SIST EN ISO 15796:2008

SLOVENSKI STANDARD
01-oktober-2008
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Gas analysis - Investigation and treatment of analytical bias (ISO 15796:2005)
Gasanalyse - Untersuchung und Behandlung von systematischen Abweichungen (ISO
15796:2005)
Analyse des gaz - Investigation et traitement des biais analytiques (ISO 15796:2005)
Ta slovenski standard je istoveten z: EN ISO 15796:2008
ICS:
71.040.40 Kemijska analiza Chemical analysis
2003-01.Slovenski inštitut za standardizacijo. Razmnoževanje celote ali delov tega standarda ni dovoljeno.

EUROPEAN STANDARD
EN ISO 15796
NORME EUROPÉENNE
EUROPÄISCHE NORM
August 2008
ICS 71.040.40
English Version
Gas analysis - Investigation and treatment of analytical bias
(ISO 15796:2005)
Analyse des gaz - Investigation et traitement des biais Gasanalyse - Untersuchung und Behandlung von
analytiques (ISO 15796:2005) systematischen Abweichungen (ISO 15796:2005)
This European Standard was approved by CEN on 30 July 2008.
CEN members are bound to comply with the CEN/CENELEC Internal Regulations which stipulate the conditions for giving this European
Standard the status of a national standard without any alteration. Up-to-date lists and bibliographical references concerning such national
standards may be obtained on application to the CEN Management Centre or to any CEN member.
This European Standard exists in three official versions (English, French, German). A version in any other language made by translation
under the responsibility of a CEN member into its own language and notified to the CEN Management Centre has the same status as the
official versions.
CEN members are the national standards bodies of Austria, Belgium, Bulgaria, Cyprus, Czech Republic, Denmark, Estonia, Finland,
France, Germany, Greece, Hungary, Iceland, Ireland, Italy, Latvia, Lithuania, Luxembourg, Malta, Netherlands, Norway, Poland, Portugal,
Romania, Slovakia, Slovenia, Spain, Sweden, Switzerland and United Kingdom.
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EUROPÄISCHES KOMITEE FÜR NORMUNG
Management Centre: rue de Stassart, 36  B-1050 Brussels
© 2008 CEN All rights of exploitation in any form and by any means reserved Ref. No. EN ISO 15796:2008: E
worldwide for CEN national Members.

Contents Page
Foreword.3

Foreword
The text of ISO 15796:2005 has been prepared by Technical Committee ISO/TC 158 “Analysis of gases” of
the International Organization for Standardization (ISO) and has been taken over as EN ISO 15796:2008 by
Technical Committee CEN/SS N21 “Gaseous fuels and combustible gas” the secretariat of which is held by
CMC.
This European Standard shall be given the status of a national standard, either by publication of an identical
text or by endorsement, at the latest by February 2009, and conflicting national standards shall be withdrawn
at the latest by February 2009.
Attention is drawn to the possibility that some of the elements of this document may be the subject of patent
rights. CEN [and/or CENELEC] shall not be held responsible for identifying any or all such patent rights.
According to the CEN/CENELEC Internal Regulations, the national standards organizations of the following
countries are bound to implement this European Standard: Austria, Belgium, Bulgaria, Cyprus, Czech
Republic, Denmark, Estonia, Finland, France, Germany, Greece, Hungary, Iceland, Ireland, Italy, Latvia,
Lithuania, Luxembourg, Malta, Netherlands, Norway, Poland, Portugal, Romania, Slovakia, Slovenia, Spain,
Sweden, Switzerland and the United Kingdom.
Endorsement notice
The text of ISO 15796:2005 has been approved by CEN as a EN ISO 15796:2008 without any modification.

INTERNATIONAL ISO
STANDARD 15796
First edition
2005-03-01
Gas analysis — Investigation and
treatment of analytical bias
Analyse des gaz — Investigation et traitement des biais analytiques

Reference number
ISO 15796:2005(E)
©
ISO 2005
ISO 15796:2005(E)
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ii © ISO 2005 – All rights reserved

ISO 15796:2005(E)
Contents Page
Foreword. iv
Introduction . v
1 Scope. 1
2 Terms and definitions. 1
3 Symbols. 3
4 Bias related to instrumental drift. 4
4.1 Principle. 4
4.2 Stability monitoring. 4
4.3 Drift correction. 6
5 Bias related to effects of sample composition . 10
5.1 Principles. 10
5.2 Local bias handling. 11
5.3 Bias handling for an extended measuring range . 23
6 Treatment of matrix interferences. 27
Annex A (normative)  Critical values for the trend test . 29
Annex B (informative) Uncertainty issues . 30
Bibliography . 33

ISO 15796:2005(E)
Foreword
ISO (the International Organization for Standardization) is a worldwide federation of national standards bodies
(ISO member bodies). The work of preparing International Standards is normally carried out through ISO
technical committees. Each member body interested in a subject for which a technical committee has been
established has the right to be represented on that committee. International organizations, governmental and
non-governmental, in liaison with ISO, also take part in the work. ISO collaborates closely with the
International Electrotechnical Commission (IEC) on all matters of electrotechnical standardization.
International Standards are drafted in accordance with the rules given in the ISO/IEC Directives, Part 2.
The main task of technical committees is to prepare International Standards. Draft International Standards
adopted by the technical committees are circulated to the member bodies for voting. Publication as an
International Standard requires approval by at least 75 % of the member bodies casting a vote.
Attention is drawn to the possibility that some of the elements of this document may be the subject of patent
rights. ISO shall not be held responsible for identifying any or all such patent rights.
ISO 15796 was prepared by Technical Committee ISO/TC 158, Analysis of gases.

iv © ISO 2005 – All rights reserved

ISO 15796:2005(E)
Introduction
Traceability is considered as one of the key items of quality assurance in gas analysis. In general, it is defined
by the existence of unbroken chains of comparisons, relating the analytical result to acknowledged standards
of measurement. More specifically, an analytical result is considered traceable if, by way of these
comparisons, it has been demonstrated to be free of significant bias, significance referring to the specified
uncertainty of the result.
As a rule, traceability is not demonstrated individually for a single analytical result but for a defined analytical
procedure with specified ranges of analyte concentration and matrix composition. An analytical procedure is
considered traceable if it has been demonstrated to be free of significant bias, or if significant bias has been
corrected, by measurement on representative samples of known traceable composition. These may be
samples of appropriate reference gas mixtures. Alternatively, other representative samples may be analysed
in parallel using an accepted reference procedure.
This International Standard provides generic methods for demonstrating, or establishing, traceability of
analytical procedures using reference gas mixtures or reference analytical procedures, implementing
[1] [2]
principles laid out in ISO 14111 and ISO/TS 14167 , and respecting the principles of the Guide to the
[3]
Expression of Uncertainty in Measurement (GUM) .
In this International Standard, the term “concentration” is used for two different purposes:
 as a general term for quantities measured in gas composition analysis, replacing the term “content” (see
[4]
ISO 7504 );
 as a generic substitute for any of the specific quantities measured in gas composition analysis such as
[4]
the mass concentration or the mole fraction of a specified analyte (see ISO 7504 ).

INTERNATIONAL STANDARD ISO 15796:2005(E)

Gas analysis — Investigation and treatment of analytical bias
1 Scope
This International Standard specifies generic methods for detecting and correcting bias (systematic errors) of
analytical procedures for the analysis of gases, using reference gas mixtures or reference analytical
procedures, as well as for estimating the correction uncertainty.
The main sources of (and parameters affecting) bias of analytical procedures are instrumental drift (time) and
matrix interferences (matrix composition). Moreover, bias normally varies with analyte concentration. This
International Standard therefore establishes protocols for
 detecting and correcting drift for an analytical system of limited stability,
 investigating and handling bias of a stable analytical system for a specified range of sample composition,
which are intended to be used in method development and method validation studies, either separately or
sequentially.
This International Standard specifies procedures for two options, applicable to systematic effects, as follows:
a) tracing the observed pattern of deviations and correcting for their effect,
b) averaging over their effects and increasing the uncertainty,
where normally the first option entails lower uncertainty at the expense of higher effort.
For the convenience of the user, the methods specified in this International Standard are described for
procedures of composition analysis, i.e. procedures for measuring the concentration of a specified analyte in a
gas mixture. However, they are equally applicable to measurements of physico-chemical properties of a gas
or gas mixture relevant to gas analysis, and translation into this subject field is straightforward.
2 Terms and definitions
For the purposes of this document, the following terms and definitions apply.
2.1
bias
estimate of systematic error
NOTE Since the true value of a measurand cannot be known exactly, systematic errors cannot be determined exactly
but have to be estimated using reference values.
2.2
correction
procedure by which the uncorrected result of a measurement is adjusted to compensate for systematic error
NOTE 1 Since systematic errors cannot be determined exactly, a correction can never be complete.
[5]
NOTE 2 In the VIM , the term correction is used with a different meaning.
ISO 15796:2005(E)
2.3
uncertainty
parameter, associated with the result of a measurement, that characterizes the dispersion of the values that
could reasonably be attributed to the measurand
[3]
[GUM:1993 , definition 2.3.2]
2.4
traceability
property of the result of a measurement or the value of a standard whereby it can be related to stated
references, usually national or international standards, through an unbroken chain of comparisons
[5]
[VIM:1993 , definition 6.10]
[1]
NOTE In ISO 14111 , the term traceability is defined as the ability to provide evidence of the overall accuracy
attributed to measurement results through documented calibrations, using measurement standards of known accuracy
and comparison measurements of known performance.
2.5
reference value
estimate of a quantity, with sufficiently well established traceability and specified uncertainty, used as a
reference for a specified purpose
NOTE In gas analysis, reference values of composition or physico-chemical properties are most often provided by
reference gas mixtures and reference analytical procedures.
2.6
reference gas mixture
calibration gas mixture whose composition is sufficiently well established and stable to be used as a reference
standard of composition from which other composition data are derived
[4]
[ISO 7504:2001 , definition 4.1.1]
2.7
reference analytical procedure
analytical procedure which is capable of providing traceable results with sufficiently well established
uncertainty for use as reference values
2.8
drift
slow change of output, at constant input, of a measuring system
2.9
stability
〈of a measuring system〉 absence of significant drift
2.10
matrix interference
change in analytical response for a specified analyte, caused by variations in matrix composition
2 © ISO 2005 – All rights reserved

ISO 15796:2005(E)
3 Symbols
A, B specified drift-control mixtures
b parameters of a bias correction model
i
δ deviation (from a reference value)
I interferent under consideration
M gas mixture under consideration
m, n, N number of data in a data series
p number of correction parameters
Q recovery (with respect to a reference value)
r number of reference gas mixtures used for bias investigation
R reference gas mixtures used for bias investigation
i
s standard deviation of a data series
s relative standard deviation of a data series (coefficient of variation)
r
s variance of a data series
t time
u(x) standard uncertainty of an estimated quantity x
u (x) variance of an estimated quantity x
u (x) relative standard uncertainty of an estimated quantity x
r
u(x, y) covariance between two estimated quantities x and y
x, y quantity under consideration
〈x〉 mean value of several quantities x
i
X analyte under consideration
∆ mean-square successive difference of a data series
ISO 15796:2005(E)
4 Bias related to instrumental drift
4.1 Principle
This clause specifies procedures for investigating potential drift of an analytical system and taking corrective
actions, if significant drift is encountered.
If the analytical system is expected to be stable, a “drift-control mixture” is measured on a regular basis. For
each specified analyte, the results are recorded on a control chart, and the time series of control data is
examined continuously. As long as these data vary at random within established control limits, the analytical
system has been demonstrated to be stable. Monotonic decrease or increase in control data indicates drift. As
an alternative to visual inspection, a statistical test based on successive differences may be used to detect a
significant trend. As soon as drift becomes significant, e.g. when data exceed control limits, or when a
significant trend is observed, the analytical system is removed from service. After adjustment and re-
calibration, the analytical system is returned to service.
The “drift-control mixture” should contain all analytes currently being measured. Given sufficient information
on the response behaviour of the analytical system, a representative subset of analytes may be used.
If the analytical system is known to exhibit significant drift, it can at least be expected that the drift behaviour of
the system does not significantly depend upon sample composition, since this would allow for drift correction
based on measurements of appropriate “drift-correction mixtures”. This expectation is tested by analysing two
mixtures of distinct composition (different concentrations of the analytes under consideration, different matrix
compositions) on a regular basis. The results are recorded, and for each analyte the two time-series of drift
measurement data are compared in order to investigate whether drift behaviour can be expressed in a
concentration-invariant manner. Given this for every analyte under consideration, the two time-series for each
analyte are pooled to derive a drift correction. In fortunate cases, a joint drift correction may be used for
several or even all analytes.
If the system exhibits significant drift, and if moreover drift characteristics depend upon concentration, drift
correction needs to be integrated with calibration. This topic is beyond the scope of this International Standard.
4.2 Stability monitoring
4.2.1 General considerations
A drift-control mixture is required which is typical of the gases for which the analytical procedure is used. The
composition of the mixture shall be stable, but the concentration of the specified analytes used for stability
monitoring does not have to be established in advance with high accuracy.
An analysis of the drift-control mixture should be carried out with each batch of samples. Its composition is
unvarying so the results of this analysis can be used as an indication as to whether the procedure is no longer
working satisfactorily or re-calibration of the instrument is necessary, or both.
Stability can be monitored using either concentration data or the corresponding response data.
4.2.2 Use of Shewhart control charts
Before first use, the drift-control mixture is analysed at least 10 times in order for precision data to be
calculated. For each specified analyte in the drift-control mixture, the mean concentration (or response) and its
standard deviation are calculated. If the within-day standard deviation is less than the between-day standard
deviation, then these precision data need to be collected one a day for 10 days.
For each specified analyte in the drift-control mixture, a control chart is constructed with points marked on the
Y-axis representing
a) the mean concentration (or response),
4 © ISO 2005 – All rights reserved

ISO 15796:2005(E)
b) the mean ± 1 standard deviation,
c) the mean ± 2 standard deviations (warning limits), and
d) the mean ± 3 standard deviations (action limits).
Lines parallel to the X-axis are drawn from these points. Each time the drift-control mixture is analysed, the
value is plotted using the X-axis as a time scale. As more information becomes available the means and
standard deviations can be updated. This assumes that the analytical system has remained stable. Data
which clearly indicate some fault shall not be used to revise the control limits.
The plotted values from the analysis of the control gas are compared with the mean value and the ± 1, ± 2 and
± 3 standard deviation lines. It is assumed that the composition of the drift-control mixture is stable and that
the analytical results for this follow the normal distribution. If this is true, then while the system is behaving
normally, any individual results for the components of the drift-control mixture may fall outside the warning
limits on 1 occasion in 20. This means that if individual results fall outside the warning limits more than just
occasionally, this can indicate that either there is a systematic tendency for the results to be too high (or too
low) or the random error for measurement of that component has increased. Likewise, individual results may
fall outside the action limits on 3 occasions out of 1 000.
[6]
ISO 8258 contains the following tests which can be used for indicating the presence of variation:
 one point exceeding ± 3 standard deviations;
 nine points in a row on one side of the mean;
 six points in a row steadily increasing or decreasing;
 fourteen points in a row alternating up and down;
 two out of three points in a row exceeding +2 standard deviations or −2 standard deviations;
 four out of five points in a row exceeding +1 standard deviation or −1 standard deviation;
 fifteen points in a row above and below the mean, but not exceeding ± 1 standard deviation;
 eight points in a row above and below the mean, but all exceeding ± 1 standard deviation.
If any of these tests indicates the presence of variation, then that shall be diagnosed and corrected. If this
investigation indicates that there is no fault with the measuring procedure, then re-calibration of the instrument
is required.
4.2.3 Statistical trend test
As an alternative to monitoring monotonic increase or decrease, drift-control data may be investigated for
trends using a statistical test based on successive differences. Given a time-series of drift-control data x , x ,
1 2
…, x with mean value 〈x〉, the mean-square successive difference ∆ is determined according to
N
22 2 2

∆=−()xx +(x−x)+.+(x −x)/(N−1) (1)
12 2 3 NN−1

This quantity is compared with the variance s given by
22 2 2

sx=()−〈〉x +(x −〈〉x) +.+(x −〈x〉)/(N−1) (2)
12 N

ISO 15796:2005(E)
2 2
If successive values in the series are independent (and moreover from a normal distribution), then ∆ ≈ 2 s . In
2 2
case of a trend ∆ < 2 s because successive values are closer than to be expected for values drawn at
random from a normal distribution.
2 2
For a significance test, the test statistic ∆ /s is compared with the critical value for the specified length N of
the series under investigation and the specified significance level. Values of the test statistic below the critical
value indicate a significant trend. In this International Standard a significance level of 95 % or 99 % is
recommended. Critical values for these significance levels are given in Table A.1, Annex A.
EXAMPLE Consider a series of drift-control data (carbon monoxide in nitrogen, expressed in mmol/mol): 1,28; 1,30;
2 −4
1,30; 1,28; 1,26; 1,24; 1,27; 1,27; 1,24; 1,26. For these data the mean-square successive difference ∆ is 38 × 10 /9,
2 −4 2 2
while the variance s is 40 × 10 /9. Hence the test statistic ∆ /s takes a value of 0,95. For N = 10, the critical value is
0,751 8 for a significance level of 99 % and 1,062 3 for a significance level of 95 %. Therefore, under the assumptions of
independence and normality, the drift-control data exhibit a significant trend on the 95 % level, while the trend is not
significant at the 99 % level.
Consider now the modified data series generated by interchange of the 3rd and 9th datum: 1,28; 1,30; 1,24; 1,28; 1,26;
2 −4
1,24; 1,27; 1,27; 1,30; 1,26. For these data, the mean square successive difference ∆ is now 98 × 10 /9, while the
2 −4 2 2
variance s still is 40 × 10 /9. Hence the test statistic ∆ /s takes a value of 2,45 which means that the modified data
series does not exhibit any indication of drift, under the above assumptions.
For stability monitoring based on regular drift-control measurements, a moving window comprising 10 to 20
data is recommended.
If any of these tests indicates the presence of variation, then that shall be diagnosed and corrected. If this
investigation indicates that there is no fault with the measuring procedure, then re-calibration of the instrument
is required.
4.3 Drift correction
4.3.1 General considerations
This clause specifies a general method for post-processing analytical data to correct for instrumental drift. For
this purpose an analytical system is treated as a “black box”. Here the input is the value of the measurand, i.e.
the (true) concentration of the analyte under consideration in the analysed sample, and the output is the
measured value of this analyte concentration.
This clause is applicable for absolute methods, i.e. analytical methods where analyte concentration is
determined directly, or relative methods where the relationship between measured response and analyte
concentration is known. It is also applicable for comparison methods, i.e. analytical methods where the
relationship between measured response and analyte concentration is determined empirically by calibration.
Two drift-correction mixtures are required which are typical of the gases for which the analytical procedure is
used. Each analyte to be determined by the procedure shall be present in both mixtures, at different levels
bracketing an appropriate concentration range. The composition of the mixtures shall be stable, and the
concentration of the analytes used for drift investigation shall be known with specified uncertainty.
4.3.2 and 4.3.3 specify two complementary approaches, based on additive and multiplicative drift modelling
respectively. Usually only one or neither of these procedures will work. If in a particular case both approaches
work, the one with the better performance, i.e. with lower correction uncertainty, should be used.
NOTE 1 For an analytical comparison method, drift correction is sometimes better performed using measured
responses instead of analyte concentrations.
NOTE 2 Using reference gas mixtures for drift control has the advantage of providing an “absolute” drift correction, i.e.
relative to reference values of analyte concentration. As an alternative, less well-characterized gas mixtures could be used
for drift correction relative to analyte concentrations measured at a specified time t . The latter approach would, in addition,
require a proof of stability of the drift-control mixtures. Secondly, the concentrations measured at t would have to be
investigated for bias in a later stage.
6 © ISO 2005 – All rights reserved

ISO 15796:2005(E)
4.3.2 Additive drift correction
In this subclause, instrumental drift is presented as an additive bias according to Equation (3):
xt =+x δ x,t (3)
( ) ( )
where
x(t) is the measured concentration of the analyte under consideration at time t,
x is the true analyte concentration,
δ (x,t) is the bias at analyte level x, due to drift at time t.
If, for a given analyte, this bias should be the same for different levels of analyte concentration, it can be
corrected by determining the bias obtained on a sample with known concentration of the analyte as a function
of time, and subtracting the applicable bias from the results obtained on other samples.
To this end, the concentrations of two mixtures (called A and B) as specified above are measured on a regular
basis, and the time-series of results are recorded. For the given analyte, these are x , x , …., x and x ,
A1 A2 AN B1
x , …., x . The two time-series are smoothed by interpolation or regression, yielding two curves (or
B2 BN
functions) x (t) and x (t). Given concentration-invariant additive bias for that analyte, these curves should be
A B
parallel, with a distance of x (t) − x (t) = x − x where x and x are the reference values given for
A B A,ref B,ref A,ref B,ref
mixture A and B.
If this is true (within experimental variability) the differences x − x and x − x are pooled and the
Ai A,ref Bi B,ref
combined time-series is smoothed yielding a curve (or function) δ (t). This curve is then used to correct the
result obtained on another mixture M at any time t within the period covered according to
xx=−t δt (4)
( ) ( )
MM
The standard uncertainty of the corrected result is determined by
22 2
ux=+ux t uδt (5)
( ) () ()
MM
  
In this uncertainty budget, the first term is obtained from the uncertainty budget of the analytical procedure.
The second term is estimated from the residual scattering of the pooled differences used to determine the
correction curve δ (t). In addition, the uncertainty contributions of the drift measurements and the composition
of the drift-correction mixtures are included if significant.
If bias corrections should be approximately the same for different analytes, then a joint correction may be
derived for a group of such analytes from pooled time-series.
4.3.3 Multiplicative drift correction
In this subclause, instrumental drift is presented as a recovery factor according to Equation (6):
xt() =Q x,t x (6)
( )
where
x(t) is the measured concentration of the analyte under consideration at time t;
x is the true analyte concentration;
Q(x,t) is the recovery factor at analyte level x, due to drift at time t.
ISO 15796:2005(E)
If, for the given analyte, this recovery factor should be the same for different levels of analyte concentration, it
can be corrected by determining the recovery on a sample with known concentration of the analyte as a
function of time, and dividing the results obtained on other samples by the applicable recovery factor.
To this end, two mixtures (called A and B) as specified above are measured on a regular basis, and the time
series of results are recorded. For the given analyte , these are x , x , …., x and x , x , …., x . The
A1 A2 AN B1 B2 BN
two time-series are smoothed by interpolation or regression, yielding two curves (or functions) x (t) and x (t).
A B
Given concentration-invariant recovery for that analyte, these curves should be proportional, with a
proportionality factor x (t)/x (t) = x /x where x and x are the reference values given for mixture A
A B A,ref B,ref A,ref B,ref
and B.
If this is true (within experimental variability), the quotients x /x and x /x are pooled and the combined
Ai A,ref Bi B,ref
time series is smoothed yielding a curve (or function) Q(t). This curve is then used to correct the result
obtained on another mixture M at any time t within the period covered according to
xt()
M
x = (7)
M
Qt
()
EXAMPLE Consider two drift-control mixtures (carbon monoxide in nitrogen) A and B with established analyte
concentrations c = 1,295 ± 0,006 mmol/mol and c = 21,65 ± 0,15 µmol/mol (where standard uncertainties are
A,ref B,ref
specified). Using an automated system, these gases are analysed alternately every 4 h between batches of samples with
CO concentrations in the range from 10 µmol/mol to 5 mmol/mol. For a measurement campaign over 80 h, drift control
data were obtained as shown in Table 1 [elapsed time t − t in hours, concentration c (t ) for gas A measured at time t in
i 0 A i i
mmol/mol, concentration c (t ) for gas B measured at time t in µmol/mol].
B i i
Table 1 — Time-series of drift-control data
t − t
0 h 4 h 8 h 12 h 16 h 20 h 24 h 28 h 32 h 36 h 40 h
i 0
c (t )
A i
1,28 1,30 1,30 1,28 1,26 1,24
mmol/mol
c (t )
B i
21,7 21,3 21,0 21,0 21,0
µmol/mol
t − t
44 h 48 h 52 h 56 h 60 h 64 h 68 h 72 h 76 h 80 h
i 0
c (t )
A i
1,27 1,27 1,24 1,26 1,25
mmol/mol
c (t )
B i
21,3 20,9 21,2 20,6 21,0
µmol/mol
The times-series of measurements on gas A and gas B are smoothed (sm) using ordinary linear least squares regression
(as available in common software). This gives two straight-line equations
−4
c (t) = 1,291 − 5,682 × 10 (t − t ) for gas A
A,sm 0
−3
c (t) = 21,41 − 7,727 × 10 (t − t ) for gas B
B,sm 0
The regression lines give the impression of a slightly decreasing detector sensitivity.
8 © ISO 2005 – All rights reserved

ISO 15796:2005(E)
The next step is to investigate whether the two drift-control data series may be combined to obtain a common drift
correction. For this purpose, the approach using recovery factors looks promising. According to the specified procedure,
the quotients c (t)/c (t) of smoothed drift-control data for gases A and B are examined for significant departure from
A,sm B,sm
the quotient c /c of reference data for these gases. An equivalent test is to compare the smoothed recoveries
A,ref B,ref
c (t)/c and c (t)/c for significant differences. Using the regression equations obtained previously, the
A,sm A,ref B,sm B,ref
difference d (t) = [(c (t)/c ) − (c (t)/c )] of recoveries at time t is given by
A,B A,sm A,ref B,sm B,ref
−5
d (t) = 0,007 97 − 8,183 × 10 (t − t )
A,B 0
Table 2 records values of this difference at specified times t, and the standard uncertainty of these values.
Table 2 — Differences of smoothed recovery data
t − t
0 h 10 h 20 h 30 h 40 h 50 h 60 h 70 h 80 h
d (t)
0,008 0 0,007 2 0,006 3 0,005 5 0,004 7 0,003 9 0,003 1 0,002 2 0,001 4
A,B
u[d (t)] 0,012 7 0,011 5 0,010 5 0,009 8 0,009 5 0,009 7 0,010 4 0,011 3 0,012 6
A,B
The (standard) uncertainty of the differences d (t) is obtained by uncertainty propagation from the uncertainties of the
A,B
calculated data c (t), c (t) and the uncertainties of the reference data c , c . Due to the fact that the recoveries
A,sm B,sm A,ref B,ref
are close to unity, relative uncertainties may be used instead of absolute uncertainties, yielding
2 2 2 2 2
u [d (t)] ≈ u [c (t)] + u (c ) + u [c (t)] + u (c )
A,B r A,sm r A,ref r B,sm r B,ref
Here u [c (t)] and u [c (t)] are obtained from the confidence interval for the regression line (where, depending on the
r A,sm r B,sm
software used, division by a default t-factor may be necessary), while u (c ) and u (c ) are obtained from the
r A,ref r B,ref
specification of the drift-control gases.
Examining the data in Table 2, no significant differences (i. e. d > 2u[d]) between smoothed recoveries for gases A and B
are encountered. Therefore the experimental recovery data Q (t ) = c (t )/c and Q (t ) = c (t )/c are pooled, and the
A i A i A,ref B i B i B,ref
combined time series is smoothed by ordinary least-squares regression, yielding a linear equation for a mean recovery
factor Q(t) as follows.
−4
Q(t) = 0,993 2 − 4,037 × 10 (t − t )
This equation would then be used to correct measurements on other samples carried out in the course of the measuring
campaign.
The relative standard uncertainty of the corrected result is determined by
22 2
 
ux=+ux ()t u Qt (8)
() ()
rM rM r
 
In this uncertainty budget, the first term is obtained from the uncertainty budget of the analytical procedure.
The second term is estimated from the residual scattering of the pooled quotients used to determine the
recovery factor Q(t). In addition, the uncertainty contributions of the drift measurements and the composition of
the drift-correction mixtures are included if significant.
If the recovery is approximately the same for different analytes, then a joint recovery factor may be derived for
a group of such analytes from pooled time series.
ISO 15796:2005(E)
5 Bias related to effects of sample composition
5.1 Principle
5.1.1 Basics
This clause specifies methods and protocols for investigation and handling of the bias of an analytical
procedure due to effects of sample composition, within a specified measuring range. Throughout this clause, it
is assumed that the measuring system under investigation is stable. Where appropriate, it should be
confirmed that this is the case. The measuring range normally includes variations in the concentration of the
analyte under consideration as well as variations in matrix composition. In this clause, the focus is on the
investigation of bias as a function of analyte concentration. Bias investigation and handling may include
effects due to within-specification variations in matrix composition. If matrix interferences are significant,
corrections derived from the bias study data include averaged matrix contributions, and the uncertainty on the
corrections includes contributions associated with the spread of biases due to these interferences. Principles
for systematic investigation of matrix interferences are considered in Clause 6.
This clause is applicable for absolute methods, i.e. analytical methods where analyte concentration is
determined directly, or where the relationship between measured response and analyte concentration is
known. It is also applicable for comparison methods, i.e. analytical methods where the relationship between
measured response and analyte concentration is determined empirically by calibration. If this calibration is
[7]
performed according to ISO 6143 , and if the analytical procedure is used strictly within specification, then
no bias investigation is necessary as long as the analytical system is stable. However, if the calibration is
performed by a less rigorous procedure (e.g. single-level calibration), or if a procedure calibrated according to
[7]
ISO 6143 is used out of its original specification (range of analyte concentration, matrix composition), bias
shall be investigated, and accounted for if significant.
Two different cases are considered:
a) Case A — Intra-laboratory assessment of a fully developed uncertainty budget
An analytical procedure is investigated for bias as a final step after an exhaustive evaluation of
measurement uncertainty. The aim of this investigation is to test the assumption that the uncertainty
evaluation has properly accounted for all relevant random and systematic effects impacting the
measurement result.
b) Case B — Estimation of measurement uncertainty from intra-laboratory validation data
An analytical procedure is investigated for bias in addition to, or jointly with a precision study. The aim of
these investigations is to obtain an estimate of measurement uncertainty by combination of bias and
precision estimates.
5.1.2 Main steps involved in investigation and handling of bias
Potential bias is investigated by comparing results obtained on “known samples” with the corresponding
reference values, and by examining whether any of the differences encountered are significant in comparison
with the relevant uncertainty on that difference. If no significant bias (difference) is found, and provided that
the samples are representative for the specified measuring range and the reference values are well
established, then the analytical procedure has thereby been demonstrated to be unbiased. Depending on the
type of bias study, no further action is required in case A (in addition to regular quality control), while in case B
the observed bias and its associated uncertainty are included in the estimation of measurement uncertainty.
If significant bias is found, this requires corrective action. Depending on whether the bias is judged to be
technically serious or acceptable, different actions are applicable.
For the purpose of this International Standard, actions on bias are recommended as shown in Table 3:
10 © ISO 2005 – All rights reserved

ISO 15796:2005(E)
Table 3 — Recommended actions on bias
Bias Case A Case B
Serious bias
Examine and amend the analytical procedure Examine and amend the analytical procedure
to remove/reduce bias; or to remove/reduce bias.
examine and amend the uncertainty budget for
missing or underestimated uncertainty
components.
Acceptable bias
Apply a correction for bias in the data Apply a correction for bias in the data
evaluation procedure; or evaluation procedure; or
include an allowance for uncorrected bias in include an allowance for uncorrected bias in
the uncertainty estimation. the uncertainty estimation.
Insignificant bias (no action) Include an allowance for uncorrected bias in
the uncertainty estimation.
Criteria for the assessment of bias (significant/insignificant and serious/acceptable) and procedures for:
 correcting for bias and accounting for the uncertainty associated with a bias estimate,
 including an allowance for uncorrected bias in the uncertainty estimation,
are specified in subsequent clauses.
5.2 deals with local bias handling using a single reference sample, with separate subclauses for case A (5.2.1)
and case B (5.2.2), or several matrix-varied reference samples (5.2.3). Bias handling for extended measuring
ranges, using several reference samples, is addressed in 5.3.
By way of the procedures specified in this clause, the measurement uncertainty for an analytical procedure is
made traceable to the reference values, including uncertainties, attributed to the reference samples (most
often calibration gas mixtures). To this end it is important to ensure that
 the reference values and their uncertainties are well established,
 the reference samples are representative for the range of samples to be analysed,
 the variability of measuring conditions in the bias study covers the variability in the intended applications.
Normally bias investigations are repeated on a regular basis. If this is the case, then it is important to compare
the data from the curren
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