be answered, and
⎯ to provide input data to be evaluated.
Starting from a proper problem specification, this International Standard provides guidance to statistical
analysis and to evaluation methods which are applicable without mathematical expertise. Problem
specification requires expert knowledge of technical aspects of the measurement considered and at least a
basic understanding of the general statistical concept of uncertainty estimation described by the GUM. A brief
introduction to the statistical aspects of uncertainty estimation is provided in 5.2, 5.3 and 5.4.
5.2 Measurement uncertainty
Measurement uncertainty is defined a “parameter associated with the result of a measurement, that
characterizes the dispersion of the values that could reasonably be attributed to the measurand” (see 3.1).
An appropriate uncertainty parameter can be:
⎯ the (combined) standard uncertainty u(y) of a result of measurement y;
⎯ the expanded uncertainty U (y) of a result of measurement y on a specified level of coverage p.
p
In accordance with definition 3.1, the (combined) standard uncertainty u(y) of a result of measurement y is the
positive square root of an estimate var(Y) of the variance of the population of possible results of measurement
Y that could reasonably be attributed to the same measurand by independent replication of the measurement.
Accordingly, a basic task in uncertainty estimation is to provide an estimate var(Y) of the variance of the
population of possible results of measurement Y. A detailed statistical discussion is provided in Clause 7.
Following definition 3.4, the expanded uncertainty U (y) describes an interval [y − U (y); y + U (y)] about a
p p p
specific result of measurement y, which is expected to encompass a large fraction p of the possible results
that could reasonably be attributed to the same measurand by independent replication of the measurement.
For a specified coverage probability p, the corresponding expanded uncertainty U (y) is obtained as a multiple
p
of the (combined) standard uncertainty u(y). This implies a Gaussian distribution of possible results of
measurement about the unique but unknown value of the measurand. For details, see 9.3.
The common understanding of an uncertainty interval [y − U (y); y + U (y)] is that of an estimate characterizing
p p
the range of values within which the true value of the measurand lies (see ISO/IEC Guide 98:1995, 2.2.4), i.e.
[4]
within which the value of the measurand is confidently believed to lie . The coverage probability p describes
the degree of belief that the true value of the measurand is covered by the interval [y − U (y); y + U (y)].
p p
Given a specified expanded uncertainty U (y) and an appropriate set of input data, the coverage probability p
p
of the uncertainty interval [y − U (y); y + U (y)] about an observed result of measurement y can be tested in a
p p
robust manner. This method does not imply a Gaussian distribution of possible results of measurement about
the unknown value of the measurand. Details are given in Annex A.
If appropriate, the combined standard uncertainty u(y) can be described as a function of the result of
measurement y, e.g. w(y) = u(y)/y = constant. An uncertainty function of this kind can be closely linked to a
method model equation y = f(x ,., x ) used to obtain results of measurement y. This concept is illustrated by
1 K
Figure 2.
ISO 20988:2007(E)
Figure 2 — Method model equation and uncertainty function
It is implicit in this International Standard that an uncertainty parameter obtained by evaluation of a specified
set of input data shall be appropriate to predict the uncertainty of future results of measurement obtained by
means of the same method of measurement under conditions represented by the input data evaluated. In
order to ensure this, it is essential to provide supporting evidence that the evaluated input data are
representative of the application of the method of measurement that will produce the results to be qualified by
an uncertainty parameter.
5.3 Correction for systematic effects
Correction for systematic effects is an integral part of a measurement as far as required by the method
documentation. In general, correction for systematic effects is achieved by comparison with one or more
reference standards, e.g. in calibration or in drift control procedures. Appropriate reference standards can be
provided by certified reference materials or by certified reference methods of measurement. By comparison
with reference materials of SI units, traceability of possible results of measurement can be established. For a
reference method being considered a primary measurement standard, comparison with other reference
standards is not necessary for the purpose of correction.
It is a general recommendation of the GUM that corrections should be applied for all recognized significant
systematic effects (see ISO/IEC Guide 98:1995, 3.2.4). In general, a correction procedure described by the
method documentation can exhibit a certain degree of imperfection, e.g. due to its statistical character and
due to the uncertainty of the reference standards used for this purpose. As an expression of the imperfection
of a correction procedure, a series of corrected results of measurement obtained by the same measuring
system can exhibit a residual bias, which is considered a random variable of expected value zero.
If a correction is applied in a measurement by means of a method model equation used to calculate the result
of measurement, the uncertainty of the applied correction is taken into account properly.
If a bias is not corrected for, it shall be taken into account as an additional source of uncertainty.
10 © ISO 2007 – All rights reserved

ISO 20988:2007(E)
In conclusion, for uncertainty estimation, it is necessary to collect series of observations that allow the user to
evaluate both the variations and the bias occurring in the intended use of the method of measurement. If
uncorrected significant bias was not taken into account, the estimation of measurement uncertainty is
incomplete.
NOTE The terms “effect”, “influence” and “source of uncertainty” are used with synonymous meaning in this
International Standard.
5.4 Provision of input data
Input data for uncertainty estimation shall be representative of all effects causing variation or bias in results of
measurement. Appropriate input data can be provided either by series of observations, or by external sources,
or by expert judgement.
From a practical point of view, uncertainty estimation can be realized either in an indirect approach or in a
direct approach.
In an indirect approach, variations and bias are, in a first step, evaluated separately for the input quantities x
i
of the method model equation y = f(x ,., x ) used to obtain results of measurement y. For this purpose,
1 K
estimates of the variances and covariances of the input quantities x can be provided by a Type A evaluation
i
of series of observations or by a Type B evaluation based on expert judgement. Finally, a weighted sum of
variances and covariances provides the wanted uncertainty estimate.
In a direct approach, the influences of the dominating effects causing variation and bias of the result of
measurement y are investigated in a pooled way by comparison with one or more reference values of the
measurand. Effects not varied in a direct approach shall be taken into account separately, e.g. by a Type B
evaluation based on expert judgement. In a direct approach, the uncertainty estimation can be much simpler
than in an indirect approach.
The focus of the GUM is on the indirect approach without excluding the direct approach.
The basic Type A evaluation method described by the GUM requires a series of unbiased observations of the
same unchanged measurand obtained by the same measuring system. This experimental design is called
simple random sampling. From a practical point of view, simple random sampling requires complete
randomization of all effects between repeated observations of the same unchanged measurand. Simple
random sampling is rarely realized under conditions of intended use of methods of air quality measurement,
mainly due to the potential presence of uncorrected bias. The considerations of the GUM concerning a Type A
evaluation are not exhaustive. There are many situations that can be treated by statistical methods different
from the basic Type A evaluation described by the GUM (see ISO/IEC Guide 98:1995, 4.2.8).
In air quality measurements, it is often more convenient and cost-effective to provide input data for uncertainty
estimation in experimental designs different from simple random sampling. In this International Standard, the
following experimental designs are considered:
A1: simple random sampling;
A2: repeated observation of a reference material by a measuring system;
A3: observation of different reference materials in a calibration procedure;
A4: repeated observation of different reference materials by identical measuring systems;
A5: parallel measurements with a reference method of measurement;
A6: paired measurements of two identical measuring systems;
A7: interlaboratory comparison of identical measuring systems;
A8: parallel measurement of identical measuring systems.
ISO 20988:2007(E)
The experimental designs of types A1 to A8 are applicable in indirect as well as in direct approaches for
uncertainty estimation of methods of air quality measurement, comprising the following:
⎯ methods of measurement corrected for systematic effects by (repeated) observation of reference
material;
⎯ methods of measurement evaluated by repeated observation of reference materials of the measurand
prior to routine application;
⎯ methods of measurement calibrated by parallel measurement with a reference method of measurement;
⎯ methods of measurement verified by parallel measurement with a reference method of measurement;
⎯ legal or other accepted reference methods of measurement validated by inter-comparison tests.
Appropriate series of observations can be provided, e.g. by one of the following procedures:
⎯ QA/QC procedure applied repeatedly to the measuring system;
⎯ verification procedure applied once to the measuring system;
⎯ evaluation procedure applied to several measuring systems of the same type;
⎯ validation procedure applied once to several measuring systems of the same type;
⎯ another performance test applied to the measuring system.
Input data for uncertainty estimation can also be provided by external sources if these data are based on
statistical evaluation of series of observations, such as accepted values and uncertainties of reference
materials, values and uncertainties of instrument constants provided by independent reports or values and
uncertainties of physical or chemical constants provided by handbooks (see ISO/IEC Guide 98:1995, 4.1.3).
NOTE The use of external data on reproducibility and trueness of a method of measurement that were obtained by
[5] [6] [7] [8] [9]
application of ISO 5725-2 , ISO 5725-3 , ISO 5725-4 and ISO 5725-5 is described in ISO/TS 21748 .
If input data cannot be provided as a series of observations or from an external source, such data can be
obtained by expert judgement and evaluated by a method of Type B.
The applicability of an uncertainty parameter for future results of measurement obtained by the evaluated
method of measurement depends on the representativeness of the input data. The degree of
representativeness achieved by a set of input data depends on the following:
⎯ effects described by the input data;
⎯ sample size of the collected series of observations;
⎯ uncertainty of the reference standards applied in this investigation.
The closer the input data describe all effects influencing the measurement, and the smaller the uncertainty of
the reference standards, the better is the predictive power of an obtained uncertainty parameter for future
results of measurement.
Of course, it is an important issue to test the predictive power of an uncertainty parameter, e.g. by another
independent evaluation of measurement uncertainty.
For estimating an expanded uncertainty U (y) on a level of confidence of 95 %, it is recommended to
0,95
provide a series of observations comprising at least 20 applications of the specified method of measurement.
Otherwise, the applicability of the obtained uncertainty parameter cannot be subjected to a meaningful test.
12 © ISO 2007 – All rights reserved

ISO 20988:2007(E)
For estimating an expanded uncertainty U (y) on a level of confidence of 66 %, it is recommended to
0,66
provide a series of observations comprising at least seven applications of the specified method of
measurement. Otherwise, the applicability of the obtained uncertainty parameter cannot be subjected to a
meaningful test.
For details on the provision of input data and the applicable mathematical evaluation methods, see 6.4 and
8.2, respectively.
6 Problem specification
6.1 Objectives
The objective of problem specification in uncertainty estimation is to identify
⎯ the measurement to be considered,
⎯ the required uncertainty parameter,
⎯ the input data to be evaluated, and
⎯ the effects not described by input data.
Figure 3 outlines the relationships between the elements of problem specification in uncertainty estimation.
Problem specification requires expert knowledge of technical aspects of the measurement considered.
Guidance provided in 6.2 to 6.4 is applicable without expertise in statistical modelling of measuring processes.

Figure 3 — Elements of problem specification in uncertainty estimation
6.2 Measurement
The measurement shall be specified (at least) in terms of
⎯ measurand,
⎯ method of measurement,
⎯ method model equation y = f(x ,., x ), if results of measurement y are calculated from observed or
1 K
otherwise known input quantities x , and
i
⎯ intended application of the method of measurement.
ISO 20988:2007(E)
The measurand shall be specified in such a way that it is expected to exhibit an unknown, but unique, value
µ at least for the time period needed to perform a single measurement.
The measurand is the physical quantity to be assigned a numerical value and a unit of measurement by
means of the specified measurement. Furthermore, the measurand shall be specified in such a way that it
could be subjected, at least in principle, to more than a single measurement. This is more important for the
provision of input data for uncertainty estimation than for routine execution of a considered method of
measurement. In air quality, the measurand can change value as a function of time and space.
The method of measurement shall be specified completely, e.g. by
⎯ the applicable procedure, e.g. the standard operating procedure (SOP),
⎯ the type of application (e.g. in routine monitoring of stationary source emissions, in routine monitoring of
workplace atmospheres, in routine monitoring of ambient air, or as a reference standard in a laboratory),
⎯ the ambient conditions of that application (e.g. variations in ambient conditions), and
⎯ the conditions of control, (e.g. for calibration or drift control).
Of
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