Water quality — Calibration and evaluation of analytical methods and estimation of performance characteristics — Part 2: Calibration strategy for non-linear second-order calibration functions

It is not always possible to accurately describe the relationship between a set of calibration points with a rectilinear curve, even by decreasing the working range. Instead of the linear regression analysis, a least-squares fit to a second-order polynomial is applied (see test for linearity in 4.1.3 of ISO 8466-1:1990[1]). Using this fit, it is possible to calculate not only the calibration function but also the confidence interval associated with it. This part of ISO 8466 is intended primarily for use in method development and may not necessarily be applicable to all routine analyses.

Qualité de l'eau — Étalonnage et évaluation des méthodes d'analyse et estimation des caractères de performance — Partie 2: Stratégie d'étalonnage pour fonctions d'étalonnage non linéaires du second degré

Il n'est pas toujours possible d'établir une relation exacte entre un ensemble de valeurs d'étalonnage et une droite, même en réduisant l'étendue de dosage. On utilise alors, au lieu d'une droite de régression, une fonction polynomiale de second degré (voir test de linéarité en 4.1.3 de l'ISO 8466-1:1990 [1]). Il est alors possible de calculer la fonction d'étalonnage, mais aussi l'intervalle de confiance associé. La présente partie de l'ISO 8466 est essentiellement destinée à la mise au point de méthodes d'analyse et n'est pas forcément applicable à toutes les analyses de routine.

Kakovost vode - Umerjanje in vrednotenje analitskih metod in določitev delovnih karakteristik - 2. del: Načrtovanje umerjanja za nelinearne umerjalne funkcije drugega reda

General Information

Status
Published
Publication Date
31-Oct-2001
Current Stage
9020 - International Standard under periodical review
Start Date
15-Oct-2011
Completion Date
15-Jul-2022

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INTERNATIONAL ISO
STANDARD 8466-2
Second edition
2001-11-01
Water quality — Calibration and evaluation
of analytical methods and estimation of
performance characteristics —
Part 2:
Calibration strategy for non-linear
second-order calibration functions
Qualité de l'eau — Étalonnage et évaluation des méthodes d'analyse et
estimation des caractères de performance —
Partie 2: Stratégie d'étalonnage pour fonctions d'étalonnage non linéaires
du second degré
Reference number
ISO 8466-2:2001(E)
ISO 2001
---------------------- Page: 1 ----------------------
ISO 8466-2:2001(E)
PDF disclaimer

This PDF file may contain embedded typefaces. In accordance with Adobe's licensing policy, this file may be printed or viewed but shall not

be edited unless the typefaces which are embedded are licensed to and installed on the computer performing the editing. In downloading this

file, parties accept therein the responsibility of not infringing Adobe's licensing policy. The ISO Central Secretariat accepts no liability in this

area.
Adobe is a trademark of Adobe Systems Incorporated.

Details of the software products used to create this PDF file can be found in the General Info relative to the file; the PDF-creation parameters

were optimized for printing. Every care has been taken to ensure that the file is suitable for use by ISO member bodies. In the unlikely event

that a problem relating to it is found, please inform the Central Secretariat at the address given below.

© ISO 2001

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.ch
Web www.iso.ch
Printed in Switzerland
ii © ISO 2001 – All rights reserved
---------------------- Page: 2 ----------------------
ISO 8466-2:2001(E)
Contents Page

Foreword.....................................................................................................................................................................iv

1 Scope..............................................................................................................................................................1

2 Symbols..........................................................................................................................................................1

3 Performance...................................................................................................................................................2

3.1 Choice of working range...............................................................................................................................2

3.2 Test for the homogeneity of the variances .................................................................................................2

3.3 Measurement..................................................................................................................................................4

4 Estimation of the polynomial coefficients ..................................................................................................4

5 Performance characteristics........................................................................................................................5

5.1 Residual standard deviation.........................................................................................................................5

5.2 Instrument sensitivity of the analytical procedure ....................................................................................5

5.3 Standard deviation of the procedure...........................................................................................................5

5.4 Relative standard deviation of the procedure ............................................................................................6

6 Analysis of a sample .....................................................................................................................................6

6.1 General considerations.................................................................................................................................6

6.2 Test for minima or maxima...........................................................................................................................6

6.3 Calculation of the analytical result ..............................................................................................................6

6.4 Confidence interval of the analytical result (see Figure 1).........................................................................7

7 Example..........................................................................................................................................................7

7.1 Calibration, performance characteristics and evaluation .........................................................................7

7.2 Single measurement analysis ......................................................................................................................8

Annex A (normative) F-table (99 %) ........................................................................................................................10

Bibliography..............................................................................................................................................................12

© ISO 2001 – All rights reserved iii
---------------------- Page: 3 ----------------------
ISO 8466-2:2001(E)
Foreword

ISO (the International Organization for Standardization) is a worldwide federation of national standards bodies (ISO

member bodies). The work of preparing International Standards is normally carried out through ISO technical

committees. Each member body interested in a subject for which a technical committee has been established has

the right to be represented on that committee. International organizations, governmental and non-governmental, in

liaison with ISO, also take part in the work. ISO collaborates closely with the International Electrotechnical

Commission (IEC) on all matters of electrotechnical standardization.

International Standards are drafted in accordance with the rules given in the ISO/IEC Directives, Part 3.

Draft International Standards adopted by the technical committees are circulated to the member bodies for voting.

Publication as an International Standard requires approval by at least 75 % of the member bodies casting a vote.

Attention is drawn to the possibility that some of the elements of this part of ISO 8466 may be the subject of patent

rights. ISO shall not be held responsible for identifying any or all such patent rights.

International Standard ISO 8466-2 was prepared by Technical Committee ISO/TC 147, Water quality,

Subcommittee SC 2, Physical, chemical, biochemical methods.

This second edition cancels and replaces the first edition (ISO 8466-2:1993), which has been technically revised.

ISO 8466 consists of the following parts, under the general title Water quality — Calibration and evaluation of

analytical methods and estimation of performance characteristics:
 Part 1: Statistical evaluation of the linear calibration function
 Part 2: Calibration strategy for non-linear second-order calibration functions
Annex A forms an integral part of this part of ISO 8466.
iv © ISO 2001 – All rights reserved
---------------------- Page: 4 ----------------------
INTERNATIONAL STANDARD ISO 8466-2:2001(E)
Water quality — Calibration and evaluation of analytical methods
and estimation of performance characteristics —
Part 2:
Calibration strategy for non-linear second-order calibration
functions
1 Scope

It is not always possible to accurately describe the relationship between a set of calibration points with a rectilinear

curve, even by decreasing the working range. Instead of the linear regression analysis, a least-squares fit to a

[1]

second-order polynomial is applied (see test for linearity in 4.1.3 of ISO 8466-1:1990 ). Using this fit, it is possible

to calculate not only the calibration function but also the confidence interval associated with it.

This part of ISO 8466 is intended primarily for use in method development and may not necessarily be applicable to

all routine analyses.
2 Symbols
a, b, c Coefficients of the calibration function
E Instrument sensitivity in the centre of the working range

e Instrument sensitivity, defined as the first derivative of the calibration function

F(f , f , P) Tabled value of the F-distribution with f and f degrees of freedom and a confidence level of P (%)

1 2 1 2
F Test value calculated for the F-test
calc
f Number of degrees of freedom for the residual standard deviation (f = N - 3)
I(ˆx) Confidence interval for the concentration xˆ
i Subscript of the concentration levels, where i = 1, 2, ..., N
j Subscript of the replicates of level i, where j = 1, 2, ..., n
N Number of concentration levels (for this part of ISO 8466, N = 10)
N Number of replicates for the same analytical sample
n Number of replicates per level x
i i
s Standard deviation of the procedure
© ISO 2001 – All rights reserved 1
---------------------- Page: 5 ----------------------
ISO 8466-2:2001(E)
s Residual standard deviation

s Variance of the response variable values for the analyses of standard samples, having the

concentration x

t(f , P) Tabled value of the t-distribution with f = N - 3 degrees of freedom and a confidence interval of P (%)

1 1
(t-factor of Student's distribution)
V Coefficient of variation of the procedure

x Concentration of the standard sample at the lower level of the working range (1st standard sample)

x Concentration of the standard sample at the upper level of the working range (10th standard sample)

x Concentration of the ith standard sample

x Mean of the standard concentrations x , resulting from the calibration experiment

x Concentration at which the calibration function has a minimum or a maximum value

xˆ Concentration of the analytical sample, calculated from the response variable value yˆ

y jth response variable value for the concentration x
i,j i

Mean of the response variable values y , resulting from the calibration experiment

y Mean of the response variable values y of standard samples, having the concentration x

i,j i
yˆ Response variable value of an analytical sample

yˆ Response variable value of the standard concentration x calculated from the calibration function

3 Performance
3.1 Choice of working range

The calibration experiment requires that the preliminary working range be established according to the following.

a) Define the objective of the calibration with respect to the practical application.

The working range may cover the application range required for the analysis of water, wastewater and sludge.

The most frequently expected sample concentration should lie near the centre of the working range.

b) Make sure the values obtained near the lower limit of the working range are distinguishable from the blanks of

the procedure.

The lower limit of the working range should therefore be equal to or greater than the limit of quantitation of the

procedure. Dilution or concentration steps should be feasible and free from the risk of bias.

3.2 Test for the homogeneity of the variances

The variance of the values determined from selected standard solutions shall be homogeneous and independent of

the concentration.
2 © ISO 2001 – All rights reserved
---------------------- Page: 6 ----------------------
ISO 8466-2:2001(E)

After establishing the preliminary working range, determine the response variable values of at least N = 5

(recommended N = 10) standard solutions. Select the standard solution concentrations, x , so as to distribute them

equidistantly over the working range. In order to examine the homogeneity of the variances, s , make replicate

measurements of each of the lowest and highest concentrations of the standard solutions of the working range. n

values (y ) result from these series of measurements.
i,j
2 2

Both data sets of the concentrations x and x are used to calculate the variances s and s as given in

1 10
1 10
equation (1):
yy-
 ij, i
j=1
s = (1)
n -1
where
f = n - 1
i i
y is the mean as given in Equation (2)
 ij,
j=1
y = (2)
for i = 1 or i = 10.

The variances are submitted to a simple test of variance (one-sided F-test), in order to examine for significant

differences at the lower and upper limits of the working range.
Determine the test value F as follows:
calc
10 22
F=>for ss (3)
calc 10 1
F=>for ss (4)
calc 1 10

Compare the value of F with the tabled values of the F-distribution given in Table A.1 of annex A.

calc
Make the following decision:

a) if F u F(f , f , 99 %), the difference between the variances is not significant;

calc 1 2
b) if F > F(f , f , 99
...

SLOVENSKI STANDARD
SIST ISO 8466-2:2004
01-junij-2004
.DNRYRVWYRGH8PHUMDQMHLQYUHGQRWHQMHDQDOLWVNLKPHWRGLQGRORþLWHYGHORYQLK
NDUDNWHULVWLNGHO1DþUWRYDQMHXPHUMDQMD]DQHOLQHDUQHXPHUMDOQHIXQNFLMH
GUXJHJDUHGD

Water quality -- Calibration and evaluation of analytical methods and estimation of

performance characteristics -- Part 2: Calibration strategy for non-linear second-order

calibration functions

Qualité de l'eau -- Étalonnage et évaluation des méthodes d'analyse et estimation des

caractères de performance -- Partie 2: Stratégie d'étalonnage pour fonctions
d'étalonnage non linéaires du second degré
Ta slovenski standard je istoveten z: ISO 8466-2:2001
ICS:
13.060.50 3UHLVNDYDYRGHQDNHPLþQH Examination of water for
VQRYL chemical substances
SIST ISO 8466-2:2004 en

2003-01.Slovenski inštitut za standardizacijo. Razmnoževanje celote ali delov tega standarda ni dovoljeno.

---------------------- Page: 1 ----------------------
SIST ISO 8466-2:2004
---------------------- Page: 2 ----------------------
SIST ISO 8466-2:2004
INTERNATIONAL ISO
STANDARD 8466-2
Second edition
2001-11-01
Water quality — Calibration and evaluation
of analytical methods and estimation of
performance characteristics —
Part 2:
Calibration strategy for non-linear
second-order calibration functions
Qualité de l'eau — Étalonnage et évaluation des méthodes d'analyse et
estimation des caractères de performance —
Partie 2: Stratégie d'étalonnage pour fonctions d'étalonnage non linéaires
du second degré
Reference number
ISO 8466-2:2001(E)
ISO 2001
---------------------- Page: 3 ----------------------
SIST ISO 8466-2:2004
ISO 8466-2:2001(E)
PDF disclaimer

This PDF file may contain embedded typefaces. In accordance with Adobe's licensing policy, this file may be printed or viewed but shall not

be edited unless the typefaces which are embedded are licensed to and installed on the computer performing the editing. In downloading this

file, parties accept therein the responsibility of not infringing Adobe's licensing policy. The ISO Central Secretariat accepts no liability in this

area.
Adobe is a trademark of Adobe Systems Incorporated.

Details of the software products used to create this PDF file can be found in the General Info relative to the file; the PDF-creation parameters

were optimized for printing. Every care has been taken to ensure that the file is suitable for use by ISO member bodies. In the unlikely event

that a problem relating to it is found, please inform the Central Secretariat at the address given below.

© ISO 2001

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.ch
Web www.iso.ch
Printed in Switzerland
ii © ISO 2001 – All rights reserved
---------------------- Page: 4 ----------------------
SIST ISO 8466-2:2004
ISO 8466-2:2001(E)
Contents Page

Foreword.....................................................................................................................................................................iv

1 Scope..............................................................................................................................................................1

2 Symbols..........................................................................................................................................................1

3 Performance...................................................................................................................................................2

3.1 Choice of working range...............................................................................................................................2

3.2 Test for the homogeneity of the variances .................................................................................................2

3.3 Measurement..................................................................................................................................................4

4 Estimation of the polynomial coefficients ..................................................................................................4

5 Performance characteristics........................................................................................................................5

5.1 Residual standard deviation.........................................................................................................................5

5.2 Instrument sensitivity of the analytical procedure ....................................................................................5

5.3 Standard deviation of the procedure...........................................................................................................5

5.4 Relative standard deviation of the procedure ............................................................................................6

6 Analysis of a sample .....................................................................................................................................6

6.1 General considerations.................................................................................................................................6

6.2 Test for minima or maxima...........................................................................................................................6

6.3 Calculation of the analytical result ..............................................................................................................6

6.4 Confidence interval of the analytical result (see Figure 1).........................................................................7

7 Example..........................................................................................................................................................7

7.1 Calibration, performance characteristics and evaluation .........................................................................7

7.2 Single measurement analysis ......................................................................................................................8

Annex A (normative) F-table (99 %) ........................................................................................................................10

Bibliography..............................................................................................................................................................12

© ISO 2001 – All rights reserved iii
---------------------- Page: 5 ----------------------
SIST ISO 8466-2:2004
ISO 8466-2:2001(E)
Foreword

ISO (the International Organization for Standardization) is a worldwide federation of national standards bodies (ISO

member bodies). The work of preparing International Standards is normally carried out through ISO technical

committees. Each member body interested in a subject for which a technical committee has been established has

the right to be represented on that committee. International organizations, governmental and non-governmental, in

liaison with ISO, also take part in the work. ISO collaborates closely with the International Electrotechnical

Commission (IEC) on all matters of electrotechnical standardization.

International Standards are drafted in accordance with the rules given in the ISO/IEC Directives, Part 3.

Draft International Standards adopted by the technical committees are circulated to the member bodies for voting.

Publication as an International Standard requires approval by at least 75 % of the member bodies casting a vote.

Attention is drawn to the possibility that some of the elements of this part of ISO 8466 may be the subject of patent

rights. ISO shall not be held responsible for identifying any or all such patent rights.

International Standard ISO 8466-2 was prepared by Technical Committee ISO/TC 147, Water quality,

Subcommittee SC 2, Physical, chemical, biochemical methods.

This second edition cancels and replaces the first edition (ISO 8466-2:1993), which has been technically revised.

ISO 8466 consists of the following parts, under the general title Water quality — Calibration and evaluation of

analytical methods and estimation of performance characteristics:
 Part 1: Statistical evaluation of the linear calibration function
 Part 2: Calibration strategy for non-linear second-order calibration functions
Annex A forms an integral part of this part of ISO 8466.
iv © ISO 2001 – All rights reserved
---------------------- Page: 6 ----------------------
SIST ISO 8466-2:2004
INTERNATIONAL STANDARD ISO 8466-2:2001(E)
Water quality — Calibration and evaluation of analytical methods
and estimation of performance characteristics —
Part 2:
Calibration strategy for non-linear second-order calibration
functions
1 Scope

It is not always possible to accurately describe the relationship between a set of calibration points with a rectilinear

curve, even by decreasing the working range. Instead of the linear regression analysis, a least-squares fit to a

[1]

second-order polynomial is applied (see test for linearity in 4.1.3 of ISO 8466-1:1990 ). Using this fit, it is possible

to calculate not only the calibration function but also the confidence interval associated with it.

This part of ISO 8466 is intended primarily for use in method development and may not necessarily be applicable to

all routine analyses.
2 Symbols
a, b, c Coefficients of the calibration function
E Instrument sensitivity in the centre of the working range

e Instrument sensitivity, defined as the first derivative of the calibration function

F(f , f , P) Tabled value of the F-distribution with f and f degrees of freedom and a confidence level of P (%)

1 2 1 2
F Test value calculated for the F-test
calc
f Number of degrees of freedom for the residual standard deviation (f = N - 3)
I(ˆx) Confidence interval for the concentration xˆ
i Subscript of the concentration levels, where i = 1, 2, ..., N
j Subscript of the replicates of level i, where j = 1, 2, ..., n
N Number of concentration levels (for this part of ISO 8466, N = 10)
N Number of replicates for the same analytical sample
n Number of replicates per level x
i i
s Standard deviation of the procedure
© ISO 2001 – All rights reserved 1
---------------------- Page: 7 ----------------------
SIST ISO 8466-2:2004
ISO 8466-2:2001(E)
s Residual standard deviation

s Variance of the response variable values for the analyses of standard samples, having the

concentration x

t(f , P) Tabled value of the t-distribution with f = N - 3 degrees of freedom and a confidence interval of P (%)

1 1
(t-factor of Student's distribution)
V Coefficient of variation of the procedure

x Concentration of the standard sample at the lower level of the working range (1st standard sample)

x Concentration of the standard sample at the upper level of the working range (10th standard sample)

x Concentration of the ith standard sample

x Mean of the standard concentrations x , resulting from the calibration experiment

x Concentration at which the calibration function has a minimum or a maximum value

xˆ Concentration of the analytical sample, calculated from the response variable value yˆ

y jth response variable value for the concentration x
i,j i

Mean of the response variable values y , resulting from the calibration experiment

y Mean of the response variable values y of standard samples, having the concentration x

i,j i
yˆ Response variable value of an analytical sample

yˆ Response variable value of the standard concentration x calculated from the calibration function

3 Performance
3.1 Choice of working range

The calibration experiment requires that the preliminary working range be established according to the following.

a) Define the objective of the calibration with respect to the practical application.

The working range may cover the application range required for the analysis of water, wastewater and sludge.

The most frequently expected sample concentration should lie near the centre of the working range.

b) Make sure the values obtained near the lower limit of the working range are distinguishable from the blanks of

the procedure.

The lower limit of the working range should therefore be equal to or greater than the limit of quantitation of the

procedure. Dilution or concentration steps should be feasible and free from the risk of bias.

3.2 Test for the homogeneity of the variances

The variance of the values determined from selected standard solutions shall be homogeneous and independent of

the concentration.
2 © ISO 2001 – All rights reserved
---------------------- Page: 8 ----------------------
SIST ISO 8466-2:2004
ISO 8466-2:2001(E)

After establishing the preliminary working range, determine the response variable values of at least N = 5

(recommended N = 10) standard solutions. Select the standard solution concentrations, x , so as to distribute them

equidistantly over the working range. In order to examine the homogeneity of the variances, s , make replicate

measurements of each of the lowest and highest concentrations of the standard solutions of the working range. n

values (y ) result from these series of measurements.
i,j
2 2

Both data sets of the concentrations x and x are used to calculate the variances s and s as given in

1 10
1 10
equation (1):
yy-
 ij, i
j=1
s = (1)
n -1
where
f = n - 1
i i
y is the mean as given in Equation (2)
 ij,
j=1
y = (2)
for
...

NORME ISO
INTERNATIONALE 8466-2
Deuxième édition
2001-11-01
Qualité de l'eau — Étalonnage et évaluation
des méthodes d'analyse et estimation des
caractères de performance —
Partie 2:
Stratégie d'étalonnage pour fonctions
d'étalonnage non linéaires du second degré
Water quality — Calibration and evaluation of analytical methods and
estimation of performance characteristics —
Part 2: Calibration strategy for non-linear second-order calibration functions
Numéro de référence
ISO 8466-2:2001(F)
ISO 2001
---------------------- Page: 1 ----------------------
ISO 8466-2:2001(F)
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© ISO 2001

Droits de reproduction réservés. Sauf prescription différente, aucune partie de cette publication ne peut être reproduite ni utilisée sous quelque

forme que ce soit et par aucun procédé, électronique ou mécanique, y compris la photocopie et les microfilms, sans l'accord écrit de l’ISO à

l’adresse ci-après ou du comité membre de l’ISO dans le pays du demandeur.
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.ch
Web www.iso.ch
Imprimé en Suisse
ii © ISO 2001 – Tous droits réservés
---------------------- Page: 2 ----------------------
ISO 8466-2:2001(F)
Sommaire Page

Avant-propos .............................................................................................................................................................iv

1 Domaine d'application..................................................................................................................................1

2 Symboles........................................................................................................................................................1

3 Réalisation de l'étalonnage ..........................................................................................................................2

3.1 Choix de l'étendue de dosage ......................................................................................................................2

3.2 Test d'homogénéité des variances..............................................................................................................3

3.3 Mesurage........................................................................................................................................................4

4 Estimation des coefficients polynomiaux...................................................................................................4

5 Caractères de performance ..........................................................................................................................5

5.1 Écart-type résiduel........................................................................................................................................5

5.2 Sensibilité de la méthode d'analyse ............................................................................................................5

5.3 Écart-type de la méthode..............................................................................................................................6

5.4 Écart-type relatif de la méthode ...................................................................................................................6

6 Analyse d'un échantillon ..............................................................................................................................6

6.1 Généralités.....................................................................................................................................................6

6.2 Recherche des minima ou maxima..............................................................................................................6

6.3 Calcul de la concentration la plus probable ...............................................................................................7

6.4 Intervalle de confiance du résultat d'analyse (voir Figure 1) .....................................................................7

7 Exemple..........................................................................................................................................................8

7.1 Étalonnage, caractères de performance et évaluation..............................................................................8

7.2 Réalisation d'analyses................................................................................................................................10

Annexe A (normative) Table de la loi F (99 %).......................................................................................................11

Bibliographie.............................................................................................................................................................13

© ISO 2001 – Tous droits réservés iii
---------------------- Page: 3 ----------------------
ISO 8466-2:2001(F)
Avant-propos

L'ISO (Organisation internationale de normalisation) est une fédération mondiale d'organismes nationaux de

normalisation (comités membres de l'ISO). L'élaboration des Normes internationales est en général confiée aux

comités techniques de l'ISO. Chaque comité membre intéressé par une étude a le droit de faire partie du comité

technique créé à cet effet. Les organisations internationales, gouvernementales et non gouvernementales, en

liaison avec l'ISO participent également aux travaux. L'ISO collabore étroitement avec la Commission

électrotechnique internationale (CEI) en ce qui concerne la normalisation électrotechnique.

Les Normes internationales sont rédigées conformément aux règles données dans les Directives ISO/CEI, Partie 3.

Les projets de Normes internationales adoptés par les comités techniques sont soumis aux comités membres pour

vote. Leur publication comme Normes internationales requiert l'approbation de 75 % au moins des comités

membres votants.

L’attention est appelée sur le fait que certains des éléments de la présente partie de l’ISO 8466 peuvent faire

l’objet de droits de propriété intellectuelle ou de droits analogues. L’ISO ne saurait être tenue pour responsable de

ne pas avoir identifié de tels droits de propriété et averti de leur existence.

La Norme internationale ISO 8466-2 a été élaborée par le comité technique ISO/TC 147, Qualité de l'eau,

sous-comité SC 2, Méthodes physiques, chimiques et biochimiques.

Cette deuxième édition annule et remplace la première édition (ISO 8466-2:1993), dont elle constitue une révision

technique.

L'ISO 8466 comprend les parties suivantes, présentées sous le titre général Qualité de l'eau — Étalonnage et

évaluation des méthodes d'analyse et estimation des caractères de performance:
 Partie 1: Évaluation statistique de la fonction linéaire d'étalonnage

 Partie 2: Stratégie d'étalonnage pour fonctions d'étalonnage non linéaires du second degré

L’annexe A constitue un élément normatif de la présente partie de l’ISO 8466.
iv © ISO 2001 – Tous droits réservés
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NORME INTERNATIONALE ISO 8466-2:2001(F)
Qualité de l'eau — Étalonnage et évaluation des méthodes
d'analyse et estimation des caractères de performance —
Partie 2:
Stratégie d'étalonnage pour fonctions d'étalonnage non linéaires
du second degré
1 Domaine d'application

Il n’est pas toujours possible d’établir une relation exacte entre un ensemble de valeurs d’étalonnage et une droite,

même en réduisant l’étendue de dosage. On utilise alors, au lieu d’une droite de régression, une fonction

[1]

polynomiale de second degré (voir test de linéarité en 4.1.3 de l’ISO 8466-1:1990 ). Il est alors possible de

calculer la fonction d’étalonnage, mais aussi l’intervalle de confiance associé.

La présente partie de l’ISO 8466 est essentiellement destinée à la mise au point de méthodes d’analyse et n’est

pas forcément applicable à toutes les analyses de routine.
2 Symboles
a, b, c Coefficients de la fonction d’étalonnage
E Sensibilité au centre de l’étendue de dosage
e Sensibilité = dérivée première de la fonction d’étalonnage
F Valeur d’essai calculée pour le test F
calc

F(f , f , P) Valeur tabulée de la loi de F pour les nombres de degrés de liberté f et f et un intervalle de confiance

1 2 1 2
de P (%)

f Nombre de degrés de liberté intervenant dans le calcul de l’écart-type résiduel (f = N - 3)

I(ˆx) Intervalle de confiance pour la concentration xˆ
i Indice 1, 2, ..., N des niveaux de concentration
j Indice 1, 2, ..., n des répétitions effectuées pour le niveau i

N Nombre de niveaux de concentration utilisés (valeur recommandée pour la présente partie de

l’ISO 8466, N = 10)
N Nombre de répétitions effectuées sur un même échantillon pour analyse
n Nombre de répétitions effectuées pour chaque concentration x
i i
© ISO 2001 – Tous droits réservés 1
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ISO 8466-2:2001(F)
s Écart-type de la méthode
s Écart-type résiduel

s Variance des valeurs d’information obtenues pour l’ensemble des échantillons étalons de concentra-

tion x

t(f , P) Valeur tabulée de la loi de t, pour f = N - 3 degrés de liberté et un intervalle de confiance de P (%)

1 1
(variable t de la loi de Student)
V Coefficient de variation de la méthode

x Concentration de l’échantillon étalon correspondant à la borne inférieure de l’étendue de dosage

(1 échantillon étalon)

x Concentration de l’échantillon étalon correspondant à la borne supérieure de l’étendue de dosage

(10 échantillon étalon)
ème
x Concentration du i échantillon étalon
x Moyenne des concentrations étalons x résultant de l’expérience d’étalonnage

x* Concentration correspondant à un minimum ou à un maximum de la fonction d’étalonnage

xˆ Concentration de l’échantillon pour analyse calculée à partir de la valeur d’information yˆ

ème
y j valeur d’information obtenue pour la concentration x
i,j i
y Moyenne des valeurs d’information y résultant de l’expérience d’étalonnage

y Moyenne des valeurs d’information y obtenues pour l’ensemble des échantillons étalons de

i i,j
concentration x
yˆ Valeur d’information obtenue pour un échantillon pour analyse

yˆ Valeur d’information calculée à l’aide de la fonction d’étalonnage pour la concentration étalon x

i i
3 Réalisation de l'étalonnage
3.1 Choix de l'étendue de dosage

L'expérience d'étalonnage commence par l'établissement d'une étendue de dosage préliminaire, en fonction des

facteurs suivants.
a) L'objectif pratique de l'étalonnage.

L'étendue de dosage peut couvrir la gamme de concentrations requise pour l'analyse de l'eau, des eaux usées

et des boues. Il convient que la concentration la plus probable de l'échantillon soit voisine du centre de

l'étendue de dosage.

b) Les valeurs obtenues au voisinage de la borne inférieure de l'étendue de dosage à distinguer des valeurs

obtenues pour les blancs.

Il est donc souhaitable que la borne inférieure de l'étendue de dosage soit égale ou supérieure à la limite de

détection de la méthode. Il convient que les opérations de dilution ou de concentration soient réalisables sans

risque d'introduction d'un biais.
2 © ISO 2001 – Tous droits réservés
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ISO 8466-2:2001(F)
3.2 Test d'homogénéité des variances

La variance des valeurs d'information doit être homogène et indépendante de la concentration.

Une fois établie l'étendue de dosage préliminaire, déterminer les valeurs d'information correspondant à au moins

N = 5 échantillons étalons (valeur recommandée: N = 10). Répartir les concentrations x de ces échantillons de

façon équidistante sur l'ensemble de l'étendue de dosage. Pour vérifier l'homogénéité des variances, s , effectuer

n analyses (n répétitions) pour la concentration la plus élevée et la concentration la plus basse de l'étendue de

i i
dosage.

On obtient ainsi deux séries de n valeurs d'information y , à partir desquelles on calcule, d'après l'équation (1), les

i i,j
2 2
variances s et s correspondant aux concentrations x et x .
1 10
1 10
yy-
ij, i
j=1
s = (1)
n -1
f = n - 1
i i
y est la moyenne telle que donnée par l’équation (2)
 ij,
j=1
y = (2)
pour i = 1 ou i = 10.

On applique aux variances un test simple (test F) afin de mettre en évidence d'éventuelles différences aux bornes

de l'étendue de dosage.
Déterminer comme suit la valeur F à laquelle est appliqué le test F:
calc
10 22
F=>pourss (3)
calc 10 1
1 22
F=>pour ss (4)
calc 1 10
Comparer la valeur de F aux valeurs de la loi F indiquées dans le Tableau A.1 de
...

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