EN ISO 10723:2002

SLOVENSKI STANDARD
01-december-2002
Zemeljski plin – Vrednotenje zmogljivosti “on-line” analitskih sistemov (ISO
10723:1995)
Natural gas - Performance evaluation for on-line analytical systems (ISO 10723:1995,
including Technical Corrigendum 1:1998)
Erdgas - Bewertung der Leistungsfähigkeit von On-line-Analysensystemen (ISO
10723:1995, einschließlich Technische Korrektur 1:1998)
Gaz naturel - Evaluation des performances des systemes d'analyse en ligne (ISO
10723:1995, Rectificatif Technique 1:1998 inclus)
Ta slovenski standard je istoveten z: EN ISO 10723:2002
ICS:
75.060 Zemeljski plin Natural gas
2003-01.Slovenski inštitut za standardizacijo. Razmnoževanje celote ali delov tega standarda ni dovoljeno.

EUROPEAN STANDARD
EN ISO 10723
NORME EUROPÉENNE
EUROPÄISCHE NORM
September 2002
ICS 75.060
English version
Natural gas - Performance evaluation for on-line analytical
systems (ISO 10723:1995)
Gaz naturel - Evaluation des performances des systèmes Erdgas - Bewertung der Leistungsfähigkeit von On-line-
d'analyse en ligne (ISO 10723:1995) Analysensystemen (ISO 10723:1995)
This European Standard was approved by CEN on 19 August 2002.
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 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 Management Centre has the same status as the official
versions.
CEN members are the national standards bodies of Austria, Belgium, Czech Republic, Denmark, Finland, France, Germany, Greece,
Iceland, Ireland, Italy, Luxembourg, Malta, Netherlands, Norway, Portugal, Spain, Sweden, Switzerland and United Kingdom.
EUROPEAN COMMITTEE FOR STANDARDIZATION
COMITÉ EUROPÉEN DE NORMALISATION
EUROPÄISCHES KOMITEE FÜR NORMUNG
Management Centre: rue de Stassart, 36  B-1050 Brussels
© 2002 CEN All rights of exploitation in any form and by any means reserved Ref. No. EN ISO 10723:2002 E
worldwide for CEN national Members.

CORRECTED 2002-11-13
Foreword
The text of ISO 10723:1995 has been prepared by Technical Committee ISO/TC 193 "Natural
gas” of the International Organization for Standardization (ISO) and has been taken over as
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 March 2003, and conflicting national
standards shall be withdrawn at the latest by March 2003.
According to the CEN/CENELEC Internal Regulations, the national standards organizations of
the following countries are bound to implement this European Standard: Austria, Belgium, Czech
Republic, Denmark, Finland, France, Germany, Greece, Iceland, Ireland, Italy, Luxembourg,
Malta, Netherlands, Norway, Portugal, Spain, Sweden, Switzerland and the United Kingdom.
Endorsement notice
The text of ISO 10723:1995 has been approved by CEN as EN ISO 10723:2002 without any
modifications.
INTERNATIONAL
ISO
STANDARD
First edition
1995-12-15
Natura1 gas - Performance evaluation for
on-line analytical Systems
Gaz na turel - haluation des petformances des systemes d ’analyse en
ligne
Reference number
ISO 10723: 1995(E)
ISO 10723:1995(E)
Contents
Page
1 Scope .
....................... .................. 1
2 Normative references . .
......................... .......... 1
..........................................
3 Principle . . . 2
4 Suitability of analytical Systems
....... ......................................... 2
. . . . . . . . . . . . . . . . . . .*.m.
5 Test gases .I. 3
. . . . . . . . . . . . . . . .
5.1 Definition
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.2 Test gas compositions . . . . . . . . . . . . . . . . . . . . . . .*. 4
6 Test procedures . . . . . . . . . . .
6.1 System efficiency test . .
6.2 Repeatability . . . . . . . . . . . . . .
6.3 Response concentration relationship .
6.4 Component separationlinterference
..................................... 13
7 Evaluation of results . . .
7.1 System efficiency .
................................. 14
7.2 Repeatability . .
................. 14
7.3 Response/concentration relationship
................................... 14
7.4 Component separation/interference
..................................... 15
7.5 Further testing and evaluation . . 15
Annexes
A Example of application using chromatography . 16
B Statistical tests and methods .
..................... 31
C Bibliography . .
..................... 43
0 ISO 1995
All rights reserved. Unless otherwise specified, no part of this publication may be reproduced
or utilized in any form or by any means, electronie or mechanical, including photocopying and
microfilm, without Permission in writing from the publisher.
International Organization for Standardization
Case Postale 56 l CH-l 211 Geneve 20 l Switzerland
Printed in Switzerland
ii
0 ISO ISO 10723:1995(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. Esch 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.
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.
International Standard ISO 10723 was prepared by Technical Committee
ISO/TC 193, Natura/ gas, Subcommittee SC 1, Analysis of natura/ gas.
Annexes A, B and C of this International Standard are for information only.
. . .
Ill
0 ISO
ISO 10723:1995(E)
This International Standard describes a method for evaluating the per-
formante of analytical Systems intended for the analysis of natura1 gas.
Natura1 gas is assumed to consist predominantly of methane, with other
saturated hydrocarbons and non-combustible gases.
Performance evaluation makes no assumptions about equipment for
and/or methodology of analysis, but gives test methods which tan be ap-
plied to the Chosen analytical System, including the method, equipment
and Sample handling.
This International Standard contains an informative annex (annex A) which
Shows the application for an on-line gas chromatographic System which,
as described, is assumed to have a response/concentration relationship for
all components which is represented by a straight line through the origin.
lt contains two additional informative annexes (annexes B and C).

INTERNATIONAL STANDARD 0 ISO ISO 10723:1995(E)
Natura1 gas - Performance evaluation for on-line
analytical Systems
1 Scope
This International Standard specifies a method of determining whether an analytical System for natura1 gas is sat-
isfactory, on the assumptions that
a) the analytical requirement has been clearly and unambiguously defined, for the range and uncertainty of
component concentration measurements, and the uncertainty of properties which may be calculated from
these measurements;
b) the analytical and calibration procedures have been fully described;
c) the method is intended to be applied to gases having compositions which vary over ranges normally found in
transmission and distribution networks.
If the Performance evaluation Shows the System to be unsatisfactory, all the stages, such as
- the analytical requirement;
- the analytical procedure;
- the choice of equipment;
- the choice of calibration gas;
- the calculation procedure;
must be re-examined in the light of the test data to assess where improvements tan be obtained.
This International Standard is applicable to analytical Systems which give the component concentrations and re-
sulting uncertainties. With the present state of knowledge, the method Chosen is likely to be gas chromatography.
Performance evaluation of an analytical System should be performed during installation, then at regular intervals,
according to the application, and/or whenever any critical component of the analytical System is changed or re-
placed.
2 Normative references
The following Standards contain provisions which, through reference in this text, constitute provisions of this
International Standard. At the time of publication, the editions indicated were valid. All Standards are subject to
revision, and Parties to agreements based on this International Standard are encouraged to investigate the possi-
bility of applying the most recent editions of the Standards indicated below. Members of IEC and ISO maintain
registers of currently valid International Standards.

0 ISO
ISO 10723:1995(E)
Preparation of calibration gas mixtures - Weighing methods.
ISO 6142:1981, Gas analysis -
ISO 6974:1984, Natura1 gas - Determination of hydrogen, inert gases and hydrocarbons up to C8 - Gas chro-
ma tographic me thod.
ISO 6976:1995, Natura/ gas - Cakulation of calorific values, density, relative density and Wobbe index from
composition.
ISO 7504:1984, Gas analysk - Vocabulary.
3 Principle
The analytical System is set up according to the instructions so as to carry out the specified compositional analysis.
The effectiveness of the System is demonstrated by analysing test gases with compositions covering a range
rather wider than that for which the System has been specified.
Test gases prepared according to an appropriate Standard are injected into the analyser to test:
the ability of the System to measure the components specified in the analytical method (System efficiency);
a)
the repeatability of measurement of individual components over their specified ranges;
b)
the relationship between response and concentration of individual components over their specified ranges;
d
the absence of interference between components at different concentration ratios.
d)
The tests required for b) and c) above are conducted over intervals of time comparable with the normal period of
use between regular calibrations. Because a number of Parameters which tan influence the analytical Performance
may vary on a day-to-day basis (barometric pressure variations are a case in Point), it is recommended that the
tests be repeated on at least three separate intervals, so that occasional inconsistencies may be recognized.
However, it is acknowledged that there are circumstances (such as testing analysers installed in remote locations)
where only a Single set of tests tan be obtained.
The results of the tests are analysed to assess analyser Performance with respect to bias, repeatability and inter-
ference. The repeatability test b) Shows the random error associated with the measurement of a component and
whether this varies with concentration. The response function c) Shows the likelihood of bias error arising from
different component concentrations in the calibration Standard and Sample; bias tan also result from component
interference d).
Accuracy of measurement is not included in this list, since analytical accuracy is fundamentally and principally
controlled by the accuracy with which the calibration gas composition is known. The procedures described in this
International Standard allow a judgement as to the ability of the analytical method to provide accurate results if
used with an accurate and appropriate calibration gas.
4 Suitability of analytical Systems
The analytical System to be evaluated shall satisfy the following criteria.
The analytical requirement has been carefully defined, for the range and uncertainty of component concen-
tration measurement, or of physical or Chemical property calculation, or of both.
b) The analytical and calibration procedures, whether manual or automated, laboratory or process, have been fully
described, preferably following appropriate interlaboratory testing. Changes in details of the method are not
permissible during the series of tests. If, at the end of the tests, it is clear that the method fails to provide the
desired Performance, it shall be modified suitably and the entire test procedure reapplied.

0 ISO ISO 10723:1995(E)
c) The method is not intended to be applied to gases having composition or physical or Chemical properties that
vary over a wider range than would be acceptable for mixing into a normal transmission or distribution System.
Thus, in practical terms, it is unlikely that the concentration will vary for an individual component by more than
a factor of 20, and the Variation for most components,is likely to be less than a factor of 10.
d) The analytical System shall be capable of measuring, either individually or in groups, all components which are
significant for the analytical requirement. Thus, for the measurement of calorific value, nitrogen, carbon diox-
ide, individual hydrocarbons from C, to C, and a composite C,, are commonly required.
When a number of hydrocarbons are identified and quantified as a group or groups, either the total is reported
NOTE 1
as though the group extends from the lowest carbon number of that group (e.g. Cg+, which indicates all hydrocarbons of
carbon number 6 and above), or separate groups may be reported as the total of each carbon number (e.g. total Cg, total
C7, etc.), or further broken down to component types (e.g. CG alkanes, as distinct from benzene and C, cycloalkanes or
naphthenes).
5 Test gases
5.1 Definition
Test gases are mixtures which are used to evaluate the response of the analyser to individual natura1 gas com-
ponents, so that the measured response tan be compared with the assumed one. They may be multi-component
or binar-y mixtures. In all cases, the matrix gas shall be methane, so that the behaviour of the test gases is as
similar as possible to that of natura1 gases. Binary mixtures tan be prepared with smaller uncertainties than
multi-component ones, but more mixtures must be made, one set for each non-methane component to be tested.
Multi-component mixtures allow more repeats to be performed for each component/concentration combination.
Obviously, similar mixtures tan be used to define the response functions of an analyser when it is initially installed,
in which case they shall be referred to as range calibration gases.
NOTE 2 The analytical method may require that the response functions be defined upon installation, or, in the absence of
such a requirement, the user may choose to establish them. Alternatively, the user may rely on the supplier ’s or manufacturer ’s
assumptions about response function, which is usually that the response to all components is represented by a straight line
through the origin. This latter approach is not likely to take full advantage of the potential accuracy of the method.
There is, of course, n 0 poi nt in defining a mo re CO mplex response function if the data handling System available
with the analyser will not f it response data to such a function.
range calibration gases at a particular time (for example, on Day 1) to define the response, yi, of a
Havi ng used
com ponent i in terms of its concentration, Xi, as:
subsequent analyses allow the concentrations of unknown samples to be calculated as
Xi = gi-
’ (Yi>
Rather than redefine the instrument response to each component for each new period of use, the assumption is
usually made that each response function, gi, remains broadly unchanged, but that it needs the minor adjustment
of a scaling, or calibration factor, which is derived from the regular use of a Single calibration gas. This Single cali-
bration gas would invariably be a multi-component mixture, Chosen to have similar component concentrations to
those anticipated in the unknowns. The scaling or calibration factor, a, is defined as
Response to component i in Single calibration gas on Day 1
a, =
Response to component i in Single calibration gas on Day j
and the concentrations of the unknowns are calculated as

ISO 10723:1995(E)
Xi = Si- ’ (aijmYi>
The frequency with which the Single calibration gas needs to be used is a matter of experience, and instead of
Day 1, we could refer to Hour 1 or Week 1 or Month 1. This frequency shall be defined as part of the analytical
method.
The frequency with which the response function, g, if measured by the User, needs to be re-estab.lished will be
found by applying these test procedures.
From the above, it tan be seen that test gases and range calibration gases could be very similar, if not the Same,
mixtures. When referred to as test gases in this International Standard, they are used to define the up-to-date re-
sponse function, fi which is then compared with the previously established or the assumed function 8.
5.2 Test gas compositions
Test gases shall be Chosen to be suitable for the intended application. However, it is not practicable to make up
test gases which contain all the components in natura1 gas, given the complexity of the higher hydrocarbons which
are commonly found, and the difficulty of preparing high quality mixtures containing condensible components.
or total C, be used. lt is therefore common to use test gases which
Neither tan grouped components, such as C, +
contain only the major components; nitrogen, carbon dioxide, methane, ethane, propane and butane are commonly
used, but any component expected to be present in a concentration greater than 1 % should be included.
Helium, C, and heavier hydrocarbons are usually present at such low concentrations that non-linearity of response
is unlikely to be a Problem. Their repeatability of measurement tan be tested using real natura) gases, ideally with
a range of concentrations appropriate to the application.
The response/concentration relationship shall be tested over the range specified for each component present in
the test gases, and ideally over a slightly greater range. lt is unlikely that a response function more complex than
a third-Order polynomial will be useful and this is satisfactorily defined with seven Points. In those instances where
the range specified for a component is relatively large, it is possible that the repeatability may vary across the
range. For this reason, repeatability testing is carried out with the Same mixtures that are used to evaluate the
response/concentration relationship.
lt is rare that an analyser, however well configured, will measure the sum of components in a natura1 gas to be
exactly 100 %. Consequently, it is common for analysers which have been set up for natura1 gas analysis to nor-
malize the composition data to 100 %, or to some slightly lesser value if there is a small, constant and recognized
contribution from an unmeasured component such as helium. This is based on the obvious premise that a natura1
gas contains 100 % of components, and not some other value. The method should quote limits within which such
normalization would be acceptable; a measured total of between 99 % and 101 % may be deemed to be usual,
with analyses producing wider-ranging totals being rejected. Analytical methods which calculate the methane by
differente do not normalize in this way, but instead forte the total to 100 %, with the calculated methane value
absorbing the errors in all the other component measurements.
Repeatability is influenced by the normalization procedure; normalized data are usually significantly more precise
than unnormalized data. At the same time, normalization allocates the errors involved in the fact that the total does
not resch 100 % or thereabouts between the components pro rata. If the error is produced mainly by one com-
ponent (for example, methane), the normalization process slightly increases the errors for all other components.
This shall be recognized in the procedure. Simplistically, there are two types of error which contribute to totals
other than 100 %, and hence to the need to normalize. The first type affects all components to the Same extent,
and in the case of a gas analyser is typically caused by, among other influences, variations in Sample pressure
within the Sample introduction device. The second type affects components to a different extent, and could be for
example due to random noise, or to variations between the measured and assumed response functions for indi-
vidual components.
The first type tan be compensated for by normalization, but not the second. Furthermore, normalization takes
according to the equation
account of the total calculated composition,

0 ISO ISO 10723:1995(E)
. .
= Txi = zgr ’ (aijmYi)
Unnormalized total
i=l i=l
Consequently, while it might be interesting to use normalized calculated data, or to normalize raw instrument-
response data according to the calculated unnormalised total, this requires assumptions about the response
function, gi, and the short-term calibration factor, au, which are unlikely to be justified at this Stage. The test gases
should be used in circumstances which minimize errors of the first type, such as shutting off the Sample flow
before introduction of the Sample. Only unnormalized data should be used for these tests.
Esch component shall be tested at seven values of concentration. These shall be, so far as possible, equally
spaced across the specified range, and also covering one Point below and one Point above the range. If the lowest
and highest concentrations specified are xL % and xU %, the mixtures should contain:
Mixture Concentration (%)
1 xL - 0,25 (x, - xL)
XL
xL + 0,25 (x, - xL)
$ + 0,5 (x, - XL)
5 XL + 0,75 (X” - XL)
Tl
7 xu + 0,25 (x, - xL)
Achieving these exact values may not always be possible, in which case the nearest practicable concentration
10, the concentration value for mixture 1 would be negative, and so a
should be the aim. Thus if xL = 1 and xu =
value of (0,5x,) % may be Chosen. If xL = 0, mixture 1 may be Chosen to be near the limit of detection, and mixture
2 to be between this value and mixture 3. Similar Problems may occur for methane. The uncertainty with which
these target concentrations are met should be not greater than &- 0,l (xu - xL) %. The uncertainty relating to
knowledge of the exact concentrations achieved should, of course, be significantly smaller than this.
Where multi-component mixtures are to be used, it is unlikely that each one tan be formulated to have a com-
Position similar to that of an anticipated Sample gas, and particular mixtures may contain more propane than
ethane, for example. However methane will always be the major component.
These mixtures shall be prepared or certified by a method whose Overall uncertainty is not greater than that
specified for the analytical System under test, and preferably rather less.
6 Test procedures
6.1 System efficiency test
The analytical System shall be capable of measuring each component for which the method has been specified,
over the expected range of concentrations. lt shall not give false indications for any other components not speci-
fied in the analytical requirement, but which may reasonably be expected to be occasional contaminants in a
Sample. Furthermore, the System should not give any response for specified components in their absence.
The ability of the method to cope with the specified components shall be assessed by analysis of Standard gases
which have been prepared to contain these components at appropriate levels, or of natura1 gases the compositions
of which have been defined by comparison with such Standards. Exact quantitative accuracy is not needed here,
so the methods of preparation may be selected for Speed or convenience.
If the method is configured in such a way that one or more groups of components are measured as a Single
“pseudo-component” or series of “pseudo-components ”, the correct allocation of components to these groups
shall be checked. A typical example would be a recombined (e.g. backflushed) C,, group, consisting of all C, and
ISO 10723:1995(E) 0 ISO
heavier hydrocarbons. The timing of the backflushing Operation shall not allow any C, or heavier components to
fail to be included, nor C, or lighter components to be grouped where they should not be .
The approach to the presence of contaminants in a Sample will vary according to whether or not remedial action
is required. Air is a common contaminant if samples are taken’ for laboratory analysis, and tan be recognized by
the presence of Oxygen. Usually, an analytical method will permit the composition to be recalculated on an air-free
basis, provided that the concentration of air is below a defined value. In this case, the Oxygen shall be measured
with high accuracy, since the adjustment for a given observed amount of Oxygen involves the removal of a cal-
culated amount of nitrogen which is about four times larger. On the other hand, in particular circumstances other
components may be expected to be present at concentrations comparable to those of the C, or C, hydrocarbons,
but their measurement is not required for the purpose for which the analysis is performed. In this case, it shall
be established whether or not the contaminant interferes with measurement of any of the expected components,
and if so, how large an effect is Seen.
Any response for a component in its absence tan be tested by a blank experiment, which simulates all the ac-
tivities of the analytical System. Thus, in the case of a chromatographic method, injection of carrier gas instead
of Sample gas would be appropriate.
Any detecta ble response at this Stage should, if possible, be eliminated by suitable adjustment of the method.
Otherwise, it will impose a fixed bias error on the response/concentration relationship.
6.2 Repeatability
Repeatability is often measured as that of instrument response; the Standard deviation of peak area counts in the
case of a chromatographic method. This measurement cannot be used in isolation for two reasons. The mean and
Standard deviation of a normally distributed (Gaussian) set of data are measures such that 67 % of all the data
Points lie within + 1 Standard deviation of the mean; thus, while the Standard deviation is a convenient measure
-
to use while assessing error contributions, it shall be converted at the end of the calculations to a value which
more nearly describes what we understand by repeatability (see clause 8.4). Also, a typical analytical result is de-
rived using a relationship of the type
& = y;td x -%td
is the concentration in unknown (Sample);
%
is the response to unknown (Sample);
Ys
is the response to Standard;
%td
is the concentration in Standard.
Ystd
Consequently, the repeatability of the result is influenced by the repeatability of both the unknown and of the
Standard. Uncertainty associated with the calibration gas Standard also contributes, but is outside the scope of this
International Standard. The evaluation procedure assesses the ability of the analytical System to provide high
quality data, if used with a calibration Standard which has a weil-known composition and is appropriate for the
application. The quality of such calibration Standards is properly dealt with in other International Standards.
The repeatability of measurement of a component may be uniform over the expected concentration range, or it
may vary as a function of concentration. Figure 1 illustrates the former Situation, where the Gaussian curves
superimposed on the response/concentration plot represent the repeatability distribution, which tan be seen to
be uniform across the range.
Figure2 Shows a plot where the repeatability increases with concentration. The Iikelihood of any particular
measurement Point deviating from the plotted line is indicated by the width of the Gaussian curve in that region.
of behaviour is important, so that the repeatability for different components
The differente between these forms
pressed appropriately.
at different concentrations may be ex

ISO 10723:1995(E)
I
Component (%)
Actuat curve
Figure 1 - Uniform repeatability
4 6 12 14 16
0 1 2 8 10
Component 1%)
Actual curve
Figure 2 - Variable repeatability
6.2.1 Calibration interval
For the purpose of this test, the calibration interval is defined as that period of time during which the analytical
System would normally be used between recalibrations. Experience will show over how long a period an instru-
ment may be judged to be stable, and hence what the recalibration frequency should be. A laboratory instrument
may be used throughout the working day after having been calibrated first thing in the morning, or may require
separate calibrations for the morning and afternoon. A process analyser may operate for 24 h a day with automatic
recalibration at midnight. lt is important that one set of tests is conducted within one calibration interval and that
they are spaced uniformly throughout it. The longer the calibration period, the longer the time for one set of tests.
0 ISO
ISO 10723:1995(E)
6.2.2 Procedure
Calculate the number of analyses that tan be performed within the calibration interval and then analyse the seven
concentration levels, using a random sequence, as many times as possible. Five repeats at each level will usually
give statistically useful data. (lt is hardly practicable to exceed 10 repeats at each level: this implies 10 x 7 = 70
analyses during the calibration interval.)
Where possible, repeat this set of tests so as to have at least three sets of results, each ac during a different
calibration interval.
For each of e components (i = [l, e]), at each of seven concentration Ievels 0’ = [l, .-, 7]), performf repeat
. . . .
fl) during each of g calibration intervals (I = [1, . . . .
analyses (k = [l, . . . . g]). Record each analyser response,
yjjkl, together with the component concentration, xij, which generated it.
Group the results by component and level from within one calibration interval, yijll, yij21, etc. Inspect each group
for outliers or stragglers using Grubbs’ test or some other suitable outlier test (see annex B). After rejection of
any outliers, calculate the means, yijl, Standard deviations, sijl, and adjusted numbers of analyses, n,,.
Where tests have been performed during different calibration intervals, compare the precision of sets of results
between the calibration intervals sijll sij2, . . . . sijg, by Cochran ’s test (see annex B). If any group of results is shown
to be significantly less precise than the others, the reason for this shall be investigated. In the absence of a clear
reason, and one which would be expected to be evident in normal use, the tests shall be repeated.
Assuming that each component at each level Shows uniform precision between the calibration intervals, a com-
bined mean and Standard deviation tan be derived. The mean, yij, is calculated as
l=g
Yijlmnijl
c
i=l
Yij =
[= g
nijl
c
l=l
The combined Standard deviation, sij, is calculated as
If, in the examination of error structure (see 6.3.11, the Standard deviation, sij, appears to be independent of the
concentration, xj, a combined Standard deviation, Si, covering the full concentration range for component i, tan be
calculated from the Standard deviations at each level, sij, and the total number of measurements at each level
across all the calibration intervals, nij:
j=7
xCnij - 1) ‘(sijJ2
j=l
j=7
nq - 1
c
j=l
0 ISO ISO 10723:1995(E)
If there is a dependence of Standard deviation on concentration, it tan be expressed as
= a + b-Xi + cmxi
si
or
= a + bmxi + C-X~ + d-xl!
si
where a, b, c and d are the coefficients of linear regression of sij on xij. The indication as to which polynomial to
use is made in the Same way as for the response/concentration relationship described below. The choice of
polynomial should take into account this indication, but also a reasonable interpretation of how the Standard devi-
ation might be expected to vary with concentration. A second-Order polynomial tan, within the range tested,
contain a maximum or a minimum; a third-Order tan contain both. If such a maximum or minimum is Seen, the
higher Order polynomial should be rejected if it is reasonable to assume that the relationship should be monotonic,
i.e. continuously increasing or decreasing, though not necessarily following a straight line.
The Standard deviation, s(xi), of the amount of a component, Xi, is calculated from the Standard deviations of the
the Sample and from the Standard, using the equation
responses due to that component from
[ sy ’- [BI ’+ [*
where
yis and Yistd are the instrument responses to component i in the Sample and Standard;
s(yis) and S(Yistd) are the respective Standard deviations.
Standard deviations of component amount are calculated for a number of gas compositions across the anticipated
range. The rigorous way of calculating the repeatability of component measurement, Y(Xi), is
Y(Xi) =t 2S(Xi)
J-
where
t is taken from the two-sided t-table at the 5 % level with the number of degrees of freedom appropriate
to whether the Standard deviation has been found to be uniform ( = Cnij - 1) or a function of concen-
j
tration ( = Cngl - 1);
2 reflects the fact that repeatability is the differente between two Single measurements.
Ir
However, the confidence interval for the Standard deviation is likely to be so wide that such nice distinctions are
unjustified, and the repeatability tan in all cases be expressed as
r(i) = 2,8s(xi)
Compare the repeatability of measurement for each component with the analytical requirement.
6.3 Response concentration relationship
Use of the test gases defines the relationship between the concentration of a component, Xi, and the response
t0 it, yi, as
Yi =fi(xi>
This relationship tan then be used to calculate the concentration of component in a Sample, Xi, within the range
tested using the equation
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xj = .ij - ’ (Yi)
<
If, in fact, the analytical System assumes that a different response characteristic, for example JQ = gi(xi), is obtained,
an error will be introduced which depends on the differente between the functionsh and gi, and on the differente
in concentration of component i between calibration gas and Sample.
The scale of the direct measurement error may be calculated using the equation
Ei=gl--’ [ “i(;;;z;J ] -xis
as the amounts of component in the Standard and Sample
and therefore tan be seen to tend towards zero either
converge (Xis- ‘Xistd) , or as functions& and gi converge.
Most analytical Systems assume that gi(xi) = constant=+ This is the equation of a straight-line plot through the
origin, and justifies Single-Point calibration, as only the constant needs to be defined. In this case, the error de-
pends on how close the true response function,$$ is to a straight line through the origin, and on the differente
between Standard and Sample concentrations.
This is illustrated in figure3. The solid line Shows a response curve which deviates somewhat from a straight Iine.
The two broken lines are straight lines through the origin, coinciding with the actual curve at 8 % and 15 % re-
spectively. The area between the broken Iines Shows the area of uncertainty, depending upon whether an 8 %
or a 15 % calibration Standard is used.
If the resulting error is small by comparison with other variations (e.g. the repeatability), it may be acceptable.
Otherwise, the response curve tan be used for quantitative purposes, usually in a subsequent data-handling Stage.
Even this is not completely satisfactory, because to define the shape of the curve is time-consuming, and therefore
not likely to be rechecked very frequently. The most satisfactory outcome shall be confirmation of the straight line
through the origin.
Regression analysis is applied to the data generated in 6.2.2 from the mixtures containing the seven component
levels. A judgement is made as to whether a first-Order (i.e. a straight line), second-Order, or third-Order polynomial
represents the “best fit ”.
-
\o
x--
25 25
v:
c
E
kc 20
CY
0 5
10 15
Component(%)
-W---W---------B 8 Yo Line
Actual curve
- - - - - 15 % line
Figure 3 - Response curve/straigth lines
IO
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6.3.1 Examination of error structure
Normal regression analysis assumes that errors in measurement
a) are independent;
have a zero mean;
b)
d have a constant variance;
are normally distributed.
d
In analytical methods for natura1 gas, assumption c) may not always be true. Considering the repeatability error,
it is likely to be constant for methane over a range 75 % to 95 %, but may weil vary for ethane over a range 1 %
to 10 %. Rigorously, the approach to determination of the response function by regression analysis depends upon
whether the errors are constant or vary across the range, and consequently whether the data should be used di-
rectly or weighted. In fact, the equation of the line is influenced only marginally according to whether weighted
or unweighted regression is used; the differente Shows in the associated uncertainties when values are calculated
from the regression equation. Only the equation of the response function is required in this subclause, and so
weighting of data is not necessary.
6.3.2 Regression analysis
The aim is to decide whether the relationship between response and concentration of a component is best de-
scribed by a polynomial function of
- first Order
or
- second Order
= a + hmXi + C ’Xi
Yi
or
- third Order
yi = a + bmxi + CgXl' + dgx[’
(If none of these functions gives a good fit to the data, then the instrument response is more complex than would
normally be considered to be useful for accurate analysis. Although complicated response characteristics tan be
accounted for by a good data System, System accuracy inevitably deteriorates with increasingly complex algo-
rithms.)
Two procedures are described in annex B, orthogonal polynomials and backwards elimination by the sequential
F-test. Orthogonal polynomials differ from conventional polynomials (as above) in that the coefficients describe the
mean height or centre of gravity of the x data, the mean slope of the line, the mean curvature, etc. The coefficients
are therefore independent of each other, and tan be tested simultaneously. The sequential F-test uses data from
an ANalysis Of VAriance (ANOVA) table, and tests each highest conventional coefficient in turn to judge whether
it offers a more significant improvement in fit than the polynomial of the next lower Order.
6.3.3 Stalle of error
Any error resulting from the concentration/response relationship will be a bias which depends, as described above,
upon the differente between the measured relationship and that assumed as part of the analytical method, and
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upon the differente between component concentrations in th,e Standard and Sample. If the method requires that
the results be normalized, a further error will be introduced as a result of this procedure.
The significance of this depends on the analytical procedure and on the component. If the only component dis-
playing bias error is methane, the effect of normalization is to remove most of this error. This is not likely to be
the case for other components, and the effect on their final value depends both on their own bias and on that for
methane.
For each component, i, the response has been shown to be of the form yi =J(xi), where the function f is a first-,
second- or third-Order polynomial. This is the “true” response function. A different response function, yi = Ei,
may be claimed by the supplier of the analyser, or have been established in a previous evaluation. In the absence
of any such information, the function may be taken to be of the form yi = constan+, which is the equation of a
straight line through the origin; the constant may be assumed, initially at least, to have the value b, the polynomial
coefficient Of Xi*
Consider particular values for component concentrations in a Standard and a Sample, Xistd and Xis. These are Iikely
to be the preferred or recommended value for the Standard, and one extreme of Sample composition. The
“true” and assumed responses of the calibration Standard, yt+id and yaiStd, would be
Ytistd = A cXistd)
In fact, with Single Point calibration, the only information available is the concentration of and response to the
Standard. Two different responses for the Standard are not possible, so a coefficient, ki, is calculated such that
The coefficient, ki, performs the regular calibration role of re ating response to concentration at the value of the
Standard.
The assumption is now made that this relationship extends to the Sample, i.e.
Y* 1s = kimgi Cxis>
and so the Sample concentration, x ’is, is calculated as
= gi- ’ (kl ’ n yis)
“is
xlis=gi-l [ giyd~~s~ ]
For each component present in the test gases, set xis in turn to the lowest and highest value anticipated by the
to the recommended value for the calibration gas. Calculate xjs and the error Ei = x ’is - xis.
method, and Xistd
NOTE 3 The inverse g- ’ of the function g cannot always be found. In the case of a first-Order polynomial
y=a+bx
the inverse is
X= y-a
h
For a second-Order polynomial
y = a + bx + cx*
the inverse is
-
h+j/b * - 4(a - y)c
xzz -
2c
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ns will fall w ithin the range of interes t. (If both solutions fall within the range, the res Ponse function
to which one of the solutio
or a mt nrmum withi n the working range in s uch a way as to be unusable.
Shows a maxrmum
A third-Order polynomial
= a + bx + c2 + dx3
Y
does not permit
...