SIST EN ISO 6143:2026
(Main)Gas analysis - Comparison methods for determining and checking the composition of calibration gas mixtures (ISO 6143:2025)
Gas analysis - Comparison methods for determining and checking the composition of calibration gas mixtures (ISO 6143:2025)
This document specifies 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;
— consistency testing and outlier search in suites of calibration gas mixtures of closely related composition.
NOTE 1 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, need 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.
NOTE 2 Comparison methods based on one- and two-point calibration are described in ISO 12963.
Gasanalyse - Vergleichsverfahren zur Bestimmung und Überprüfung der Zusammensetzung von Kalibriergasgemischen (ISO 6143:2025)
Dieses Dokument 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;
Prüfung der Konsistenz und Suche nach Ausreißern bei Kalibriergasgemischen nahe benachbarter Zusammensetzung.
ANMERKUNG 1 Im Prinzip ist das in diesem Dokument beschriebene Verfahren auch anwendbar auf die Analyse (weitgehend) unbekannter Proben anstelle prospektiver Kalibriergasgemische (d. h. Gasgemische, die zur Verwendung als Kalibriergasgemische vorgesehen sind). Solche Anwendungen bedürfen jedoch besonderer Vorsichtsmaßnahmen und der Betrachtung zusätzlicher Unsicherheitskomponenten, beispielsweise im Hinblick auf den Einfluss von Matrixunterschieden zwischen den zur Kalibrierung benutzten Referenzgasen und der Analysenprobe.
ANMERKUNG 2 Vergleichsverfahren auf der Grundlage von Ein- und Zwei-Punkt-Kalibrierung sind in ISO 12963 beschrieben.
Analyse des gaz - Méthodes de comparaison pour la détermination et la vérification de la composition des mélanges de gaz d’étalonnage (ISO 6143:2025)
Le présent document spécifie des méthodes pour:
— déterminer la composition d’un mélange de gaz d’étalonnage par comparaison avec des mélanges appropriés de gaz de référence;
— calculer l’incertitude de la composition d’un mélange de gaz d’étalonnage par rapport à l’incertitude connue de la composition des mélanges de gaz de référence avec lesquels il a été comparé;
— vérifier la composition établie pour un mélange de gaz d’étalonnage par comparaison avec des mélanges appropriés de gaz de référence;
— procéder à des tests de cohérence et à la recherche de valeurs aberrantes dans des ensembles de mélanges de gaz d’étalonnage dont la composition est très proche.
NOTE 1 En principe, la méthode décrite dans le présent document est également applicable à l’analyse d’échantillons (en grande partie) inconnus à la place de potentiels mélanges de gaz d’étalonnage (c’est-à-dire des mélanges de gaz destinés à être employés comme mélanges de gaz d’étalonnage). Toutefois, ces applications nécessitent une attention particulière et la prise en compte de composantes supplémentaires de l’incertitude, concernant notamment l’effet des différences de matrice entre les gaz de référence utilisés pour l’étalonnage et l’échantillon analysé.
NOTE 2 Les méthodes de comparaison fondées sur l’étalonnage en un point et en deux points sont décrites dans l’ISO 12963.
Analiza plinov - Primerjalne metode za določanje in preverjanje sestave kalibrirnih plinskih zmesi (ISO 6143:2025)
General Information
Relations
Standards Content (Sample)
SLOVENSKI STANDARD
01-januar-2026
Nadomešča:
SIST EN ISO 6143:2006
Analiza plinov - Primerjalne metode za določanje in preverjanje sestave kalibrirnih
plinskih zmesi (ISO 6143:2025)
Gas analysis - Comparison methods for determining and checking the composition of
calibration gas mixtures (ISO 6143:2025)
Gasanalyse - Vergleichsverfahren zur Bestimmung und Überprüfung der
Zusammensetzung von Kalibriergasgemischen (ISO 6143:2025)
Analyse des gaz - Méthodes de comparaison pour la détermination et la vérification de la
composition des mélanges de gaz d’étalonnage (ISO 6143:2025)
Ta slovenski standard je istoveten z: EN ISO 6143:2025
ICS:
71.040.40 Kemijska analiza Chemical analysis
2003-01.Slovenski inštitut za standardizacijo. Razmnoževanje celote ali delov tega standarda ni dovoljeno.
EN ISO 6143
EUROPEAN STANDARD
NORME EUROPÉENNE
June 2025
EUROPÄISCHE NORM
ICS 71.040.40 Supersedes EN ISO 6143:2006
English Version
Gas analysis - Comparison methods for determining and
checking the composition of calibration gas mixtures (ISO
6143:2025)
Analyse des gaz - Méthodes de comparaison pour la Gasanalyse - Vergleichsverfahren zur Bestimmung und
détermination et la vérification de la composition des Überprüfung der Zusammensetzung von
mélanges de gaz d'étalonnage (ISO 6143:2025) Kalibriergasgemischen (ISO 6143:2025)
This European Standard was approved by CEN on 3 June 2025.
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-CENELEC 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-CENELEC Management
Centre has the same status as the official versions.
CEN members are the national standards bodies of Austria, Belgium, Bulgaria, Croatia, Cyprus, Czech Republic, Denmark, Estonia,
Finland, France, Germany, Greece, Hungary, Iceland, Ireland, Italy, Latvia, Lithuania, Luxembourg, Malta, Netherlands, Norway,
Poland, Portugal, Republic of North Macedonia, Romania, Serbia, Slovakia, Slovenia, Spain, Sweden, Switzerland, Türkiye and
United Kingdom.
EUROPEAN COMMITTEE FOR STANDARDIZATION
COMITÉ EUROPÉEN DE NORMALISATION
EUROPÄISCHES KOMITEE FÜR NORMUNG
CEN-CENELEC Management Centre: Rue de la Science 23, B-1040 Brussels
© 2025 CEN All rights of exploitation in any form and by any means reserved Ref. No. EN ISO 6143:2025 E
worldwide for CEN national Members.
Contents Page
European foreword . 3
European foreword
This document (EN ISO 6143:2025) has been prepared by Technical Committee ISO/TC 158 "Analysis
of gases" in collaboration with Technical Committee CEN/TC 238 “Test gases, test pressures, appliance
categories and gas appliance types” the secretariat of which is held by AFNOR.
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 2025, and conflicting national standards
shall be withdrawn at the latest by December 2025.
Attention is drawn to the possibility that some of the elements of this document may be the subject of
patent rights. CEN shall not be held responsible for identifying any or all such patent rights.
This document supersedes EN ISO 6143:2006.
Any feedback and questions on this document should be directed to the users’ national standards
body/national committee. A complete listing of these bodies can be found on the CEN website.
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,
Croatia, Cyprus, Czech Republic, Denmark, Estonia, Finland, France, Germany, Greece, Hungary, Iceland,
Ireland, Italy, Latvia, Lithuania, Luxembourg, Malta, Netherlands, Norway, Poland, Portugal, Republic of
North Macedonia, Romania, Serbia, Slovakia, Slovenia, Spain, Sweden, Switzerland, Türkiye and the
United Kingdom.
Endorsement notice
The text of ISO 6143:2025 has been approved by CEN as EN ISO 6143:2025 without any modification.
International
Standard
ISO 6143
Third edition
Gas analysis — Comparison
2025-06
methods for determining and
checking the composition of
calibration gas mixtures
Analyse des gaz — Méthodes de comparaison pour la
détermination et la vérification de la composition des mélanges
de gaz d’étalonnage
Reference number
ISO 6143:2025(en) © ISO 2025
ISO 6143:2025(en)
© ISO 2025
All rights reserved. Unless otherwise specified, or required in the context of its implementation, no part of this publication may
be reproduced or utilized otherwise in any form or by any means, electronic or mechanical, including photocopying, or posting on
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Published in Switzerland
ii
ISO 6143:2025(en)
Contents Page
Foreword .iv
Introduction .vi
1 Scope . 1
2 Normative references . 1
3 Terms and definitions . 1
4 Symbols and abbreviated terms. 3
5 Principle . 4
6 General procedure . 5
6.1 Determination of the analysis function . .5
6.2 Validation of the analysis function .9
6.2.1 Purpose .9
6.2.2 Validation of the response model .9
6.2.3 Examining conformance with uncertainty requirements .10
6.2.4 Drift control of the measuring system.10
6.2.5 Validation of applicability to mismatching calibration gases .11
6.3 Determination of the composition of a calibration gas mixture . 12
6.4 Supplementary instructions . 13
6.4.1 Exceptional uncertainties . 13
6.4.2 Correlation between reference gas mixtures . 13
7 Special procedures . 14
7.1 Checking of a pre-assigned composition .14
7.2 Comparison of several calibration gas mixtures .14
8 Report of results .15
Annex A (informative) Procedures for data evaluation .16
Annex B (informative) Examples .22
Annex C (informative) Computer implementation of recommended methods .31
Annex D (informative) Additional information on data evaluation .33
Bibliography .40
iii
ISO 6143:2025(en)
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.
The procedures used to develop this document and those intended for its further maintenance are described
in the ISO/IEC Directives, Part 1. In particular, the different approval criteria needed for the different types
of ISO document should be noted. This document was drafted in accordance with the editorial rules of the
ISO/IEC Directives, Part 2 (see www.iso.org/directives).
ISO draws attention to the possibility that the implementation of this document may involve the use of (a)
patent(s). ISO takes no position concerning the evidence, validity or applicability of any claimed patent
rights in respect thereof. As of the date of publication of this document, ISO had not received notice of (a)
patent(s) which may be required to implement this document. However, implementers are cautioned that
this may not represent the latest information, which may be obtained from the patent database available at
www.iso.org/patents. ISO shall not be held responsible for identifying any or all such patent rights.
Any trade name used in this document is information given for the convenience of users and does not
constitute an endorsement.
For an explanation of the voluntary nature of standards, the meaning of ISO specific terms and expressions
related to conformity assessment, as well as information about ISO's adherence to the World Trade
Organization (WTO) principles in the Technical Barriers to Trade (TBT), see www.iso.org/iso/foreword.html.
This document was prepared by Technical Committee ISO/TC 158, Analysis of gases, in collaboration with the
European Committee for Standardization (CEN) Technical Committee CEN/TC 238, Test gases, test pressures,
appliance categories and gas appliance types, in accordance with the Agreement on technical cooperation
between ISO and CEN (Vienna Agreement).
This third edition cancels and replaces the second edition (ISO 6143:2001), which has been technically
revised.
The main changes are as follows:
— update of definitions, in particular those taken from the VIM;
— update of the bibliography and the corresponding references in the text;
— update of the information in Annex C on the computer programme B_LEAST; information on alternative
software (Annex D);
— amendment of 6.2 (now 7.2) “Comparison of several calibration gas mixtures” and related statements in
other parts of the document
— amendment of the recommendations concerning the number of replicate measurements per sample;
— revision of the requirements for the report of results (“Test report”);
— new Annex D (informative) “Additional information on data evaluation”;
— deletion of A.1 “Uncertainty specifications for reference gas mixtures”;
— additional references to relevant ISO standards (ISO 12963, ISO 14912, ISO 15796);
— correction of Formula (4) for the power functions.
iv
ISO 6143:2025(en)
— recommendation added to Annexes B and C not to use B_LEAST for evaluations using the exponential
function (due to recently demonstrated errors) or to calculate the parameter uncertainties (standard
uncertainties and covariances) separately.
Any feedback or questions on this document should be directed to the user’s national standards body. A
complete listing of these bodies can be found at www.iso.org/members.html.
v
ISO 6143:2025(en)
Introduction
In gas analysis, calibration of analytical systems is most often 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). This approach was also adopted in the first
edition (ISO 6143:1981). However, this document is intended for a specific task: the derivation of calibration
gases from appropriate reference gases. Consequently, the multiplier effect of errors in calibration gases
– an error in a calibration gas can cause errors in thousands of analytical results – implies high demands
on the metrological quality of the analysis of calibration gases. In the development of the second edition
(ISO 6143:2001), it was therefore decided to use the best available measurement strategy and data evaluation
method. The main changes in the revision of ISO 6143:1981 related to calibration as well as to uncertainty
evaluation:
— 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.
After twenty years, the principles and procedures specified in the second edition of this document are still
fit for purpose. The current revision therefore mainly concerns additional supporting information.
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. A dedicated program (B_LEAST) is available and provided without cost as
1)
a part of this document (see Annex C) . Information on other publicly available software that can be used for
at least the vast majority of the calculations required by this document is given in Annex D. As an alternative,
sufficient information is given in this document to enable the user to develop a program on their own.
1) The software "B_LEAST" can be obtained via the following link: https://standards.iso.org/iso/6143/ed-3/en.
vi
International Standard ISO 6143:2025(en)
Gas analysis — Comparison methods for determining and
checking the composition of calibration gas mixtures
1 Scope
This document specifies 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;
— consistency testing and outlier search in suites of calibration gas mixtures of closely related composition.
NOTE 1 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, need 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.
NOTE 2 Comparison methods based on one- and two-point calibration are described in ISO 12963.
2 Normative references
There are no normative references in this document.
3 Terms and definitions
For the purposes of this document, the following terms and definitions apply.
ISO and IEC maintain terminology databases for use in standardization at the following addresses:
— ISO Online browsing platform: available at https:// www .iso .org/ obp
— IEC Electropedia: available at https:// www .electropedia .org/
3.1
composition
characteristic of a gas mixture given by the kind and content of each specified mixture component (analyte)
and a specification of the complementary gas (matrix)
Note 1 to entry: In this document, the analyte content is specified as an amount-of-substance fraction, exclusively.
Amount 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) can be more appropriate. Their use then requires due care concerning the dependence
on pressure and temperature. Methods for conversion between different quantities of composition are specified in
ISO 14912.
ISO 6143:2025(en)
3.2
comparison method
method for determining the content of a specified gas mixture component (analyte) by measuring an
instrument response
Note 1 to entry: Comparison measuring systems require 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.
3.3
calibration
operation that, under specified conditions, in a first step, establishes a relation between the quantity values
with measurement uncertainties provided by measurement standards and corresponding indications with
associated measurement uncertainties and, in a second step, uses this information to establish a relation for
obtaining a measurement result from an indication
[SOURCE: ISO/IEC Guide 99:2007, 2.39]
3.4
response function
functional relationship between instrument response and analyte content
Note 1 to entry: The response function can be expressed in two different ways as a calibration function (3.4.1) or an
analysis function (3.4.2), depending on the choice of the dependent and the independent variable.
3.4.1
calibration function
instrument response expressed as a function of analyte content
3.4.2
analysis function
analyte content expressed as a function of instrument response
3.5
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
[SOURCE: ISO/IEC Guide 99:2007, 2.26]
3.6
measurement standard
realization of the definition of a given quantity, with stated quantity value and associated measurement
uncertainty, used as a reference
[SOURCE: ISO/IEC Guide 99:2007, 5,1]
3.7
reference standard
reference measurement standard
measurement standard (3.6) designated for the calibration of other measurement standards for quantities of
a given kind in a given organization or at a given location
[SOURCE: ISO/IEC Guide 99:2007, 5.6]
ISO 6143:2025(en)
3.8
calibration gas mixture
gas mixture of known stability and homogeneity whose composition is well established for use in the
calibration or verification of a measuring instrument or for the validation of a measurement
[SOURCE: ISO 7504:2015, 5.1, modified — Note 1 to entry has been removed]
3.9
reference gas mixture
calibration gas mixture whose composition is well established and stable to be used as a reference standard
(3.7) of composition from which other composition data measurements are derived
[SOURCE: ISO 7504:2015, 5.2, modified — Note 1 to entry has been removed]
4 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
n number of data points
Q transform matrix
s standard deviation of a data set (sample standard deviation)
S sum of weighted squared deviations
S residual sum of weighted squared deviations
res
t quantile of the t-distribution (ν degrees of freedom, confidence level (1-α))
ν;(1-α)
U(q) expanded uncertainty of an estimated quantity q, U(q) = ku(q)
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
x amount fraction of the specified analyte
(x , y ) calibration points (i = 1, 2, ., n)
i i
adjusted calibration points (i = 1, 2, ., n)
ˆˆ
(xy )
ii,
ISO 6143:2025(en)
y instrument response of the specified analyte
2 2
χ quantile of the Chi -distribution (ν degrees of freedom, confidence level (1-α))
ν;(1-α)
γ
dilution factor
σ standard deviation of a probability distribution
Γ measure of goodness-of-fit
5 Principle
The composition of a gas mixture is determined by separate determination of the amount fraction of every
specified analyte. Therefore, the procedure for determining the amount fraction of only one specified
analyte is described. Possible interferences due to the presence 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 document.
This document is also applicable if other composition quantities than amount fraction are used. However, it
is recommended that the final result be expressed as an amount fraction. Methods for conversion between
different quantities of composition are specified in ISO 14912.
The general procedure for determining the amount 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 amount fractions x to be determined, and the
acceptable uncertainty level (see 6.1, step A).
b) Specify the analytical method and the measuring system to be used (see 6.1, 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 an
evaluation of the system characteristics 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 6.1,
step C).
d) Set up a design for the calibration experiment in which the relevant experimental parameters are
specified, such as:
— calibration range (to include the analytical range);
— composition, including uncertainty, of the reference gas mixtures for calibration;
— parameters of the analytical method;
— conditions of measurement, if relevant;
— number and sequence of calibration measurements (see 6.1, 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 6.1, step G).
f) Calculate the analysis function, x = G(y), from the calibration data, using regression analysis (see 6.1,
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 6.2.2).
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 (see 6.2.3).
ISO 6143:2025(en)
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 6.2.4). 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 6.2.5).
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 amount fraction x = G(y) using the analysis function determined in f),
— calculate the uncertainty u(x) of the amount fraction x by propagation of uncertainty on the measured
response and on the parameters of the analysis function (see 6.3).
k) State the result of the entire analysis (see clause 8).
Essentially the same steps apply if, instead of the analysis function, x = G(y), the calibration function, y = F(x),
is determined from the calibration data. Given the calibration function, the analyte content x for response y is
obtained by solving the formula y = F(x) for x, given y. To this end, if possible, the calibration function is inverted
-1
algebraically, yielding the corresponding analysis function, x = F (y). As an example, a linear calibration function
y = a + a x can be inverted yielding x = (y – a )/a . If algebraic inversion is not possible, the corresponding
0 1 0 1
analysis function is obtained by “numerical inversion”, i.e. the formula y = F(x) is solved pointwise, using an
appropriate numerical method. The approach using the calibration function is described in A.4.
In addition to determining the composition of a (prospective) calibration gas mixture, the general procedure
can 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 7 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 can also be used for consistency testing and outlier search in suites of calibration gas
mixtures of closely related composition. Clause 7 specifies a procedure where entire suites of calibration
gases are measured in a calibration experiment, using an analyser with linear response. For each analyte
concerned the calibration data are examined for compatibility with a straight-line response curve. A positive
test result provides confirmation that the assigned contents and their uncertainties are mutually consistent.
Restriction to subsets provides a tool for outlier search in cases of a negative test result.
Numerical examples for applying the methodology are given in Annex B.
6 General procedure
6.1 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 to known analyte contents x , x , ., x of appropriate reference gas mixtures. Inversely,
2 n 1 2 n
the analysis function, x = G(y), approximately expresses known analyte contents x , x , ., x in relation to
1 2 n
corresponding measured responses y , y , ., y . The analysis function is required for calculating unknown
1 2 n
analyte contents x of calibration gas mixtures from measured responses y.
ISO 6143:2025(en)
The analysis function can be determined either directly, or indirectly by determination of the calibration
function and subsequent inversion (i.e. solving the formula y = F(x) for x, given y). It is recommended to make
a direct determination of the analysis function. Therefore, only this procedure is specified in the body of this
document. In particular applications, however, indirect determination using the calibration function can be
preferable. For such applications, a brief description of this procedure is given in A.4.
The following description of the calibration experiment and its evaluation, in terms of a series of steps,
summarizes and elaborates the principles outlined in clause 5.
a) Step A: Specify the analytical range, i.e. the range of the analyte contents x in the calibration gas mix-
tures 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:
x =+ y
— linear functions b b (1)
— second-order polynomials (2)
x =+ y + y
b b b
01 2
2 3
— third-order polynomials (3)
x =+ y ++ y y
b b b b
01 2 3
()1+b
— power functions 2 (4)
x =+
y
b b
y
b
— exponential functions (5)
x =+
b b e
The parameters b of the analysis function are determined by regression analysis using the values from
j
the 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 can be linear or non-linear. Although the method described in this document is, in princi-
ple, 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.
The selection of functions in step C does not exclude the use of other functions, e.g. higher-order poly-
nomials. In addition, using the calibration function, the functions in step C (with x and y interchanged)
almost double the selection of potential response functions. However, for response curves deviating
only moderately from a straight line, the variety of functions in step C, when used as analysis function,
is expected to cover all practical needs. The computer program B_LEAST (see Annex C) is restricted to
the functions in step C in the analysis-function mode.
When using other functions, it is recommended to include a parameter for a non-zero intercept. While
often the “true” response curve can be expected to give zero response for zero analyte content, local
approximations, as considered in this document, will often not pass through the origin.
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.
The minimum number of calibration points recommended for the different types of functions considered is:
ISO 6143:2025(en)
— 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 with analyte contents x , x , ., x tailored
ref,1 ref,2 ref,n 1 2 n
to the analytical range, i.e. approximately equally spaced, with one value below the lower limit and one
value above the upper limit.
The analyte contents shall be determined independently to the greatest possible extent. Dilution series
may only be used under the conditions specified in 6.4.2.
If interferences between mixture components cannot be safely excluded, it can 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 document [see 6.1 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 according to current standard 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
min max
limit of the 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:
+ −
x x x x
maxmin maxmin
x = ; (ux ) = (6)
If the complementary gas is taken as a reference gas for zero analyte content, x = 0, and x = L . Here
min max x
L denotes the limit of detection (see reference [11]) of the analytical method used for determining the
x
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
1 2 n 1 2 n
standard uncertainties u(y ), u(y ), ., u(y ).
1 2 n
So as to establish the response data y and u(y ) for a given x , it is recommended to use the mean value
i i i
of ten individual responses, y , y , ., y , measured independently under appropriate conditions and to
i1 i2 i10
take the standard deviation of this mean value.
ISO 6143:2025(en)
10 10
1 1
yy==;(uy )( yy− ) (7)
ii∑∑j iij i
j==1 j 1
The application of the uncertainty in formula (7) requires that the numerical resolution of y is not the
limiting factor.
Influential measurement conditions (i.e. those having an influence on the performance of the analytical
system) should be kept constant. Where this is not possible, the response data shall be corrected to
appropriate reference conditions. The uncertainty relating to this correction has to be accounted for in
the uncertainty of the response data.
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 ,
ref,1
M , ., M in an irregular sequence.
ref,2 ref,n
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 (see paragraph below). Under
i i
certain conditions, however, a lower number of replicates (e.g. n=6) per sample may be sufficient.
For example, if the analytical system is used exclusively on gases of similar composition (e.g. natural
gases or automotive exhaust gases), the mean values y may be determined from a smaller number of
i
independent measurements (e.g. n=6) and the standard uncertainties u(y ) may be calculated from the
i
method standard deviation established by performance evaluation. Also, with at least five calibration
points, pooling of standard deviations obtained from a smaller number of independent measurements
can be a valid option (see Annex D for further information).
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 10 measurements it is 24 % and 36 % for 5 measurements (see
ISO/IEC Guide 98-3:2008, Annex E, Table E.1). Therefore, a smaller number of repeated measurements
should not be used when determining the standard deviation of a mean value.
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
L L
yy
y = ; u ()y = (8)
Here, the response limit of detection is the upper limit of fluctuations at zero response.
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 amount 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
The parameters are calculated by regression analysis in accordance with the method described in A.1.
In contrast with ordinary least squares regression, the regression technique used in this document
equally takes into account the uncertainties of the composition of the reference gas mixtures and the
uncertainties of the measured responses.
ISO 6143:2025(en)
6.2 Validation of the analysis function
6.2.1 Purpose
Before using the analysis function determined according to 6.1, it is necessary to perform validations. These
validations serve a number of different purposes:
— to validate the response model,
— to examine conformance with uncertainty requirements,
— to control drift of the measuring system,
— to validate the applicability to mismatching calibration gases.
6.2.2 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 (amount 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
res
calibration points less the number of response curve parameters), as given in A.1. For the purpose of this
document, 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 (xyˆˆ, ) is
i i
ii
calculated, as a by-product of the regression analysis used to determine the analysis function (see
...
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