SIST EN ISO 6143:2006
(Main)Gas analysis - Comparison methods for determining and checking the composition of calibration gas mixtures (ISO 6143:2001)
Gas analysis - Comparison methods for determining and checking the composition of calibration gas mixtures (ISO 6143:2001)
This International Standard provides methods for
_ determining the composition of a calibration gas mixture by comparison with appropriate reference gas
mixtures,
_ calculating the uncertainty of the composition of a calibration gas mixture in relation to the known uncertainty of
the composition of the reference gas mixtures with which it was compared,
_ checking the composition attributed to a calibration gas mixture by comparison with appropriate reference gas
mixtures,
_ comparing the composition of several calibration gas mixtures, e.g. for the purpose of comparing different
methods of gas mixture preparation, or for testing consistency among gas mixtures of closely related
composition.
NOTE In principle, the method described in this document is also applicable to the analysis of (largely) unknown samples
instead of prospective calibration gas mixtures (i.e. gas mixtures which are intended for use as calibration gas mixtures). Such
applications, however, require appropriate care and consideration of additional uncertainty components, for example concerning
the effect of matrix differences between the reference gases used for calibration and the analysed sample.
Gasanalyse - Vergleichsverfahren zur Bestimmung und Überprüfung der Zusammensetzung von Kalibriergasgemischen (ISO 6143:2001)
Diese Internationale Norm legt Verfahren fest zur
- Bestimmung der Zusammensetzung eines Kalibriergasgemisches durch Vergleich mit geeigneten Referenzgasgemischen,
- Berechnung der Unsicherheit der Zusammensetzung eines Kalibriergasgemisches unter Einbeziehung der bekannten Unsicherheit der Zusammensetzung der Referenzgasgemische, mit denen es verglichen wurde,
- Überprüfung der einem Kalibriergasgemisch zugeschriebenen Zusammensetzung durch Vergleich mit geeigneten Referenzgasgemischen,
- Vergleich der Zusammensetzung mehrerer Kalibriergasgemische, z. B. zwecks Vergleich verschiedener Verfahren zur Herstellung von Gasgemischen oder zwecks Prüfung der Konsistenz zwischen Gasgemischen nahe benachbarter Zusammensetzung.
ANMERKUNG Im Prinzip ist die in diesem Dokument beschriebene Methodik auch anwendbar auf die Analyse (weitgehend) unbekannter Proben anstelle prospektiver Kalibriergasgemische (d. h. Gasgemische, die zur Verwendung als Kalibriergasgemische vorgesehen sind). Solche Anwendungen erfordern jedoch besondere Vorsichtsmaßnahmen und die Betrachtung zusätzlicher Unsicherheitskomponenten, beispielsweise für den Einfluss von Matrixunterschieden zwischen den zur Kalibrierung benutzten Referenzgasen und der Analysenprobe.
Analyse des gaz - Méthodes comparatives pour la détermination et la vérification de la composition des mélanges de gaz pour étalonnage (ISO 6143:2001)
La présente Norme internationale décrit des méthodes pour
a) déterminer la composition d'un mélange de gaz pour étalonnage par comparaison avec des mélanges
appropriés de gaz de référence,
b) calculer l'incertitude de la composition d'un mélange de gaz pour étalonnage par rapport à l'incertitude connue
de la composition des mélanges de gaz de référence avec lesquels il a été comparé,
c) contrôler la composition attribuée à un mélange de gaz pour étalonnage par rapport aux mélanges appropriés
de gaz de référence,
d) comparer la composition de plusieurs mélanges de gaz pour étalonnage, par exemple afin de comparer
différentes méthodes de préparation de mélange de gaz, ou pour déterminer l'homogénéité parmi des
mélanges de gaz de composition proche.
NOTE En principe, la méthode décrite dans ce document est également applicable à l'analyse d'échantillons (largement)
inconnus plutôt que de mélanges de gaz pour étalonnage d'intérêt potentiel (c'est-à-dire mélanges de gaz destinés à être
employés commemélanges de gaz pour étalonnage). Toutefois, ces applications requièrent une attention particulière et la prise
en compte de composantes supplémentaires de l'incertitude, concernant, par exemple, l'effet des différences de matrice entre
les gaz de référence utilisés pour l'étalonnage et l'échantillon analysé.
Analiza plinov - Primerjalne metode za določevanje in preverjanje sestave kalibrirnih plinskih zmesi (ISO 6143:2001)
General Information
Relations
Standards Content (Sample)
SLOVENSKI STANDARD
01-november-2006
$QDOL]DSOLQRY3ULPHUMDOQHPHWRGH]DGRORþHYDQMHLQSUHYHUMDQMHVHVWDYH
NDOLEULUQLKSOLQVNLK]PHVL ,62
Gas analysis - Comparison methods for determining and checking the composition of
calibration gas mixtures (ISO 6143:2001)
Gasanalyse - Vergleichsverfahren zur Bestimmung und Überprüfung der
Zusammensetzung von Kalibriergasgemischen (ISO 6143:2001)
Analyse des gaz - Méthodes comparatives pour la détermination et la vérification de la
composition des mélanges de gaz pour étalonnage (ISO 6143:2001)
Ta slovenski standard je istoveten z: EN ISO 6143:2006
ICS:
71.040.40 Kemijska analiza Chemical analysis
2003-01.Slovenski inštitut za standardizacijo. Razmnoževanje celote ali delov tega standarda ni dovoljeno.
EUROPEAN STANDARD
EN ISO 6143
NORME EUROPÉENNE
EUROPÄISCHE NORM
August 2006
ICS 71.040.40
English Version
Gas analysis - Comparison methods for determining and
checking the composition of calibration gas mixtures (ISO
6143:2001)
Analyse des gaz - Méthodes comparatives pour la Gasanalyse - Vergleichsverfahren zur Bestimmung und
détermination et la vérification de la composition des Überprüfung der Zusammensetzung von
mélanges de gaz pour étalonnage (ISO 6143:2001) Kalibriergasgemischen (ISO 6143:2001)
This European Standard was approved by CEN on 21 July 2006.
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 Central Secretariat 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 Central Secretariat has the same status as the official
versions.
CEN members are the national standards bodies of Austria, Belgium, 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.
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Management Centre: rue de Stassart, 36 B-1050 Brussels
© 2006 CEN All rights of exploitation in any form and by any means reserved Ref. No. EN ISO 6143:2006: E
worldwide for CEN national Members.
Foreword
The text of ISO 6143:2001 has been prepared by Technical Committee ISO/TC 158 "Analysis
of gases” of the International Organization for Standardization (ISO) and has been taken over
as EN ISO 6143:2006 by Technical Committee CEN/SS N21 "Gaseous fuels and combustible
gas", the secretariat of which is held by CMC.
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 February 2007, and conflicting national
standards shall be withdrawn at the latest by February 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,
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 6143:2001 has been approved by CEN as EN ISO 6143:2006 without any
modifications.
INTERNATIONAL ISO
STANDARD 6143
Second edition
2001-05-01
Gas analysis — Comparison methods for
determining and checking the composition
of calibration gas mixtures
Analyse des gaz — Méthodes comparatives pour la détermination et la
vérification de la composition des mélanges de gaz pour étalonnage
Reference number
ISO 6143:2001(E)
©
ISO 2001
ISO 6143:2001(E)
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ii © ISO 2001 – All rights reserved
ISO 6143:2001(E)
Contents Page
Foreword.iv
Introduction.v
1 Scope .1
2 Terms and definitions .1
3 Symbols and abbreviated terms .3
4 Principle.4
5 General procedure.6
6 Special procedures.14
7 Test report .14
Annex A (normative) Procedures for data evaluation.16
Annex B (informative) Examples .23
Annex C (informative) Computer implementation of recommended methods .31
Bibliography.33
ISO 6143:2001(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 3.
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 International Standard may be the subject of
patent rights. ISO shall not be held responsible for identifying any or all such patent rights.
International Standard ISO 6143 was prepared by Technical Committee ISO/TC 158, Analysis of gases,tocancel
and replace the first edition (ISO 6143:1981), of which the methods for the design and evaluation of calibrations of
analytical systems have been updated and a method for estimating the uncertainty of the composition of calibration
gas mixtures has been added. It also cancels and replaces ISO 6711:1981, of which entirely new methods for
checking the composition of calibration gases have been specified, thus replacing the method which is no longer in
use.
Annex A forms a normative part of ISO 6143. Annexes B and C are for information only.
iv © ISO 2001 – All rights reserved
ISO 6143:2001(E)
Introduction
In gas analysis, calibration of analytical systems, as specified in the first edition of ISO 6143, has largely been
confined to the determination of a straight line through the origin, or of a straight-line segment, using only the
minimum number of calibration standards (one for a straight line through the origin, two for a line segment). The
approach adopted in the revision, relating to calibration as well as to uncertainty evaluation, goes far beyond this
simple scheme by
� including non-linear response curves and/or functions,
� replacing interpolation by regression,
� taking into account the uncertainty on the calibration standards,
� including validation of calculated response curves and/or functions,
� calculating uncertainties by uncertainty propagation.
As a consequence of adopting non-linear response models, advanced regression techniques (errors in both
variables) and uncertainty propagation, the main calculation procedures can only be performed on a computer,
using a specific program. Such a program is available (see annex C). As an alternative, sufficient information is
given in the document to enable the user to develop a program on his own.
INTERNATIONAL STANDARD ISO 6143:2001(E)
Gas analysis — Comparison methods for determining and
checking the composition of calibration gas mixtures
1 Scope
This International Standard provides methods for
� determining the composition of a calibration gas mixture by comparison with appropriate reference gas
mixtures,
� calculating the uncertainty of the composition of a calibration gas mixture in relation to the known uncertainty of
the composition of the reference gas mixtures with which it was compared,
� checking the composition attributed to a calibration gas mixture by comparison with appropriate reference gas
mixtures,
� comparing the composition of several calibration gas mixtures, e.g. for the purpose of comparing different
methods of gas mixture preparation, or for testing consistency among gas mixtures of closely related
composition.
NOTE In principle, the method described in this document is also applicable to the analysis of (largely) unknown samples
instead of prospective calibration gas mixtures (i.e. gas mixtures which are intended for use as calibration gas mixtures). Such
applications, however, require appropriate care and consideration of additional uncertainty components, for example concerning
the effect of matrix differences between the reference gases used for calibration and the analysed sample.
2 Terms and definitions
For the purposes of this International Standard, the following terms and definitions apply.
2.1
composition
characteristic of a gas mixture given by the kind and content of each specified mixture component (analyte) and the
composition of the complementary gas (matrix)
NOTE In this International Standard, the analyte content is specified as a mole fraction, exclusively. Mole fractions have
the advantage of being perfectly independent of the pressure and the temperature of the gas mixture. Therefore their use is
recommended. However, for specific measuring systems, other composition measures (e.g. mass concentrations) may be more
appropriate. Their use then requires due care concerning the dependence on pressure and temperature.
2.2
comparison method
method for determining the content of a specified gas mixture component (analyte) by measuring an instrumental
response
NOTE Comparison of measuring systems requires calibration, in which the relationship between response and analyte
content is established. This is achieved by measuring the response to known values of analyte content provided by reference
gas mixtures.
ISO 6143:2001(E)
2.3
calibration
set of operations that establish, under specified conditions, the relationship between values of quantities indicated
by a measuring instrument or measuring system, or values represented by a material measure or reference
material, and the corresponding values realized by standards
[VIM]
2.4
response function
functional relationship between instrumental response and analyte content
NOTE 1 The response function can be expressed in two different ways as a calibration function or an analysis function,
depending on the choice of the dependent and the independent variable.
NOTE 2 The response function is conceptual and cannot be determined exactly. It is determined approximately through
calibration.
2.4.1
calibration function
instrumental response expressed as a function of analyte content
2.4.2
analysis function
analyte content expressed as a function of instrumental response
2.5
uncertainty of measurement
parameter, associated with the result of a measurement, that characterizes the dispersion of the values that can
reasonably be attributed to the measurand
[GUM]
NOTE In keeping with the GUM, in this International Standard the uncertainty of the composition of a gas mixture is
expressed as a standard uncertainty, i.e. as a single standard deviation.
2.6
traceability
property of the result of a measurement or the value attributed to a standard whereby it can be related to stated
references, usually national or international standards, through an unbroken chain of comparisons all having stated
uncertainties
[VIM]
2.7
measurement standard
material measure, measuring instrument, reference material, or measuring system, intended to define, realize,
conserve, or reproduce a unit or one or more values of a quantity to serve as a reference
[VIM]
2.8
reference standard
standard, generally having the highest metrological quality available at a given location or in a given organization,
from which measurements made there are derived
[VIM]
2 © ISO 2001 – All rights reserved
ISO 6143:2001(E)
2.9
working standard
standard that is used routinely to calibrate or check material measures, measuring instruments or reference
materials
[VIM]
NOTE A working standard is usually calibrated against a reference standard.
2.10
reference material
material or substance one or more of whose property values are sufficiently homogeneous and well established to
be used for the calibration of an apparatus, the assessment of a measuring method, or for assigning values to
materials
[ISO Guide 30]
2.11
calibration gas mixture
gas mixture whose composition is sufficiently well established and stable to be used as a working standard of
composition
2.12
reference gas mixture
gas mixture whose composition is sufficiently well established and stable to be used as a reference standard of
composition
3 Symbols and abbreviated terms
a parameters of the calibration function F ( j = 0, 1, ., N)
j
b parameters of the analysis function G ( j = 0, 1, ., N)
j
D sensitivity matrix
F calibration function, y=F(x), for the specified analyte
G analysis function, x=G(y), for the specified analyte
k coverage factor
L limit of detection
M (sample of) calibration gas mixture
cal
M (sample of) reference gas mixture
ref
Q transform matrix
S sum of weighted squared deviations
S residual sum of weighted squared deviations
res
t Student's t-factor
U(q) expanded uncertainty of an estimated quantity q, U(q) =ku(q)
ISO 6143:2001(E)
u(q) uncertainty of an estimated quantity q, expressed as a standard deviation (standard uncertainty)
u(p,q) covariance of two estimated quantities p and q
u (q) variance of an estimated quantity q
V variance/covariance matrix
W half-width of a confidence range
x mole fraction of the specified analyte
(x , y ) calibration points (i = 1, 2, ., n)
i i
xyˆ , ˆ adjusted calibration points (i = 1, 2, ., n)
� �
ii
y instrumental response of the specified analyte
Z normal distribution percentage point
� relative analytical accuracy
� dilution factor
� measure of goodness-of-fit
4Principle
The composition of a gas mixture is determined by separate determination of the mole fraction of every specified
analyte. Therefore the procedure for determining the mole fraction of only one specified analyte is described.
Possible interferences of other components on the measurement of the analyte under consideration should be
considered by the user and taken into account. However, this subject is not addressed in this International
Standard.
This International Standard is also applicable if other composition quantities than mole fraction are used. However
it is recommended that the final result be expressed as a mole fraction.
The general procedure for determining the mole fraction x of a specified analyte in a sample of a calibration gas
mixture, or in a series of such samples, is performed in a sequence of steps summarized below.
a) Specify the analytical range of interest, i.e. the range of the mole fractions x to be determined, and the
acceptable uncertainty level (see 5.1, step A).
b) Specify the analytical method and the measuring system to be used (see 5.1, step B).
c) Examine the available information on the relevant response characteristics of the measuring system (e.g.
linearity and sensitivity), paying attention to possible interferences. If necessary, carry out a performance
evaluation to check the suitability of the system. Specify the type of mathematical function to be considered for
description of the response in the specified range (see 5.1, step C).
d) Design a calibration experiment in which the relevant experimental parameters are specified. Examples are:
� calibration range (to include the analytical range),
� composition, including uncertainty, of the reference gas mixtures for calibration,
4 © ISO 2001 – All rights reserved
ISO 6143:2001(E)
� parameters of the analytical method,
� conditions of measurement, if relevant,
� number and sequence of calibration measurements (see 5.1, steps D, E, F).
e) Perform the calibration experiment, i.e. measure the response, y, for samples of the chosen reference gas
mixtures, and estimate the uncertainty u(y) of these response values (see 5.1, step G).
f) Calculate the analysis function, x=G(y), from the calibration data, using regression analysis (see 5.1, step H).
g) Examine whether the calculated analysis function is consistent with the calibration data within the relevant
uncertainties. If the result is acceptable, proceed to h). If not, revise the calibration design (see 5.2.1).
h) Determine the uncertainty level of the prospective results based on the analysis function for the relevant
ranges of responses and analyte contents. If the result is acceptable, proceed to i). If not, revise the calibration
design(see5.2.2).
i) Prior to analysing a prospective calibration gas sample, test for instrument drift to ensure that the analysis
function is still valid for the specified analytical task (see 5.2.3). If the result is acceptable, proceed to j). If not,
recalibrate the measuring system.
If the prospective calibration gas contains other components than the reference gas mixtures used for
calibration, validate the applicability of the analysis function using at least one additional reference gas mixture
of appropriate composition (see 5.2.4).
NOTE It is not necessary to test for drift in conjunction with every analysis of a calibration gas sample. The frequency
should be based on experience concerning the stability of the measuring system.
Similarly, the composition of additional reference gas mixtures used for validation should be based on experience concerning
the cross-sensitivities of the measuring system.
j) Determine the composition of the prospective calibration gas as follows:
� measure the response y,
� determine the uncertainty u(y) of the response y,
� calculate the mole fraction x=G(y) using the analysis function determined in f),
� calculate the uncertainty u(x) of the mole fraction x using the results obtained in h) (see 5.3).
k) State the result of the entire analysis (see clause 7).
In addition to determining the composition of a (prospective) calibration gas mixture, the general procedure may be
used to check a pre-established composition. To this end, the mixture under consideration is analysed using the
procedure outlined above, and the composition obtained is compared with the pre-established composition.
Clause 6 specifies a procedure where, for each analyte concerned, the difference between the content obtained by
the confirmation analysis and the pre-established content is examined against the uncertainty on this difference for
significant departure from zero.
The general procedure may also be used to examine the mutual consistency of pre-established composition data
for a series of calibration gas mixtures or reference gas mixtures. Clause 6 specifies a procedure where, for each
analyte concerned, the measured responses and the pre-established analyte contents of all calibration gases
under consideration are tested for compatibility with the known response behaviour of the measuring system.
ISO 6143:2001(E)
5 General procedure
5.1 Determination of the analysis function
For a specified analyte and a specified measuring system, including relevant operating conditions, the calibration
function, y=F(x), is a mathematical function approximately expressing measured responses y ,y , ., y in relation
1 2 n
to known analyte contents x ,x , ., x of appropriate reference gas mixtures. Inversely, the analysis function,
1 2 n
x=G(y), approximately expresses known analyte contents x ,x , ., x in relation to corresponding measured
1 2 n
responses y ,y , ., y . The analysis function is required for calculating unknown analyte contents x of calibration
1 2 n
gas mixtures from measured responses y.
The analysis function can be determined either directly, or indirectly by determination of the calibration function and
subsequent inversion. It is recommended to make a direct determination of the analysis function. Therefore only
this procedure is specified in the body of this International Standard. In particular applications, however, indirect
determination using the calibration function may be preferable. For such applications, a brief description of this
procedure is given in A.5.
The following description, in terms of a series of steps, of the calibration experiment and its evaluation resumes and
elaborates the principles outlined in clause 4.
a) Step A: Specify the analytical range, i.e. the range of the analyte contents x in the calibration gas mixtures
considered, and the acceptable uncertainty level of analytical results.
b) Step B: Specify the measuring system to be used and its operating conditions, e.g. sample pressure, sample
temperature and sample flow.
c) Step C: Specify the type of mathematical function to be considered for the analysis function, x=G(y). Select
the function from the following:
� linear functions x= + y
bb
� second-order polynomials x= + y+ y
bb b
01 2
� third-order polynomials x= + y+yy+
bb b b
01 2 3
b
� power functions x= + y
bb
b y
� exponential functions x= +
bb e
The parameters b of the analysis function are determined by regression analysis using the values from the
j
calibration data set, i.e. the response data collected in the calibration experiment and the composition data
taken from the specification of the reference gases used for calibration.
The type of mathematical function is chosen according to the response characteristics of the measuring
system, which may be linear or non-linear. Although the method described in this International Standard is, in
principle, completely general, it is recommended to restrict its use to linear response curves and to non-linear
response curves which only moderately deviate from a straight line.
NOTE In this International Standard, only a limited number of types of functions are explicitly considered. However, the
procedures equally apply to other types of functions, e.g. the algebraic inverses of the types of functions specified above,
as far as feasible.
d) Step D: Specify the number n of calibration points (x,y ) required, depending on the type of mathematical
i i
function to be used for the analysis function.
6 © ISO 2001 – All rights reserved
ISO 6143:2001(E)
The minimum number of calibration points recommended for the different types of functions considered is:
� 3 for a linear function,
� 5 for a second-order polynomial,
� 7 for a third-order polynomial,
� 5 for a power function,
� 5 for an exponential function.
The recommended number of calibration points is greater than the number of indeterminate parameters of the
analysis function because it is also necessary to validate the function chosen. If calibration experiments were
only based on the minimum number of calibration points, it would be necessary to validate the analysis
function using additional reference gas mixtures. It is better, instead, to incorporate these additional “reference
points” into the set of calibration points so as to reduce the calibration uncertainty of the estimated parameters.
For the majority of comparison methods, an appropriate “zero gas” will provide a valid calibration point.
e) Step E: Select reference gas mixtures M ,M , ., M such that their analyte contents x ,x , ., x span
ref,1 ref,2 ref,n 1 2 n
an appropriate calibration range, i.e. approximately equally spaced, with one value below the lower limit and
one value above the upper limit of the analytical range.
The analyte contents shall be determined independently to the greatest possible extent. Dilution series may
only be used under the conditions specified in 5.4.2.
If interferences between mixture components cannot be safely excluded, it may be necessary to use reference
gases of similar composition to those of the calibration gases considered, for the critical components. In any
case, it is recommended to use reference gas mixtures with the same complementary gas.
Calibration designs using equally spaced values for analyte contents are not the optimum choice for cases of
strongly non-linear response. They are, however, well suited for linear and moderately non-linear responses,
as considered in this International Standard [see c), step C].
f) Step F: Establish the standard uncertainties u(x ),u(x ), ., u(x ) of the analyte contents x ,x , ., x .
1 2 n 1 2 n
For reference gas mixtures prepared or analysed by recently standardized methods, the standard uncertainty
for the content of each specified component should be contained in the certificate of mixture composition.
For reference gas mixtures with other specifications of uncertainty, e.g. in terms of tolerance limits, these data
have to be converted into standard uncertainties. If x and x are the lower and upper tolerance limit of the
min max
analyte content, and if all the values within this interval are equally likely as potentially true values, the data
recommended for use as the analyte content and its standard uncertainty are the mean and the standard
deviation of a rectangular distribution between the tolerance limits as follows:
+ �
xx x x
max min max min
x= , u()x =
The conversion of other uncertainty specifications is treated in A.1.
If the complementary gas is taken as a reference gas for zero analyte content, x = 0, and x =L .Here L
min max x x
denotes the limit of detection (see reference [6]) of the analytical method used for determining the potential
impurity, i.e. the maximum content of the analyte in the complementary gas that the analytical method fails to
detect.
g) Step G: Determine the responses y ,y , ., y to the analyte contents x ,x , ., x , together with their standard
1 2 n 1 2 n
uncertainties u(y ),u(y ), ., u(y ).
1 2 n
ISO 6143:2001(E)
So as to establish the response data y and u(y ) for a given x , it is recommended to use the mean value of ten
i i i
individual responses, y ,y , ., y , measured independently under appropriate reproducibility conditions and
i1 i2 i10
to take the standard deviation of this mean value.
yy�
ii�j
j�1
uy()��(y y)
ii�ji
j�1
The purpose in requiring ten independent measurements for each reference gas is to ensure that the response
data, y and u(y ), are determined with acceptable precision. If the analytical system is under statistical control,
i i
the mean value y may be determined from a smaller number of independent measurements and the standard
i
uncertainty u(y ) may be calculated from the known method standard deviation.
i
The requirement of appropriate reproducibility conditions means that the variability of the conditions of
measurement in the calibration experiment should be about the same as those in the applications.
If the complementary gas is taken as a reference gas for zero analyte content and if the response to zero
content is known to be zero response (and positive to non-zero contents), the values of y and u(y) can be
calculated from the response limit of detection, L ,as follows:
y
LL
yy
y= , u()y =
Here the response limit of detection is the upper limit of fluctuations at zero response.
To secure the independence of the individual responses, and to randomize sample interaction effects, e.g.
memory effects, it is recommended to measure the responses for the reference gas mixtures M ,M ,.,
ref,1 ref,2
M in an irregular sequence.
ref,n
Depending on the number of repeated measurements, the “uncertainty of the uncertainty” of a mean value (i.e.
the relative standard deviation of the standard deviation of a mean value) can be surprisingly large, for
example for ten measurements, it is 24 % (see reference [2] of the Bibliography). Therefore a smaller number
of repeated measurements should not be used when determining the standard deviation of a mean value.
h) Step H: Calculate the parameters b of the mathematical function to be used for the analysis function.
j
The set of input data for this calculation consists of:
� the analyte contents (expressed as mole fractions), x , x , ., x ,
1 2 n
� the standard uncertainties of the analyte contents, u(x ), u(x ), ., u(x ),
1 2 n
� the responses to the analyte contents, y , y , ., y ,
1 2 n
� the standard uncertainties of the responses, u(y ), u(y ), ., u(y ).
1 2 n
These parameters are calculated by regression analysis, according to the method described in A.2.
In contrast with ordinary least squares regression, the regression technique used in this International Standard
equally takes into account the uncertainties of the composition of the reference gas mixtures and the
uncertainties of the measured responses.
8 © ISO 2001 – All rights reserved
ISO 6143:2001(E)
5.2 Validation of the analysis function
5.2.1 Purpose
Before using the analysis function determined according to 5.1, it is necessary to perform validations. These
validations serve a number of different purposes:
� to validate the response model,
� to examine compliance with uncertainty requirements,
� to control drift of the measuring system,
� to validate the applicability to mismatching calibration gases.
5.2.2 Validation of the response model
The response model shall be validated by testing whether the selected type of analysis function is compatible with
the calibration data set:
� the analyte contents (mole fractions), x , x , ., x ,
1 2 n
� the standard uncertainties of the analyte contents, u(x ), u(x ), ., u(x ),
1 2 n
� the responses to the analyte contents, y , y , ., y ,
1 2 n
� the standard uncertainties of the responses, u(y ), u(y ), . u(y ).
1 2 n
To assess the overall fit of a calculated response curve to the calibration data, the residual sum of weighted
squared deviations, S , is compared with the relevant degrees of freedom (equal to the number of calibration
res
points less the number of response curve parameters), as given in A.2. For the purpose of this International
Standard, however, satisfactory fit is required for each individual calibration point by using the following test
procedure. For each experimental calibration point (x,y ), an adjusted calibration point xyˆ , ˆ is calculated, as a
� �
i i
ii
by-product of the regression analysis used to determine the analysis function (see A.2). The coordinates xˆ and yˆ
i i
of the adjusted calibration point are estimates of the true analyte content and of the true response, respectively, for
the reference gas M (i = 1, 2, ., n). By construction the calculated response curve passes through the adjusted
ref,i
calibration points. The selected response model is considered compatible with the calibration data set if the
following conditions are fulfilled for every calibration point (i=1,2,…, n):
xxˆ � u 2u�x � and yyˆ � u 2u�y �
ii i ii i
NOTE 1 In almost all cases, this condition is equivalent to requiring that the calculated response curve pass through every
experimental “calibration rectangle” [x � 2u(x ),y � 2u(y )], based on the expanded uncertainty U= ku with the standard
i i i i
coverage factor k=2.
If the model validation test fails, one possibility is to examine other response models until a model is found that is
compatible with the calibration data set. Another possibility is to examine, and possibly revise, the calibration data.
To effectively test the compatibility of a prospective analysis function, calculate the measure of goodness-of-fit, �,
defined as the maximum value of the weighted differences, � ux� � and yyˆ � u�y � , between the
xxˆ
ii i ii i
coordinates of measured and adjusted calibration points (i=1, 2, ., n). A function is admissible if�u 2.
If several functions are considered and found to be admissible, take the final choice as follows:
a) If a physical model of the response behaviour of the analytical system is available, and if the function
corresponding to this model is admissible, use this function.
ISO 6143:2001(E)
b) If no such physical model is available, and if several functions give about the same fit, i.e. similar values of the
goodness-of-fit parameter�, use the simplest function, i.e. the one with the lowest number of parameters.
c) If no physical model is available and admissible functions differ considerably with respect to their fit, use the
function which gives the best fit, i.e. the lowest value of�.
NOTE 2 The individual weighted differences can be used as a diagnostic tool for identifying potential outliers among the
calibration data.
In addition to the procedures described above, every calculated response curve has to be inspected visually. This
visual inspection is necessary to reveal “nonsense correlations” which can occur without being detected by local
examination of the curve fit to the calibration points. Such nonsense correlations are liable to occur in the case of
polynomial response functions, which can exhibit non-monotonic behaviour with excellent local fit. Another case of
nonsense correlations can occur if, by mistake, one of the calibration data uncertainties is very small. Then this
calibration point is given erroneously a very high weight. Consequently, the response curve is forced through this
point with little importance given to the other calibration points.
5.2.3 Examining compliance with uncertainty requirements
For the specified analytical range, an upper bound is determined for the uncertainty of the prospective results
based on the analysis function. This upper bound is compared with the acceptable uncertainty.
For determining this upper bound, the calculation described in 5.3 is performed, using simulated extreme response
data y , u(y ) and y , u(y ), respectively. The data y and u(y ) are given by the response of the reference gas
lo lo hi hi lo lo
with the lowest analyte content, and by the standard uncertainty of that response, as determined in the calibration
experiment. Analogously, y and u(y ) are given by the calibration data determined on the reference gas with the
hi hi
highest analyte content. From these response data, the values of u(x ) and u(x ) can be calculated. The larger of
lo hi
these two values, max[u(x ),u(x )], constitutes an upper bound of the uncertainty of the prospective results based
lo hi
on the analysis function.
NOTE The calculated uncertainty takes its highest values at the limits of the calibration range, as given by x and x .This
lo hi
calibration range includes the specified analytical range.
5.2.4 Drift control of the measuring system
If significant changes of the response of the analytical system cannot be safely excluded, it is necessary to perform
a drift test. A simple one-point validation procedure is described below, aimed at providing the minimum required
protection against systematic errors due to drift. If more information on the performance of the analytical system is
available, e.g. due to extensive monitoring, drift tests of better performance should be used.
Drift control means to test whether a previously determined analysis function is still valid or whether the response of
the analytical system has changed significantly.
Perform drift control in a problem-specific mode, i.e. tailored for the prospective calibration gas mixture M under
cal
investigation, by measuring the response of one of those two reference gas mixtures among M ,M ,.,M
ref,1 ref,2 ref,n
which bracket the analyte content of the calibration gas mixture M .
cal
Before and after measuring the response of the calibration gas mixture M , make ten independent measurements
cal
of the selected reference gas mixture, M . These data are used to derive mean responses, y (before) and
ref,i i
y (after), which are to be compared with the mean response, y (calib), obtained on M at the time of calibration,
i i ref,i
and with each other. The drift test is passed if none of the three differences, �y (before) � y (calib)�,
i i
�y (calib) � y (after)� and �y (before) � y (after)� exceeds the critical value for these differences. This critical value is
i i i i
given by 2,83u[y (calib)], where u[y (calib)] is the standard deviation of the mean response obtained at calibration
i i
(see 5.1, step G). Should any of these differences be greater than the critical value, then the drift control test has
failed, and the analytical system has to be recalibrated.
NOTE The drift control test assumes that for each of the series of measurements performed on the drift control mixture
M before and after measuring the calibration gas mixture M , the standard deviation is about the same as that for the
ref,i cal
series of calibration measurements performed on M . Based on this assumption and a significance level of 95 %, the critical
ref,i
10 © ISO 2001 – All rights reserved
ISO 6143:2001(E)
value for any of the three differences is given by 22 times the standard deviation of the mean response obtained in
calibration.
If it is impractical to make ten measurements (n = 10) on the drift control gas before and after measuring a
prospective calibration gas, fewer measurements (n � 10) may be made but will result in a lower drift-detection
capability. If fewer measurements are made, the critical values for the differences have to be changed accordingly.
The conditions for passing the drift control test then are given by
�y (before) � y (calib)�u21� � u[y (calib)]
i i i
n
�y (calib) � y (after)�u21� � u[y (calib)]
i i i
n
�y (before) � y (after)�u 2 � u[y (calib)]
i i i
n
The period bracketed by the two sets of measurements on the drift control gas may be extended to include
measurements of several prospective calibration gases of similar composition, at the risk of having to discard a
larger set of measurements.
If the drift control test fails, recalibrate the analytical system.
5.2.5 Validation of applicability to mismatching calibration gases
If the calibration gas mixture under investigation contains other components than the reference gas mixtures used
for determining the analysis function, it is necessary to validate the applicability of the analysis function. This
validation requires at least one additional reference gas mixture whose composition is sufficiently similar to that of
the prospective calibration gas mixture so as to ensure that the uncertainty due to matrix mismatch is kept under
adequate control.
Perform the validation as follows. First, identify the critical analytes, whose determination is likely to be sensitive to
matrix mismatch. Second, for each critical analyte, measure the response for the reference gas mixture. Thirdly,
using the response data, calculate the analyte content, x , and its standard uncertainty, u(x ), using the analysis
obs obs
function. Finally, compare the observed value, x , with the established reference value, x , of the analyte content
obs ref
of the reference gas mixture, taking into account the uncertainty of these values. If the following condition holds
true for each critical analyte:
x��x u 2 ux ux
� � � �
obs ref obs ref
the analysis function can be used for determining the composition of the mismatching gas mixture.
5.3 Determination of the composition of a calibration gas mixture
Determination of the composition of a (prospective) calibration gas mixture, M , consists in determining the
cal
content (mole fraction), x, and its standard uncertainty, u(x), of each specified analyte. For any specified analyte,
these data are determined in a series of three steps as follows.
a) Step I: Determine the response y for the analyte content together with its standard uncertainty u(y). For
establishing these data, it is recommended to use the mean value of ten individual responses, y , y , . , y ,
1 2 10
measured independently, and the standard deviation of this mean value.
yy�
� j
j�1
----
...
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