ISO 10723:2012

INTERNATIONAL ISO
STANDARD 10723
Second edition
2012-12-01
Natural gas — Performance evaluation
for analytical systems
Gaz naturel — Évaluation des performances des systèmes d’analyse
Reference number
©
ISO 2012
© ISO 2012
All rights reserved. Unless otherwise specified, no part of this publication may be reproduced or utilized in any form or by any
means, electronic or mechanical, including photocopying and microfilm, without permission in writing from either ISO at the
address below or ISO’s member body in the country of the requester.
ISO copyright office
Case postale 56 • CH-1211 Geneva 20
Tel. + 41 22 749 01 11
Fax + 41 22 749 09 47
E-mail copyright@iso.org
Web www.iso.org
Published in Switzerland
ii © ISO 2012 – All rights reserved

Contents Page
Foreword .iv
Introduction .v
1 Scope . 1
2 Normative references . 2
3 Terms and definitions . 2
4 Symbols . 3
5 Principle . 4
6 General procedure . 5
6.1 Analytical requirements . . 5
6.2 Response function types . 6
6.3 Calibration gas reference data . 7
6.4 Working measurement standards (WMS) . 8
6.5 Experimental design . 9
6.6 Calculation procedures .11
7 Interpretation .16
7.1 General considerations .16
7.2 Pre-defined performance specification .16
7.3 Determination of the analytical range of the instrument .16
7.4 Criteria for selection of hypothetical compositions .17
Annex A (informative) Example of application using chromatography .18
Annex B (informative) Explanation of approach used for instrument benchmarking .30
Bibliography .32
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 10723 was prepared by Technical Committee ISO/TC 193, Natural gas, Subcommittee SC 1, Analysis
of natural gas.
This second edition cancels and replaces the first edition (ISO 10723:1995), which has been technically
revised. It also incorporates Technical Corrigendum ISO 10723:1995/Cor.1:1998.
iv © ISO 2012 – All rights reserved

Introduction
This International Standard describes a method for evaluating the performance of analytical systems
intended for the analysis of natural gas. Natural gas is assumed to consist predominantly of methane,
with other saturated hydrocarbons and non-combustible gases.
Performance evaluation makes no assumption about equipment for and/or methodology of analysis
but gives test methods which can be applied to the chosen analytical system, including the method,
equipment and sample handling.
This International Standard contains an informative annex (Annex A) that shows the application for an
on-line gas chromatographic system which, as described, is assumed to have a response/concentration
relationship for all components that is represented by a straight line through the origin. This International
Standard contains an additional informative annex (Annex B) that gives a rationale for the approach
used for instrument benchmarking.
INTERNATIONAL STANDARD ISO 10723:2012(E)
Natural gas — Performance evaluation for analytical systems
1 Scope
1.1 This International Standard specifies a method of determining whether an analytical system for
natural gas analysis is fit for purpose. It can be used either
a) to determine a range of gas compositions to which the method can be applied, using a specified
calibration gas, while satisfying previously defined criteria for the maximum errors and uncertainties
on the composition or property or both, or
b) to evaluate the range of errors and uncertainties on the composition or property (calculable from
composition) or both when analysing gases within a defined range of composition, using a specified
calibration gas.
1.2 It is assumed that
a) for evaluations of the first type above, the analytical requirement has been clearly and unambiguously
defined, in terms of the range of acceptable uncertainty on the composition, and, where appropriate,
the uncertainty in physical properties calculated from these measurements,
b) for applications of the second type above, the analytical requirement has been clearly and
unambiguously defined, in terms of the range of composition to be measured and, where appropriate,
the range of properties which may be calculated from these measurements,
c) the analytical and calibration procedures have been fully described, and
d) the analytical system is intended to be applied to gases having compositions which vary over ranges
normally found in gas transmission and distribution systems.
1.3 If the performance evaluation shows the system to be unsatisfactory in terms of the uncertainty on the
component amount fraction or property, or shows limitations in the ranges of composition or property values
measurable within the required uncertainty, then it is intended that the operating parameters, including
a) the analytical requirement,
b) the analytical procedure,
c) the choice of equipment,
d) the choice of calibration gas mixture, and
e) the calculation procedure,
be reviewed to assess where improvements can be obtained. Of these parameters, the choice of the
calibration gas composition is likely to have the most significant influence.
1.4 This International Standard is applicable to analytical systems which measure individual component
amount fractions. For an application such as calorific value determination, the method will be typically
gas chromatography, set up, as a minimum, for the measurement of nitrogen, carbon dioxide, individual
hydrocarbons from C to C and a composite measurement representing all higher hydrocarbons of
1 5
carbon number 6 and above. This allows for the calculation of calorific value and similar properties
with acceptable accuracy. In addition, components such as H S can be measured individually by specific
measurement methods to which this evaluation approach can also be applied.
1.5 Performance evaluation of an analytical system is intended to be performed following initial
installation to ensure that errors associated with assumed response functions are fit for purpose.
Thereafter, periodic performance evaluation is recommended, or whenever any critical component of
the analytical system is adjusted or replaced. The appropriate interval between periodic performance
evaluations will depend upon both how instrument responses vary with time and also how large an
error may be tolerated. This first consideration is dependent upon instrument/operation; the second
is dependent on the application. It is not appropriate, therefore, for this International Standard to offer
specific recommendations on intervals between performance evaluations.
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 98-3:2008, Uncertainty of measurement —Part 3: Guide to the expression of uncertainty in
measurement (GUM:1995)
ISO 6143:2001, Gas analysis — Comparison methods for determining and checking the composition of
calibration gas mixtures
ISO 6974-2, Natural gas — Determination of composition and associated uncertainty by gas
chromatography — Part 2: Uncertainty calculations
ISO 6976:1995, Natural gas — Calculation of calorific values, density, relative density and Wobbe index
from composition
3 Terms and definitions
For the purposes of this document, the following terms and definitions apply.
3.1
uncertainty of measurement
parameter, associated with the result of a measurement, that characterizes the dispersion of values that
can reasonably be attributed to the measurand
NOTE In keeping with ISO/IEC Guide 98-3, in this International Standard the uncertainty of the composition
is expressed as a standard uncertainty or as an expanded uncertainty calculated through the use of an appropriate
coverage factor.
3.2
certified reference gas mixture
CRM
reference gas mixture, characterized by a metrologically valid procedure for one or more specified
properties, accompanied by a certificate that provides the value of the specified property, its associated
uncertainty, and a statement of metrological traceability
[3]
NOTE 1 The above definition is based on the definition of “certified reference material” in ISO Guide 35 .
“Certified reference material” is a generic term; “certified reference gas mixture” is more suited to this application.
NOTE 2 Metrologically valid procedures for the production and certification of reference materials (such as
[4] [3]
certified reference gas mixtures) are given in, among others, ISO Guide 34 and ISO Guide 35 .
[5]
NOTE 3 ISO Guide 31 gives guidance on the contents of certificates.
2 © ISO 2012 – All rights reserved

3.3
working measurement standard
WMS
standard that is used routinely to calibrate or verify measuring instruments or measuring systems
[ISO/IEC Guide 99:2007, 5.7]
NOTE A working measurement standard is usually calibrated against a CRM.
3.4
calibration gas mixture
CGM
gas mixture whose composition is sufficiently well established and stable to be used as a working
measurement standard of composition
NOTE In this International Standard, a CGM is used for routine (e.g. daily) component calibration of the
analyser. It is independent of the WMSs used to perform the evaluation.
3.5
response
output signal of the measuring system for each specified component
NOTE In the case of gas chromatography this will be either peak area or peak height, depending upon the
instrument configuration.
3.6
response function
functional relationship between instrumental response and component 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.
3.7
calibration function
relationship describing instrument response as a function of component content
3.8
analysis function
relationship describing component content as a function of instrument response
4 Symbols
a parameters of the calibration function (z = 0, 1, 2 or 3)
z
b parameters of the analysis function (z = 0, 1, 2 or 3)
z
x amount fraction of the specified component
xˆ adjusted (estimated) amount fraction from the response function
y′ raw instrumental response
y corrected instrumental response
s standard deviation of response
ˆy adjusted (estimated) response from the response function
F calibration function
G analysis function
M (sample of) reference gas mixture
P general characteristic (physical property)
p pressure (in kPa)
u standard uncertainty
U expanded uncertainty
k coverage factor
Γ goodness-of-fit measure in generalized least squares
δ error in the estimated value
5 Principle
Performance characteristics of the instrument are determined when used in combination with a
specified calibration gas mixture. Therefore, the evaluation procedure can be used to
— determine errors and uncertainties in measured composition and properties over a pre-defined
range for each specified component, and
— determine a range for each specified component over which the errors and uncertainties in measured
composition and properties do not exceed a predefined measurement requirement.
In each case, the performance characteristics are calculated for the instrument when used in combination
with a specified calibration gas mixture of known composition and uncertainty.
NOTE 1 The method can also be used to establish the most appropriate composition of the calibration gas
mixture to be used routinely with the instrument such that the errors and uncertainties are minimized over a
predefined range of use.
A complete assessment of the errors and uncertainties arising from the use of an instrument could be
performed by measuring an infinite series of well-defined reference gas mixtures whose compositions
lie within the specified range of operation. However, this is practically impossible. Instead, the principle
used in this International Standard is to measure a smaller number of well-defined reference gases
and to determine a mathematical description of the response functions for each specified component
over a predefined content range. The performance of the instrument can then be modelled offline using
these “true” response functions, the response functions assumed by the instrument’s data system and
the reference data for the calibration gas mixture specified for the instrument. The measurement of
a large number of gas mixtures can then be simulated offline using numerical methods to determine
performance benchmarks inherent in the measurement system.
The general procedure for determining the performance characteristics of the instrument is
summarized below.
a) Specify the components required to be measured by the instrument and the range for each over
which the instrument shall be evaluated.
b) Establish the functional descriptions of the response functions assumed by the instrument (or the
instrument’s data system) for each specified component.
NOTE 2 These functions are referred to as the assumed response functions of the system at the time of
calibration/evaluation. These are generally analysis functions used by the instrument to determine the amount
from the measured response, x = G ( y).
asm
4 © ISO 2012 – All rights reserved

c) Establish the composition and uncertainty of the calibration gas mixture specified for routine
calibration of the instrument.
d) Design a set of reference gas mixtures with compositions covering all ranges for all components
specified in a).
e) Perform a multi-point calibration experiment by collecting instrument response data to
measurements of the reference gas mixtures designed and produced in accordance with d). The
entire experiment should be conducted within a time period equivalent to that between routine
calibrations.
f) Calculate the calibration functions and analysis functions for each specified component using
regression analysis and validate the compatibility of the functions with the calibration data set.
NOTE 3 These functions are referred to as the true response functions of the system at the time of
calibration/evaluation, y = F (x) and x = G ( y).
true true
g) Calculate instrumental errors and uncertainties for each component and property over a specified
range of compositions using the functions and reference data collated in d), e) and f) above.
h) From the distribution of errors and the unbiased uncertainty estimates calculated in g) above,
determine the mean error and its uncertainty for each measurand.
The mean errors and their uncertainties on component content and properties resulting from step h)
can be compared to performance requirements for the analytical system. If performance benchmarks
are poorer than the analytical requirements of the measurement, then it is clear that the method
fails to provide the desired performance over the fully specified range. The method shall be modified
accordingly and the entire evaluation procedure repeated. Alternatively, the offline calculations shall be
repeated over a restricted range of operation in order to improve system performance. In this case, the
instrument may be shown to perform adequately over a limited range.
It may be possible to modify the data system on the instrument to allow for the difference between
the true response functions and the analysis function assumed by the instrument. In this case, the
instrument should be adjusted following the evaluation to account for this difference. If the function
form of G and G are the same, then the parameters of G in the instrument’s data system can
true asm asm
be updated with those determined for G in step f) above, thereby eliminating systematic errors due
true
to the instrument. However, it is important to remember that the parameters of G are only valid for
true
each component over the content range used to establish the analysis function. That is, the instrument
should not be used outside the ranges defined, designed and evaluated in steps a), b) and c).
6 General procedure
6.1 Analytical requirements
6.1.1 General considerations
Users of this International Standard should first decide which components measured by the instrument
are to be used in the evaluation of the performance. These are termed specified components. For each
specified component, the range of amount fractions over which the response function is to be evaluated
shall then be decided.
6.1.2 Specified components
For measurement systems set up to determine the major components in natural gas, the components
typically specified are nitrogen, carbon dioxide, methane, ethane, propane, 2-methylpropane (iso-butane),
n-butane, 2-methylbutane (iso-pentane) and n-pentane. In addition, some analytical requirements
include 2,2-dimethylpropane (neo-pentane). This component is typically present in very low amounts in
natural gas and might not be specified in many systems for measurement. In a typical chromatography
method, higher hydrocarbons are often specified as a summed component such as hexanes+ (C ) where
6+
all hydrocarbons containing six carbon atoms or greater are included in one specified component. The
instrumental method may measure such a component as an individual chromatographic peak which
is typically backflushed through the system, and all components elute at the same time through the
detector. Alternatively, in systems where valve switching is not possible, the heavier hydrocarbons
elute in a forward fashion through the columns and the component is simply measured as the sum of
individual peaks. However, the system may be set up to measure all hexanes (C s) individually and the
summed peak C + may be specified. This is often the case should the C + amount be significant and a
7 6
more detailed breakdown of this component be required to minimize errors on the measurement. This
principle can be extended such that the system is set up to measure in a C , C , C , C or even C
6+ 7+ 8+ 9+ 10+
mode. Users of this International Standard shall decide which of these components are to be included in
the evaluation of the instrument’s performance based upon the significance of the amounts of each of
the components specified in the instrument set-up.
6.1.3 Component content ranges
Once it is clear which measured components are going to be included in the evaluation, the user shall
determine, for each of these, over what range of amount fractions the instrument is expected to be used.
Such ranges shall generally be greater than that which is expected to be measured by the instrument in
regular duty. If the data from the performance evaluation is used subsequently to update the response
functions assumed by the instrument, then it is vital that the component content ranges used in the
evaluation extend beyond the specified operating range. Should this not be the case, considerable
measurement errors might result from extrapolation outside the determined response function.
6.2 Response function types
6.2.1 Assumed functional descriptions
The instrument data system will assume a relationship between response and content of a component in
the gas. This is the assumed analysis function of the instrument, x = G (y). Many instruments assume
asm
a simple first-order polynomial function in the form x = b y, where b is often referred to as the response
1 1
factor (RF) for that component. In this case a single calibration gas mixture is used and a first-order
response function is assumed, passing through the origin. Alternatively, the instrument may assume a
higher-order polynomial functional description or even an exponential or power function.
In some cases the response, particularly for a minor component, may be calculated as relative to that of
another (reference) component. Such a relative response factor shall have a response function similar to
that of the reference component.
The assumed analysis function for each component, x = G (y), shall be noted and used for subsequent
asm
calculation of the instrument’s performance characteristics described in 6.6.
The function types considered for the treatment of the performance evaluation data shall be matched to
those used by the instrument’s data system.
NOTE Occasionally, functional types other than polynomials, such as exponential relationships, are
implemented by an instrument’s data system. If the instrument uses functional types other than polynomials,
it is appropriate to use these in the determination of the analysis functions. However, for the purposes of this
International Standard, only polynomial functions up to third order are considered.
6.2.2 Selection of function types
The type of function to be used in practice is chosen according to the response characteristics of the
measuring system and that assumed by the instrument’s data system.
Polynomial functions describing the true response/amount fraction relationship can be derived in
either domain. A mathematical description of instrument response as a function of amount fraction is
termed the calibration function, whereas that describing amount fraction as a function of response is
termed the analysis function.
6 © ISO 2012 – All rights reserved

Hence, the true calibration functions, F (x ), determined for each component are in the form
i,true i
2 3
yF==()xa ++ax ax +ax (1)
ii,true ii01 2 ii3
where a are the parameters of the calibration function.
z
Similarly, the true analysis functions, G (y ), are in the form
i,true i
2 3
xG==()yb ++by by +by (2)
ii,true ii01 2 ii3
where b are the parameters of the analysis function.
z
In both cases
y is the mean response of the instrument to component i;
i
x is the amount fraction of component i.
i
The response functions above are shown in a form up to third order. However, simpler forms up to
second order or simply first order may be considered. Choose the form of the response functions with
the following considerations:
a) the simplest form that gives an adequate fit to the data should be used to avoid over-parameterizing
the response function;
b) the number of calibration points, and hence the number of reference gases required to satisfactorily
describe a polynomial, increases with the order of the function (see 6.4.2);
c) if there is an a priori reason to assume that a lower-order polynomial will always be suitable, then
this should be chosen and a lower number of reference gases may be used (see 6.4.2).
6.3 Calibration gas reference data
6.3.1 General considerations
The performance benchmarks from this evaluation procedure are calculated for the instrument used
in combination with the proposed/current calibration gas mixture. This is the working calibration gas
used for routine, often daily, calibration.
NOTE The design of the calibration gas mixture can have significant influence on the distribution of bias
errors for the instrument. Similarly, the uncertainties on the amount fraction of each component in the calibration
gas can make a significant contribution to the uncertainty on the measurement results. Hence, the design and
uncertainty of composition of the calibration mixture shall be chosen carefully.
6.3.2 Composition and uncertainty
The amount fraction, x , and standard uncertainty, u(x ), for each component in the calibration gas
i,cal i,cal
mixture shall be obtained or derived from the certificate of calibration.
If the uncertainty quoted on the certificate is not a standard uncertainty (k = 1), then the standard
uncertainties shall be derived using the manufacturer’s stated coverage factor.
ux()=Ux()/k (3)
ii,,calcertcal
6.4 Working measurement standards (WMS)
6.4.1 Definition
The WMSs used for the determination of the response functions are gas mixtures whose composition
is known with a well-defined uncertainty. They may be multi-component or binary mixtures. In all
cases, the matrix gas should be methane, so that the behaviour of the WMS is as similar as possible to
that of natural gases. Binary mixtures can generally be prepared with lower uncertainties than multi-
component mixtures. However, many more mixtures shall be made; one set for each non-methane
component to be tested. Generally, multi-component mixtures should be used as they allow more repeat
measurements to be performed for each component/amount fraction combination.
The WMS should be chosen so as to be suitable for the intended analytical application as discussed in
6.1. However, it is not practicable to manufacture and calibrate WMSs which contain all the components
in natural gas, given the complexity of the higher hydrocarbons that are commonly found and the
difficulty of preparing high-quality mixtures containing condensable components. In the majority of
applications, the major components in natural gas, nitrogen, carbon dioxide, methane, ethane, propane,
2-methylpropane (iso-butane) and n-butane are generally specified and normally included in the
reference gas mixtures. In addition, 2-methylbutane (iso-pentane), n-pentane and a representative C
6+
component such as n-hexane are often included. If 2,2-dimethylpropane (neo-pentane) is a specified
component in the analytical requirement, it may also be included in the WMS. Any component expected
to be present in an amount fraction greater than 0,01 should be included.
NOTE The WMS used in this evaluation procedure can also be used to define the analysis function of an
analyser when it is initially installed or on other occasions when a primary calibration is required to define the
analysis function assumed by the instrument’s data system.
6.4.2 Composition and uncertainties
For each specified component that will be included in the WMS, the number of levels, calibration points,
at which the evaluation shall be performed depends upon the form of the function type selected for the
evaluation (see 6.2.2).
The minimum number of calibration points recommended to give sufficient degrees of freedom for the
unbiased estimate of the response function is as follows:
3 (three) for a first-order polynomial;
5 (five) for a second-order polynomial;
7 (seven) for a third-order polynomial.
The WMSs shall be selected such that their amount fractions are approximately equally spaced across
the defined evaluation range (see 6.1.3) with one at (or below) the lower limit and one at (or above) the
higher limit.
NOTE 1 Depending on the intended application, the lower end of the range might be close to the limit of
detection, in which case it might not be possible to include a component amount fraction below the lower end of
the application range.
In the design of the recipe of the set of WMSs, the user shall be careful not to include all high-amount
fractions of the higher hydrocarbons together in the same mixture. Should this be the case, the pressure
of the mixture would be limited due to the potential of retrograde hydrocarbon condensation due to the
high dewpoint of the mixture. The higher amounts of higher hydrocarbons should, where possible, be
distributed amongst the set of WMSs.
Once designed and manufactured, the composition and uncertainties of the WMS should be determined
by a comparison method in accordance with ISO 6143. Certified reference gas mixtures (CRMs) of
an appropriate metrological quality shall be used as the source of traceability for this comparison
step. Whether binary or multi-component mixtures are used, each WMS shall have compositional
8 © ISO 2012 – All rights reserved

uncertainties which are small by comparison with the anticipated measurement uncertainties of the
analytical system under evaluation.
NOTE 2 Helium, C and heavier hydrocarbons are usually present at sufficiently low mole fractions that
nonlinearity of response is unlikely to be a problem. If not specified in the reference gas mixtures, the assumption
of a first-order response/amount fraction relationship can be tested using natural gases of certified composition
containing these components covering a range of amount fractions appropriate to the application.
6.5 Experimental design
6.5.1 General considerations
Each WMS shall be measured several times by the instrument in order to obtain a reasonable estimate
of the response functions for each component. It is strongly recommended that each gas be analysed
10 times. However, where this number of repeats would be impractical (for example requiring the test
period to extend beyond the normal calibration interval), a smaller number of repeats may be used,
but not less than six. When changing between WMSs, regulators, valves and tubing need to be fully
purged otherwise the first or more replicates of a fresh WMS may not be fully representative of the gas
contained within the cylinder. The measurement might be biased due to the presence of residues of the
preceding gas or of the ingress of air occurring during changeover.
The entire calibration procedure is likely to take several hours depending upon the instrument cycle
time. Over such a period, it is quite common for the ambient atmospheric pressure to change by as much
as 0,5 % relative and in extreme cases by up to 2 % relative. Gas samples are typically introduced into
analysers by being purged through an injector device to a vent which is at, or referenced to, atmospheric
pressure. Hence, ambient pressure variations cause a change in the effective sample size. This has the
effect of raising or decreasing the response of the instrument to the same gas mixture. Hence, there will
be an inherent drift in the absolute response of the instrument over time, dependent upon the change in
atmospheric pressure over that period. There are other parameters that influence the effective sample
size or the detector sensitivity, but atmospheric pressure variation is the most significant.
There is a choice of procedures for the measurement of each reference gas which depends on the
availability of time and equipment. There are two general approaches to implementing the calibration
procedure which are termed as follows:
a) batch-wise calibration;
b) drift compensation calibration.
The first, in which replicate measurements of each mixture are carried out in sequence, is the most
practical implementation but has the disadvantage of not compensating for the inherent drift in a
system over the time of the calibration. The second, in which replicate measurements of each mixture
are performed separately and independently, will compensate for the inherent instrumental drift over
the time of the calibration but is considerably more time-consuming and more suited to implementation
in an automated system.
Whichever experimental procedure is used, the entire calibration experiment should be conducted
within a time period equivalent to that between routine calibrations.
6.5.2 Batch-wise calibration
The WMSs are introduced in sequence, with all the replicate measurements on the first gas being
completed before the second is introduced and so on. The sampling sequence in time is:
M , M , M , …, M  (n replicate measurements in succession on gas M ), then
1,1 1,2 1,3 1,n 1
M , M , M , …, M  (n replicate measurements in succession on gas M ), then
2,1 2,2 2,3 2,n 2
M , M , M , …, M  (n replicate measurements in succession on gas M ).
p,1 p,2 p,3 p,n p
This is the simplest and most practicable method for a manually implemented field-use application as
it requires only the changeover of p gases on the test instrument. However, the change in atmospheric
pressure during the test will have a greater influence on the variation between the reference gases than
within the repeat measurements for any single one.
Significant instrumental drift between gases will likely give rise to higher residuals and hence poor
goodness-of-fit parameters in the generalized least-squares regression procedure. To minimize the
goodness-of-fit parameters, it may be necessary to correct for the instrumental drift by correcting for
the effective sample size of each reference gas mixture at the time of injection. This can be done by drift
correction (6.5.4).
6.5.3 Drift compensation calibration
This procedure separates the repeat measurements on each reference gas mixture in such a way as to limit
the effect of sample size variations and compensate for the instrumental drift over the calibration period.
The sampling sequence in time is:
M , M , M , …, M  (1st repeat measurement on each of p gases), then
1,1 2,1 3,1 p,1
M , M , M , …, M  (2nd repeat measurement on each of p gases), then
1,2 2,2 3,2 p,2
th
M , M , M , …, M  (n repeat measurement on each of p gases).
1,n 2,n 3,n p,n
The first repeat measurement on reference gas 1 is followed by the first on gas 2 and so on. Then
the second repeat on reference gas 1 follows the completion of the first repeat measurement on all p
reference gases. This procedure is continued throughout the number of repeats required.
This approach ensures that variations due to external influences are shared or smeared out throughout
the repeats on each reference gas. The instrumental drift is effectively compensated for by the
experimental procedure. This occurs in such a way that the within-gas variations may be higher but the
between-gas variations are more consistent. With this approach, the goodness-of-fit parameters in the
generalized least squares regression procedure are usually good.
The major disadvantage to this method is that the gases have to be changed much more frequently. In
addition, after each change, it is advisable for at least one and possibly two analyses to be performed
before data are recorded, to allow for sufficient purging between the gases. This means that the
procedure is much lengthier than the first, and, to be practicable, requires an automated changeover
and purging system to handle the introduction of the reference gases.
6.5.4 Drift correction
During either of the two experimental procedures described above (6.5.2 or 6.5.3), the instrumental
response may be corrected for drift due to changes in atmospheric pressure (for reasons described
earlier). The atmospheric pressure is measured and recorded at the start of each repeat on each of the
WMSs. This allows the pressure-influenced variations in sample size to be corrected to a reference
value. In this way the data will be more consistent both within and between reference gases. While
this approach may be used for the drift-compensation-type calibration (6.5.3), it is often more useful to
correct instrumental responses obtained during batch-wise calibration as the result of this experimental
approach is much more sensitive to instrumental drift.
NOTE If time and automation techniques are available, the combination of a drift compensation experiment
with drift correction for atmospheric pressure will lead to the most precise and inter-consistent calibration data set.
6.5.5 Collation of calibration data
Whichever calibration method is used, the collation of raw calibration data are identical. For each of q
components, (i = [1, ., q]), at each of p amount fractions, ( j = [1, ., p]), collect n (preferably 10) repeat
measurements, (k = [1, ., n]). Collate each instrument response, y′ , with the corresponding component
ijk
amount fraction, x .
ij
10 © ISO 2012 – All rights reserved

If pressure correction (drift correction) is not used, set y equal to y′ . Alternatively, record the
ijk ijk
atmospheric pressure, P , in kPa, at the start of each instrument cycle, and correct the analyser response
ijk
data for atmospheric pressure according to
P
ref
′
y =× y (4)
ijk ijk
P
ijk
where P is a reference pressure in kPa, such as 101,325 kPa.
ref
Group the calibration data by component and level, y , y , y . Inspect each group for outliers or
ij1 ij2 ijn
stragglers using Grubbs’ test or some other suitable outlier test.
NOTE 1 In any set of data, individual results can be found which are not consistent with the other members
of that set. These are regarded as outliers or stragglers, and can be eliminated from the data set according to the
recommendations of the outlier test used. Inspection of the data is the first stage, identifying problems such as
transcription errors. The order in which tests were carried out is also relevant, since rogue results can arise in
cases where the previous test gas was not fully purged from the system before the first results from a new test gas
[7] [8]
are recorded. More detailed information on statistical outlier tests can be found in ISO 5725-1 , ISO 5725-2
[9]
and ISO 5479 .
After rejection of any outliers, calculate the mean response, y , standard deviations, s , and adjusted
ij ij
numbers of analyses, n for q components, (i = [1, ., q]), and at each of p amount fractions, ( j = [1, ., p]).
ij
For the purposes of this method, an estimate of the standard uncertainty on the mean response for each
component at each level, u(y ), is given simply by the standard deviation of repeat measurements, s .
ij ij
NOTE 2 An estimate of u( y ) using the standard deviation of the mean, where u(y ) = s /√n, would most likely
ij ij ij
underestimate the uncertainty as all measurements were likely not made independently under appropriate
reproducibility conditions.
6.6 Calculation procedures
6.6.1 General considerations
The relationship between component amount fraction and instrument response is found by regression
analysis, using the technique of generalized least squares (GLS) in accordance with ISO 6143:2001,A.2.
This procedure takes account of the uncertainties in both the independent and dependent variables, and
allows calculation of overall uncertainty to include contributions from the uncertainties in the reference
gas compositions, analyser response and the parameters of the response functions resulting from the
regression procedure.
NOTE The advice in this section applies to use of GLS to determine regression functions. For ordinary least
[14]
squares (OLS) methods, a statistical test, for example a sequential F-test should be used to determine the
appropriate order of the polynomial function.
In practice, the response functions are calculated independently in both domains, yielding the true
calibration function, F (x ), and the true analysis function, G (y ).
true i true i
The true calibration function is used in combination with the instrument’s assumed analysis function,
and the working calibration gas composition and uncertainty, to determine performance benchmarks in
terms of errors in measured compositions and properties, together with the uncertainties
...