ISO 4259-1:2017

Petroleum and related products - Precision of measurement methods and results - Part 1: Determination of precision data in relation to methods of test

ISO 4259-1:2017 specifies the methodology for the design of an Interlaboratory Study (ILS) and calculation of precision estimates of a test method specified by the study. In particular, it defines the relevant statistical terms (Clause 3), the procedures to be adopted in the planning of ILS to determine the precision of a test method (Clause 4), and the method of calculating the precision from the results of such a study (Clauses 5 and 6). The procedures in ISO 4259-1:2017 have been designed specifically for petroleum and petroleum related products, which are normally considered as homogeneous. However, the procedures described in ISO 4259-1:2017 can also be applied to other types of homogeneous products. Careful investigations are necessary before applying ISO 4259-1:2017 to products for which the assumption of homogeneity can be questioned.

Produits pétroliers et connexes — Fidélité des méthodes de mesure et de leurs résultats — Partie 1: Détermination des valeurs de fidélité relatives aux méthodes d'essai

ISO 4259-1:2017 spécifié la méthodologie pour la conception d'un essai interlaboratoires (ILS) et pour le calcul des estimations de fidélité d'une méthode d'essai spécifié par cet ILS. En particulier, il définit les termes statistiques concernés (Article 3), les procédures à suivre dans l'organisation d'un ILS destiné à déterminer la fidélité d'une méthode d'essai (Article 4) et la méthode de calcul de la fidélité à partir des résultats d'un tel ILS (Articles 5 et 6). Les procédures de l' ISO 4259-1:2017 ont été conçues spécifiquement pour les produits pétroliers et leurs produits connexes qui sont normalement considérés homogènes. Les procédures décrites dans le présent document peuvent cependant aussi s'appliquer à d'autres types de produits homogènes. Il est nécessaire de procéder à des contrôles attentifs avant d'appliquer ce document à des produits pour lesquels la présomption d'homogénéité peut être mise en question.

General Information

• Status: Published
• Publication Date: 31-Oct-2017
• ICS: 75.080 - Petroleum products in general
• Technical Committee: ISO/TC 28 - Petroleum and related products, fuels and lubricants from natural or synthetic sources
• Drafting Committee: ISO/TC 28/WG 2 - Determination and application of precision data in relation to methods of test
• Current Stage: 9092 - International Standard to be revised
• Start Date: 14-Feb-2024
• Completion Date: 13-Dec-2025

Relations

• Consolidates: ISO 6588-2:2005 - Paper, board and pulps - Determination of pH of aqueous extracts - Part 2: Hot extraction
• Effective Date: 06-Jun-2022
• Amended By: ISO 4259-1:2017/Amd 1:2019 - Petroleum and related products - Precision of measurement methods and results - Part 1: Determination of precision data in relation to methods of test - Amendment 1
• Effective Date: 01-Jan-2022
• Amended By: ISO 4259-1:2017/Amd 2:2020 - Petroleum and related products - Precision of measurement methods and results - Part 1: Determination of precision data in relation to methods of test - Amendment 2
• Effective Date: 04-Dec-2021
• Revises: ISO 4259:2006 - Petroleum products - Determination and application of precision data in relation to methods of test
• Effective Date: 09-Nov-2013

Overview

ISO 4259-1:2017 - Petroleum and related products - Precision of measurement methods and results - Part 1 specifies the methodology for designing an Interlaboratory Study (ILS) and calculating precision estimates for test methods. The standard defines key statistical terms, sets out planning and execution stages for ILS, and prescribes procedures for computing repeatability and reproducibility. Although written for petroleum and petroleum‑related products (assumed homogeneous), the methodology can be applied to other homogeneous materials with appropriate validation.

Key topics and technical requirements

• Definitions and terminology: statistical and metrological terms used for precision assessment (Clauses 3).
• ILS planning stages: preparing a draft test method; pilot study (≥2 laboratories); planning the full ILS; executing the ILS (Clause 4).
• Pilot study guidance: minimum of two samples covering the method range; at least 12 laboratory/sample combinations; each sample tested twice under repeatability conditions to estimate initial precision.
• ILS sample and laboratory recommendations: at least six participating laboratories (eight or more recommended) and a sufficient number of samples to represent the application range; if precision varies with level, use at least five samples.
• Statistical treatment (Clauses 5–6): pre‑screening (e.g., GESD for anomalies), data transformation, outlier tests, estimation for missing/rejected values, rejection tests for outlying laboratories, and confirmation of transformations.
• Analysis of variance (ANOVA): breakdown of total variance into components, calculation of repeatability and reproducibility standard deviations, expression of precision estimates, and specification of the method’s scope (Clause 6).
• Supplementary tests and tools: Cochran’s and Hawkins’ tests, variance-ratio (F‑test), r/R ratio treatment, and annexes for sample/laboratory number calculation and worked examples.

Applications

• Validation and development of standard test methods for petroleum products (fuel, lubricants, related materials).
• Establishing objective precision statements for method performance used in quality control, regulatory compliance and trade.
• Supporting accreditation, proficiency testing and method adoption by laboratories, manufacturers and inspection bodies.
• Adapting ILS methodology to other homogeneous product sectors where robust precision estimates are required.

Who should use this standard

• Test method developers and standards committees (ISO/TC 28 stakeholders)
• Analytical laboratories and network coordinators running interlaboratory comparisons
• Quality assurance, R&D and regulatory teams in oil & gas, petrochemicals and fuel testing
• Accreditation bodies and proficiency testing providers

Related standards

• ISO 4259-2 (companion part)
• ISO 5725-2 (accuracy - repeatability and reproducibility methodology)
• ISO 3534-2 (statistical terminology)

Keywords: ISO 4259-1:2017, interlaboratory study, precision estimates, petroleum test methods, repeatability, reproducibility, ANOVA, outlier tests.

Standards Content (Sample)

INTERNATIONAL ISO
STANDARD 4259-1
First edition
2017-11
Petroleum and related products —
Precision of measurement methods
and results —
Part 1:
Determination of precision data in
relation to methods of test
Produits pétroliers — Fidélité des méthodes de mesure et des
résultats —
Partie 1: Détermination des valeurs de fidélité relatives aux
méthodes d'essai
Reference number
©
ISO 2017
© ISO 2017, Published in Switzerland
All rights reserved. Unless otherwise specified, no part of this publication may be reproduced or utilized otherwise in any form
or by any means, electronic or mechanical, including photocopying, or posting on the internet or an intranet, without prior
written permission. Permission can be requested from either ISO at the address below or ISO’s member body in the country of
the requester.
ISO copyright office
Ch. de Blandonnet 8 • CP 401
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Tel. [phone]
Fax [phone]
[e-mail]
www.iso.org
ii © ISO 2017 – All rights reserved

Contents Page
Foreword .v
Introduction .vi
1 Scope . 1
2 Normative references . 1
3 Terms and definitions . 1
4 Stages in the planning of an interlaboratory study for the determination of the
precision of a test method . 4
4.1 General . 4
4.2 Preparing a draft method of test . 5
4.3 Planning a pilot study with at least two laboratories . 5
4.4 Planning the ILS . 5
4.5 Executing the ILS . 6
5 Statistical treatment of ILS results . 7
5.1 General recommendation . 7
5.2 Pre-screen using GESD technique . 7
5.3 Transformation of data and outlier tests . 8
5.3.1 General. 8
5.3.2 Outlier identification after pre-screening .11
5.3.3 Uniformity of repeatability .11
5.3.4 Uniformity of reproducibility.11
5.4 Rejection of complete data (from all laboratories) for a sample .11
5.5 Estimating missing or rejected values .12
5.5.1 One of the two repeat values missing or rejected .12
5.5.2 Both repeat values missing or rejected .12
5.6 Rejection test for outlying laboratories .12
5.7 Confirmation of selected transformation .13
5.7.1 General.13
5.7.2 Identification of excessively influential sample(s) .13
6 Analysis of variance, calculation and expression of precision estimates .14
6.1 General .14
6.2 Analysis of variance .14
6.2.1 Forming the sums of squares for the laboratories × samples interaction
sum of squares .14
6.2.2 Forming the sum of squares for the exact analysis of variance .15
6.2.3 Degrees of freedom . .15
6.2.4 Mean squares and analysis of variance .15
6.3 Expectation of mean squares and calculation of precision estimates .15
6.3.1 Expectation of mean squares with no estimated values .15
6.3.2 Expectation of mean squares with estimated values .16
6.3.3 Calculation of precision estimates .17
6.4 Expression of precision estimates of a method of test .18
6.5 Specification of scope for the test method .19
7 R/r ratio .20
Annex A (normative) Determination of number of samples required.21
Annex B (informative) Derivation of formula for estimating the number of laboratories and
samples required to meet minimum 30 degrees of freedom .23
Annex C (normative) Notation and tests .25
Annex D (normative) Illustration of procedures using ILS results for Bromine Number and
statistical tables .30
Annex E (normative) Types of dependence and corresponding transformations.49
Annex F (normative) Weighted linear regression analysis .55
Annex G (normative) Rules for rounding .62
Annex H (normative) GESD technique to simultaneously identify multiple outliers in a data set .64
Annex I (informative) Glossary.72
Bibliography .75
iv © ISO 2017 – All rights reserved

Foreword
ISO (the International Organization for Standardization) is a worldwide federation of national standards
bodies (ISO member bodies). The work of preparing International Standards is normally carried out
through ISO technical committees. Each member body interested in a subject for which a technical
committee has been established has the right to be represented on that committee. International
organizations, governmental and non-governmental, in liaison with ISO, also take part in the work.
ISO collaborates closely with the International Electrotechnical Commission (IEC) on all matters of
electrotechnical standardization.
The procedures used to develop this document and those intended for its further maintenance are
described in the ISO/IEC Directives, Part 1. In particular the different approval criteria needed for the
different types of ISO documents should be noted. This document was drafted in accordance with the
editorial rules of the ISO/IEC Directives, Part 2 (see www.iso.org/directives).
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. Details of
any patent rights identified during the development of the document will be in the Introduction and/or
on the ISO list of patent declarations received (see www.iso.org/patents).
Any trade name used in this document is information given for the convenience of users and does not
constitute an endorsement.
For an explanation on the voluntary nature of standards, the meaning of ISO specific terms and
expressions related to conformity assessment, as well as information about ISO's adherence to the
World Trade Organization (WTO) principles in the Technical Barriers to Trade (TBT) see the following
URL: www.iso.org/iso/foreword.html.
This document was prepared by Technical Committee ISO/TC 28, Petroleum and related products, fuels
and lubricants from natural or synthetic sources.
This first edition of ISO 4259-1, together with ISO 4259-2, cancels and replaces ISO 4259, which has
been technically revised.
A list of all parts in the ISO 4259 series can be found on the ISO website.
Introduction
For purposes of quality control and to check compliance with specifications, the properties of
commercial petroleum products are assessed by standard laboratory test methods. Two or more
measurements of the same property of a specific sample by a specific test method, or, by different test
methods that purport to measure the same property, will not usually give exactly the same result. It is,
therefore, necessary to take proper account of this fact, by arriving at statistically based estimates of
the precision for a method, i.e. an objective measure of the degree of agreement expected between two
or more results obtained in specified circumstances.
[1]
This document makes reference to ISO 3534-2 , which gives a different definition of true value
(see 3.23). This document also refers to ISO 5725-2. The latter is required in particular and unusual
circumstances (see 5.3.1) for the purpose of estimating precision.
The two parts of ISO 4259 encompass both the derivation of precision estimates and the application
[2]
of precision data. They combine the information in ASTM D6300 regarding the determination of the
[3]
precision estimates and the information in ASTM D3244 for the utilization of test data.
A glossary of the variables used in this document and ISO 4259-2 is included as Annex I in this document.
vi © ISO 2017 – All rights reserved

INTERNATIONAL STANDARD ISO 4259-1:2017(E)
Petroleum and related products — Precision of
measurement methods and results —
Part 1:
Determination of precision data in relation to methods of
test
1 Scope
This document specifies the methodology for the design of an Interlaboratory Study (ILS) and
calculation of precision estimates of a test method specified by the study. In particular, it defines the
relevant statistical terms (Clause 3), the procedures to be adopted in the planning of ILS to determine
the precision of a test method (Clause 4), and the method of calculating the precision from the results of
such a study (Clauses 5 and 6).
The procedures in this document have been designed specifically for petroleum and petroleum related
products, which are normally considered as homogeneous. However, the procedures described in this
document can also be applied to other types of homogeneous products. Careful investigations are
necessary before applying this document to products for which the assumption of homogeneity can be
questioned.
2 Normative references
The following documents are referred to in the text in such a way that some or all of their content
constitutes requirements of this document. For dated references, only the edition cited applies. For
undated references, the latest edition of the referenced document (including any amendments) applies.
ISO 5725-2, Accuracy (trueness and precision) of measurement methods and results — Part 2: Basic method
for the determination of repeatability and reproducibility of a standard measurement method
3 Terms and definitions
For the purposes of this document, the following terms and definitions apply.
ISO and IEC maintain terminological databases for use in standardization at the following addresses:
— ISO Online browsing platform: available at https://www.iso.org/obp
— IEC Electropedia: available at http://www.electropedia.org/
3.1
analysis of variance
ANOVA
technique that enables the total variance of a method to be broken down into its component factors
3.2
accepted reference value
ARV
agreed-upon reference value for a specific property of a material determined using an accepted
reference method and protocol, e.g. derived from an ILS
3.3
between laboratory variance
component of the total variance attributable to the difference between the means of different
laboratories
Note 1 to entry: When results obtained by more than one laboratory are compared, the scatter is usually wider
than when the same number of tests is carried out by a single laboratory, and there is some variation between
means obtained by different laboratories. These give rise to the between laboratory variance which is that
component of the overall variance due to the difference in the means obtained by different laboratories.
Note 2 to entry: There is a corresponding definition for between operator variance.
Note 3 to entry: The term “between laboratory” is often shortened to “laboratory” when used to qualify
representative parameters of the dispersion of the population of results, for example as “laboratory variance”.
3.4
bias
difference between the population mean of test results from a very large number
of different laboratories for the property of a material obtained using a specific test method versus the
accepted reference value for the property where this is available
Note 1 to entry: See Note 1 to entry in 3.13 for an interpretation of “population mean of test results”.
3.5
blind coding
assignment of a different number to each sample so that no other identification or information on any
sample is given to the operator
3.6
check sample
sample taken at the place where a product is exchanged, i.e. where the responsibility for the product
quality passes from the supplier to the recipient
3.7
degrees of freedom
divisor used in the calculation of variance
Note 1 to entry: The definition applies strictly only in the simplest cases. Definitions for more complex cases are
beyond the scope of this document.
3.8
determination
process of carrying out the series of operations specified in a test method, whereby a single value is
obtained
3.9
interlaboratory study
ILS
study specifically designed to estimate the repeatability and reproducibility of a standard test method
achieved at a fixed point in time by multiple laboratories through the statistical analysis of their test
results obtained on aliquots prepared from multiple materials
3.10
known value
quantitative value for a property that can be theoretically derived or calculated by the preparation of
the sample
Note 1 to entry: The known value does not always exist, for example for empirical tests such as flash point.
3.11
mean
sum of a set of results divided by the number of results
2 © ISO 2017 – All rights reserved

3.12
mean square
sum of squares divided by the degrees of freedom
3.13
normal distribution
probability distribution of a continuous random variable, x, such that, if x is any real number, the
probability density is as shown in Formula (1):
 
1 1 x−μ
 
fx =−exp,  −∞< ()
 
2 σ
σ 2π  
 
 
Note 1 to entry: In the context of modelling a distribution of test results, μ is the population mean, or true value
(see 3.23) of the property as determined by a specific test method; σ is the standard deviation of the normal
distribution used to describe the distribution of an infinite number of test results obtained using the same test
method by an infinite number of laboratories (σ > 0).
3.14
operator
person who normally and regularly carries out a particular test
3.15
outlier
result far enough in magnitude from other results to be considered not a part of the set
3.16
precision
closeness of agreement between the results obtained by applying the same test procedure several times
on essentially the same materials and under prescribed conditions
Note 1 to entry: The smaller the random part of the experimental error, the more precise the procedure.
3.17
random error
component of measurement error that in replicate measurements varies in an unpredictable manner
3.18
repeatability
limiting value for the difference between two independent results obtained in the normal and correct
operation of the same method, for test material considered to be the same, within a short interval of
time, under the same test conditions, that is expected to be exceeded with a probability of 5% due to
random variation
Note 1 to entry: Same test conditions are to be considered as same operator, same apparatus, same calibration
and same laboratory.
Note 2 to entry: The representative parameter for the dispersion of the population that can be associated with
these results is repeatability standard deviation or repeatability variance. Repeatability refers to the maximum
difference attributable to random variation between two results obtained under the state of minimum random
variability. Therefore, the period of time during which repeat results are to be obtained should be short enough
to exclude time dependent variation, for example, variation caused by environmental changes, or variation
associated with multiple calibrations”.
Note 3 to entry: The term “repeatability” is not to be confused with the terms “between repeats” or “repeats”.
3.19
reproducibility
limiting value for the difference between two independent results obtained in the normal and correct
operation of the same method, for test material considered to be the same, under different test
conditions, that is expected to be exceeded with a probability of 5 % due to random variation
Note 1 to entry: Different test conditions are to be considered as different operator, different apparatus, different
calibration, and different laboratory.
Note 2 to entry: The representative parameter of the dispersion of the population that can be associated with
these results is reproducibility standard deviation or reproducibility variance. Reproducibility refers to the
maximum difference attributable to random variation between two results obtained under the state of maximum
random variability.
3.20
result
final value obtained by following the complete set of instructions in a test method
Note 1 to entry: It is assumed that the result is rounded off according to the procedure specified in Annex G.
3.21
standard deviation
measure of the dispersion of a series of results around their mean, equal to the positive square root of
the variance and estimated by the positive square root of the mean square
3.22
sum of squares
sum of squares of the differences between a series of results and their mean
3.23
true value
for practical purposes, the value towards which the average of single results obtained by n laboratories
tends, as n tends towards infinity
Note 1 to entry: Such a true value is associated with the particular method of test.
[1]
Note 2 to entry: A different and idealized definition is given in ISO 3534-2 .
3.24
variance
mean of the squares of the deviation of a random variable from its mean, estimated by the mean square
4 Stages in the planning of an interlaboratory study for the determination of the
precision of a test method
4.1 General
The stages in planning an interlaboratory study (ILS) are as follows:
a) preparing a draft method of test;
b) planning a pilot study with at least two laboratories;
c) planning the ILS;
d) executing the ILS.
The four stages are described in turn in 4.2 to 4.5.
4 © ISO 2017 – All rights reserved

4.2 Preparing a draft method of test
This shall contain all the necessary details for carrying out the test and reporting the results. Any
condition that could alter the results shall be specified.
The ILS shall be designed so that it covers the intended range of the test method (see also 6.5). A clause
on precision is included in the draft method of the test at this stage only as a heading.
4.3 Planning a pilot study with at least two laboratories
A pilot study is necessary for the following reasons:
a) to verify the details in the operation of the test;
b) to find out how well operators can follow the instructions of the method, and thus of the ILS;
c) to check the precautions regarding samples;
d) to estimate approximately the precision of the test.
At least two samples are required, covering the range of results to which the test method is intended
to apply; however, at least 12 laboratory/sample combinations shall be included. Each sample is tested
twice by each laboratory under repeatability conditions. The samples should be equally distributed
across the test method range, and should include major product groups covered in the test method scope.
If any omissions or inaccuracies in the draft test method are revealed, they shall now be corrected. The
results shall be analysed for precision, and bias for sample(s) with accepted reference values. If either is
considered to be too large, then alterations to the test method shall be considered.
4.4 Planning the ILS
There shall be at least six participating laboratories, but it is recommended this number be increased
to eight or more in order to ensure the final precision is based on at least six laboratories and to ensure
the precision statement is more representative of the user population.
The number of samples shall be sufficient to adequately represent the types of materials to which the
test method is to be applied, to cover the range of the property measured at approximately equidistant
intervals, and to give reliability to the precision estimates. If precision is found to vary with the level
of results in the pilot study, then at least five samples shall be used in the ILS. In order to correctly
estimate precision versus level relationship, it is important that the choice of samples evenly covers the
range and materials for the property measured, so that an estimated relationship is not too dependent
upon the leverage of a sample with extreme property value.
It is strongly recommended that the leverage of each planned sample in the sample set design, lev
i,
be assessed using Formula (2). No sample shall have a leverage exceeding 0,5. See Table D.11 for an
example of leverage calculation (second column from the right under heading 'lev ').
i
()xx−
i
lev =+ (2)
i
n
n
()xx−
∑ k
k=1
where
lev is leverage of sample i;
i
n is total number of planned samples;
x is Napierian logarithm, ln (p ), with p being the planned property level for sample i;
i i i
is grand average of all x .
i
x
In any event, it is necessary to obtain at least 30 degrees of freedom for both repeatability and
reproducibility (see Annex B for the corresponding rationale). For repeatability, this means obtaining a
total of at least 30 pairs of results in the ILS.
For reproducibility, Annex A, Table A.1 gives the minimum number of samples required in terms of L,
P and Q, where L is the number of participating laboratories, and P and Q are the ratios of variance
component estimates obtained from the pilot study. Specifically, P is the ratio of the interaction
component to the repeats component and Q is the ratio of the laboratories component to the repeats
component. Annex B gives the derivation of the formula used. If Q is much larger than P, then 30 degrees
of freedom cannot be achieved; the blank entries in Table A.1 correspond to this situation (i.e. when
more than 20 samples are required). For these cases, there is likely to be a significant bias between
laboratories.
In the absence of pilot test program information to permit the use of Table A.1, the number of samples
shall be greater than five, and chosen such that the number of laboratories times the number of samples
is greater than or equal to 42.
When it is known or suspected that different types of materials exhibit different precision functional
forms when tested by the test method, consideration should be given to conducting separate ILS for
each type of material.
4.5 Executing the ILS
One person shall be responsible for the entire ILS, from the distribution of the texts of the test method
and samples to the final appraisal of the results. This person shall be familiar with the test method, but
shall not personally take part in the tests.
The text of the test method shall be distributed to all the laboratories in time to allow any queries to be
raised before the tests begin. If any laboratory wants to practice the method in advance, than this shall
be carried out with samples other than those used in the ILS.
The samples shall be accumulated, subdivided and distributed by the coordinator, who shall also keep
a reserve of each sample for emergencies. It is most important that the individual laboratory portions
be homogeneous and stable for the property of interest throughout the entire duration of the ILS. Prior
to distribution, the ILS sample set shall be blind coded in a manner that preserves the anonymity of the
nature of the test material and the expected value of the property. The following information shall be
sent with the ILS sample set.
a) Agreed (draft) method of test.
b) Handling and storage requirements for the samples.
c) Order in which the samples are to be tested. A different random order for each laboratory is highly
recommended. For large number of laboratories, several unique test orders may be randomly
assigned to groups of laboratories, with no more than 4 laboratories per group.
d) For statistical reasons, it is imperative that the repeat results are obtained independently of each
other, i.e. that the second result is not biased by knowledge of the first. This is achieved by blind
coding where the repeat for each material in the ILS design is included in the test set sent to ILS
participants without disclosing that it is a repeat, with an accompanying statement that a single
result is to be obtained on each sample in the test set, in the specified testing order, by the same
operator with the same apparatus within a short time. If this blind coding is regarded as infeasible
to achieve, then the statement shall state that a pair of results associated with a sample shall be
obtained by the same operator with the same apparatus within a short time, without disclosing the
nature of the sample.
e) Period of time within which all the samples are to be tested.
6 © ISO 2017 – All rights reserved

f) Blank form for reporting the results. For each sample, there shall be space for the date of testing,
the test results, and any unusual occurrences. The unit of accuracy for reporting the results shall
be specified.
g) Statement that the test shall be carried out under normal conditions, using qualified operators who
carry out this kind of test routinely and that the duration of the test shall be the same as normal.
h) A questionnaire requesting information on the conditions used in the application of the test
method, e.g. apparatus details, reagents and materials, calibration and verification procedures,
quality control procedure, any deviations from either the test method or the instructions supplied,
observations and suggestions for future improvement of the test method.
Operators that participated in the pilot study may also participate in the ILS. If their extra experience
in testing a few more samples produces a noticeable effect, it serves as a warning that the test method
is not satisfactory. They shall be identified in the report of the results so that any effect can be noted.
[4]
NOTE For additional guidance on the planning and execution of an ILS, consult ASTM D7778 and
[2]
ASTM D6300 .
5 Statistical treatment of ILS results
5.1 General recommendation
Although the procedures described in Clauses 5 and 6 of this document are in a form suitable for hand
calculation, it is strongly advised that these procedures be carried out using an electronic computer
with appropriately validated software designed specifically to store and analyse ILS test results based
on the procedures of this document. It is also highly recommended that these procedures be carried out
under the guidance of a statistician.
[13]
NOTE A software package extensively used in the ISO and ASTM community is D2PP . That software
package does not include GESD or Cook's Distance assessment in line with this document.
In the clauses to follow, procedures are specified to achieve the following:
a) pre-screen the results as reported from the ILS on a sample-by-sample basis for grossly discordant
results (outliers);
b) assess independence or dependence of precision and the level of results after pre-screening;
c) assess uniformity of precision from laboratory to laboratory by detecting the presence (or absence)
of additional outliers using the detection power from the entire data set.
The procedures are described in mathematical terms based on the notation of Annex C.
Illustration of the procedures is provided in referenced Annexes.
For all the procedures, it is assumed that the results are either from a single normal distribution or
capable of being transformed into such a distribution (see 5.3). Other cases (which are rare) require a
different treatment that is beyond the scope of this document. See Reference [6] for a statistical test on
normality.
5.2 Pre-screen using GESD technique
Prior to execution of 5.3 to 5.7, examine all information returned by ILS participants to determine
compliance with agreed-upon test protocol and method of test. If the investigation disclosed no clerical,
sampling or procedural errors, apply the Generalized Extreme Studentized Deviation (GESD) technique
as outlined in this clause to results received for each ILS sample to identify unusual or extreme results.
Investigation for causes associated with unusual results shall be conducted. If acceptable cause(s) is
found during the investigation, the unusual results shall be either corrected, replaced, or rejected.
Correction or replacement of the unusual results with a new set of results shall be approved by the ILS
coordinator in consultation with the ILS statistician. If no acceptable cause is found, the unusual or
extreme results as identified by the GESD technique at the 99 % confidence level shall be rejected.
An overall summary of this GESD pre-screening technique is outlined below.
For each ILS sample, execute the following steps.
1) Calculate the sample mean using all results received for the sample.
2) Calculate difference for each pair of results as received from laboratories that have reported both
results.
3) Identify outlier(s) in the data set of differences obtained from step 2) by following the methodology
outlined in Annex H.
4) For each outlying difference identified, remove the member from the pair that is farthest from the
sample mean calculated in 1) and replace it with the value of the remaining result.
5) For laboratories that have only reported one result, i.e. the other result is missing, assign the value
of the single reported result to the missing result before proceeding to step 6).
6) Calculate the sum of the pair of the results for each lab. For laboratories that have reported both
results and neither result has been rejected, this will be the sum of both reported results. In the
case where one of the pair of results is missing (not reported) or rejected from step 4), this sum
will be twice the single reported result since the missing result is assigned the same value as the
reported result.
7) Identify outlier(s) in data set of sums as obtained from step 6) by following the methodology
outlined in Annex H.
8) For each outlying sum of results, exclude both results from further statistical analysis.
9) For the pairs of results with sums that have not been rejected, retain both reported results for
analysis if both results are as originally received from the laboratories. If one of the two results of
the pair is an assigned value from step 4) or step 5), retain the reported result from the laboratories
for analysis, and treat the other result as “missing”.
10) The data set remaining after completion of step 9) then constitutes the data set to be further
analysed as per 5.3 to 5.7.
5.3 Transformation of data and outlier tests
5.3.1 General
In many test methods, the precision depends on the level of the test result, and thus the variability of the
reported results is different from sample to sample. The method of analysis outlined in this document
requires that this shall not be so and the position is rectified, if necessary, by a transformation.
The laboratories standard deviations, D , and the repeats standard deviations, d , for sample j (see
j j
Annex C for notation explanation) are calculated and plotted separately against the sample means, m ,
j
in accordance with Annexes D and E). If the points so plotted can be considered as lying about a pair of
lines parallel to the m-axis, then no transformation is necessary. If, however, the plotted points describe
non-horizontal straight lines or curves of the form D = f (m) and d = f (m), then a transformation is
1 2
necessary.
The relationships D = f (m) and d = f (m) are not, in general, identical. The statistical procedures of
1 2
this document require, however, that the same transformation be applicable both for repeatability
and for reproducibility. For this reason, the two relationships are combined into a single dependency
relationship D = f(m) (where D now includes d) by including a dummy variable, T. This takes account
of the difference between the relationships, if one exists, and provides a means of testing for this
difference (see F.1).
8 © ISO 2017 – All rights reserved

The single relationship D = f(m) is best estimated by a weighted linear regression analysis, even though
in most cases an unweighted regression gives a satisfactory approximation. The derivation of weights
is described in F.2, and the computational procedure for the regression analysis is described in F.3.
Typical forms of dependence D = f(m) are given in E.1. These are all expressed in terms of transformation
parameters B and B .
The estimation of B and B , and the transformation procedure which follows, are summarized
in E.2. This includes statistical tests for the significance of the regression (i.e. is the relationship
D = f(m) parallel to the m-axis), and for the difference between the repeatability and reproducibility
relationships, based at the 5 % significance level. If such a difference is found to exist, or if no suitable
common transformation exists, then the alternative sample by sample procedures of ISO 5725-2 shall
be used. In such an event, it is not possible to test for laboratory bias over all samples (see 5.6) or
separately estimate the interaction component of variance (see 6.2).
If it has been shown at the 5 % significance level that there is a significant regression of the form D = f(m),
then the appropriate transformation y = F(x), where x is the reported result, is given by Formula (3):
dx
Fx =K (3)
()
∫
fx
()
where K is a constant.
In that event, all results shall be transformed accordingly and the remainder of the analysis carried out
in terms of the transformed results. Typical transformations are given in E.1.
It is difficult to make the choice of transformation the subject of formalized rules. Qualified statistical
assistance can be required in particular cases. The presence of outliers can affect judgement as to the
type of transformation required, if any (see 5.7). That is why extremely discordant results shall be
removed as described in 5.1 above prior to making a judgement on transformation(s).
The transformation and outlier procedure is described in the form of a flow chart in Figure 1. Note
that the transformation process is an iterative procedure, requiring confirmation of the choice of
transformation if outliers have been rejected. If the original transformation is found to be inadequate
after outliers have been removed, then a different transformation will be required.
Figure 1 — Transformation and outlier procedure
10 © ISO 2017 – All rights reserved

5.3.2 Outlier identification after pre-screening
The pre-screened results, or if it has been decided that a transformation is necessary, the pre-screened
and transformed results, shall be further tested statistically for outliers. These are the values that are
so different from the remaining data that it can only be concluded that they have arisen from some fault
in the application of the test method or from testing a wrong sample. Many possible tests may be used
and the associated significance levels can be varied, but those that are given below have been found to
be appropriate for this document. These outlier tests all assume a normal distribution of errors (see 5.1).
5.3.3 Uniformity of repeatability
The first outlier test is concerned with detecting a discordant result for the absolute difference
[7] 2
between a pair of repeat results. This test involves calculating the e over all the laboratory/sample
ij
combinations. Cochran's criterion at the 1 % significance level is then used to test the ratio of the
largest of these e values over their sum (see C.5). If its value exceeds the value given in Table D.14,
ij
corresponding to one degree of freedom, n being the number of pairs available for comparison, then
r
the member of the pair farthest from the sample mean shall be rejected and the process repeated,
reducing n by 1, until no more rejections are called for. In certain cases, this test “snowballs” and leads
r
to an unacceptably large proportion of rejections (say more than 10 %). If this is so, this rejection test
shall be abandoned and some or all of the rejected results shall be retained. An arbitrary decision based
on judgement is necessary in this case. See D.3 for an illustration.
5.3.4 Uniformity of reproducibility
The following outlier test, Hawkins' test, see also D.4, is concerned with establishing uniformity in the
reproducibility estimate. It is designed to detect a discordant pair of results from a laboratory on a
particular sample. It involves, for each sample, forming the ratio of the largest absolute deviation of
laboratory mean from the overall sample mean to the square root of certain sums of squares (see C.6).
The ratio corresponding to the largest absolute deviation shall be compared with the critical 1 % values
given in Table D.15, where n is the number of laboratory cells in the sample concerned and where ν is
R
the degrees of freedom for the sum of squares, which is additional to that corresponding to the sample
in question. That is, for this test, ν refers to the degrees of freedom from other samples (i.e. excludes
R
the sample being tested).
If a significant value is encountered, the corresponding extreme value shall be omitted and the process
repeated.
If the test “snowballs”, leading to an unacceptably large proportion of rejections (say more than 10 %),
then this rejection test shall be abandoned and some or all of the rejected results shall be retained. An
arbitrary decision based on judgement is necessary in this case.
5.4 Rejection of complete data (from all laboratories) for a sample
The laboratories standard deviation and repeats standard deviation shall be examined for any outlying
samples. If a transformation has been carried out or any rejection made, new standard deviations shall
be calculated. See D.5 for further illustration.
If the standard deviation for any sample is excessively lar
...

© ISO 2017 – All rights reserved
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Date: 2017‐10‐02
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ISO/TC 28/WG 2
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Secretariat: NEN (U.S.)
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Petroleum and related products — Precision of measurement methods and results —
Formatted
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Part 1: Determination of precision data in relation to methods of test
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Produits pétroliers -- Fidélité des méthodes de mesure et des résultats -- Partie 1: Détermination
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Document type: International Standard
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Document stage: (50) Approval
Document language: E
STD Version 2.3
Deleted: Copyright notice¶
This ISO document is a Draft International
Standard and is copyright‐protected by ISO.
Except as permitted under the applicable
laws of the user's country, neither this ISO
draft nor any extract from it may be
reproduced, stored in a retrieval system or
transmitted in any form or by any means,
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otherwise, without prior written permission
being secured.¶
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© ISO 2017 – All rights reserved
ii
Deleted: 1 Scope 1¶
2 Normative references 1¶
3 Terms and definitions 1¶
Stages in the planning of an
Contents Page
Interlaboratory Study for the
determination of the precision of
a test method 4¶
4.1 General 4¶
4.2 Preparing a draft method of
test 4¶
4.3 Planning a pilot study with
at least two laboratories 4¶
4.4 Planning the ILS 5¶
4.5 Executing the ILS 5¶
5 Statistical treatment of ILS
results 6¶
5.1 General recommendation 6¶
5.2 Pre-screen using GESD
technique 7¶
5.3 Transformation of data and
outlier tests 8¶
5.4 Rejection of complete data
(from all laboratories) for a
sample 10¶
5.5 Estimating missing or
rejected values 10¶
5.6 Rejection test for outlying
laboratories 11¶
Confirmation of selected
5.7
transformation 11¶
6 Analysis of variance,
calculation and expression of
precision estimates 12¶
6.1 General 12¶
6.2 Analysis of variance 12¶
6.3 Expectation of mean squares
and calculation of precision
estimates 14¶
6.4 Expression of precision
estimates of a method of test 16¶
6.5 Specification of scope for the
test method 17¶
7 R / r ratio 18¶
Annex A (normative)
Determination of number of
samples required 19¶
Annex B (informative) Derivation
of formula for estimating the
number of labs and samples
required to meet minimum 30
degrees of freedom (Table
A.1) 21¶
B.1 Degrees of freedom 21¶
B.2 Explanation for choice of 30
as Minimum degrees of
freedom 22¶
Annex C (normative) Notation and
tests 23¶
C.1 Introduction 23¶
C.2 Array of duplicate
results 23¶
C.3 Array of sums of duplicate
results 24¶
C.4 Sums of squares and
variances 24¶
C.5 Cochran's test 25¶
C.6 Hawkins' test 25¶
C.7 Variance ratio test (F-
test) 27¶
Annex D (normative) Illustration
of procedures using ILS results
... [8]
© ISO 2017 – All rights reserved
iii
Foreword
ISO (the International Organization for Standardization) is a worldwide federation of national
standards bodies (ISO member bodies). The work of preparing International Standards is normally
carried out through ISO technical committees. Each member body interested in a subject for which a
technical committee has been established has the right to be represented on that committee.
International organizations, governmental and non‐governmental, in liaison with ISO, also take part in
the work. ISO collaborates closely with the International Electrotechnical Commission (IEC) on all
matters of electrotechnical standardization.
The procedures used to develop this document and those intended for its further maintenance are
described in the ISO/IEC Directives, Part 1. In particular the different approval criteria needed for the
different types of ISO documents should be noted. This document was drafted in accordance with the
editorial rules of the ISO/IEC Directives, Part 2 (see www.iso.org/directives). Deleted: www.iso.org/directives
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. Details of
any patent rights identified during the development of the document will be in the Introduction and/or
on the ISO list of patent declarations received (see www.iso.org/patents). Deleted: www.iso.org/patents
Any trade name used in this document is information given for the convenience of users and does not
constitute an endorsement.
For an explanation on the voluntary nature of standards, the meaning of ISO specific terms and
expressions related to conformity assessment, as well as information about ISO's adherence to the
World Trade Organization (WTO) principles in the Technical Barriers to Trade (TBT) see the following
URL: www.iso.org/iso/foreword.html. Deleted: www.iso.org/iso/foreword.html
This document was prepared by Technical Committee ISO/TC 28, Petroleum and related products, fuels
and lubricants from natural or synthetic sources.
This first edition of ISO 4259‐1, together with ISO 4259‐2, cancels and replaces ISO 4259, which has
been technically revised.
A list of all parts in the ISO 4259 series can be found on the ISO website.
© ISO 2017 – All rights reserved
iv
Introduction
For purposes of quality control and to check compliance with specifications, the properties of
commercial petroleum products are assessed by standard laboratory test methods. Two or more
measurements of the same property of a specific sample by a specific test method, or, by different test
methods that purport to measure the same property, will not usually give exactly the same result. It is,
therefore, necessary to take proper account of this fact, by arriving at statistically based estimates of the
precision for a method, i.e. an objective measure of the degree of agreement expected between two or
more results obtained in specified circumstances.
[1]
This document makes reference to ISO 3534‐2 , which gives a different definition of true value (see
3.23). This document also refers to ISO 5725‐2. The latter is required in particular and unusual
circumstances (see 5.3.1) for the purpose of estimating precision.
The two parts of ISO 4259 encompass both the derivation of precision estimates and the application of
[2]
precision data. They combine the information in ASTM D6300 regarding the determination of the
[3]
precision estimates and the information in ASTM D3244 for the utilization of test data.
A glossary of the variables used in this document and ISO 4259‐2 is included as Annex I in this
document.
© ISO 2017 – All rights reserved
v
Petroleum and related products — Precision of measurement
methods and results — Part 1: Determination and application of
precision data in relation to methods of test
1 Scope
This document specifies the methodology for the design of an Interlaboratory Study (ILS) and
calculation of precision estimates of a test method specified by the study. In particular, it defines the
relevant statistical terms (Clause 3), the procedures to be adopted in the planning of ILS to determine
the precision of a test method (Clause 4), and the method of calculating the precision from the results of
such a study (Clauses 5 and 6).
The procedures in this document have been designed specifically for petroleum and petroleum related
products, which are normally considered as homogeneous. However, the procedures described in this
document can also be applied to other types of homogeneous products. Careful investigations are
necessary before applying this document to products for which the assumption of homogeneity can be
questioned.
2 Normative references
The following documents are referred to in the text in such a way that some or all of their content
constitutes requirements of this document. For dated references, only the edition cited applies. For
undated references, the latest edition of the referenced document (including any amendments) applies.
ISO 5725‐2, Accuracy (trueness and precision) of measurement methods and results — Part 2: Basic
method for the determination of repeatability and reproducibility of a standard measurement method
3 Terms and definitions
For the purposes of this document, the following terms and definitions apply.
ISO and IEC maintain terminological databases for use in standardization at the following addresses:
Deleted: https://www.iso.org/obp
— ISO Online browsing platform: available at https://www.iso.org/obp
— IEC Electropedia: available at http://www.electropedia.org/ Deleted: http://www.electropedia.org/
3.1
analysis of variance
ANOVA
technique that enables the total variance of a method to be broken down into its component factors
3.2
accepted reference value
ARV
agreed‐upon reference value for a specific property of a material determined using an accepted
reference method and protocol, e.g. derived from an ILS
3.3
between laboratory variance
component of the total variance attributable to the difference between the means of different
laboratories
Note 1 to entry: When results obtained by more than one laboratory are compared, the scatter is usually wider
than when the same number of tests is carried out by a single laboratory, and there is some variation between
means obtained by different laboratories. These give rise to the between laboratory variance which is that
component of the overall variance due to the difference in the means obtained by different laboratories.
Note 2 to entry: There is a corresponding definition for between operator variance.
Note 3 to entry: The term “between laboratory” is often shortened to “laboratory” when used to qualify
representative parameters of the dispersion of the population of results, for example as “laboratory variance”.
3.4
bias
difference between the population mean of test results from a very large number of
different laboratories for the property of a material obtained using a specific test method versus the
accepted reference value for the property where this is available
Note 1 to entry: See Note 1 to entry in 3.13 for an interpretation of “population mean of test results”.
3.5
blind coding
assignment of a different number to each sample so that no other identification or information on any
sample is given to the operator
3.6
check sample
sample taken at the place where a product is exchanged, i.e. where the responsibility for the product
quality passes from the supplier to the recipient
3.7
degrees of freedom
divisor used in the calculation of variance
Note 1 to entry: The definition applies strictly only in the simplest cases. Definitions for more complex cases are
beyond the scope of this document.
3.8
determination
process of carrying out the series of operations specified in a test method, whereby a single value is
obtained
3.9
interlaboratory study
ILS
study specifically designed to estimate the repeatability and reproducibility of a standard test method
achieved at a fixed point in time by multiple laboratories through the statistical analysis of their test
results obtained on aliquots prepared from multiple materials
3.10
known value
quantitative value for a property that can be theoretically derived or calculated by the preparation of
the sample
Note 1 to entry: The known value does not always exist, for example for empirical tests such as flash point.
3.11
mean
© ISO 2017 – All rights reserved
lxxi
sum of a set of results divided by the number of results
3.12
mean square
sum of squares divided by the degrees of freedom
3.13
normal distribution
probability distribution of a continuous random variable, x, such that, if x is any real number, the
probability density is as shown in Formula (1):

11 x


fxexp ,x (1)


2 
 2

Note 1 to entry: In the context of modelling a distribution of test results, μ is the population mean, or true value
(see 3.23) of the property as determined by a specific test method; σ is the standard deviation of the normal
distribution used to describe the distribution of an infinite number of test results obtained using the same test
method by an infinite number of laboratories (σ > 0).
3.14
operator
person who normally and regularly carries out a particular test
3.15
outlier
result far enough in magnitude from other results to be considered not a part of the set
3.16
precision
closeness of agreement between the results obtained by applying the same test procedure several times
on essentially the same materials and under prescribed conditions
Note 1 to entry: The smaller the random part of the experimental error, the more precise the procedure.
3.17
random error
component of measurement error that in replicate measurements varies in an unpredictable manner
3.18
repeatability
limiting value for the difference between two independent results obtained in the normal and correct
operation of the same method, for test material considered to be the same, within a short interval of
time, under the same test conditions, that is expected to be exceeded with a probability of 5% due to
random variation
Note 1 to entry: Same test conditions are to be considered as same operator, same apparatus, same calibration
and same laboratory.
Note 2 to entry: The representative parameter for the dispersion of the population that can be associated with
these results is repeatability standard deviation or repeatability variance. Repeatability refers to the maximum
difference attributable to random variation between two results obtained under the state of minimum random
variability. Therefore, the period of time during which repeat results are to be obtained should be short enough to
© ISO 2017 – All rights reserved
lxxii
exclude time dependent variation, for example, variation caused by environmental changes, or variation
associated with multiple calibrations”.
Note 3 to entry: The term “repeatability” is not to be confused with the terms “between repeats” or “repeats”.
3.19
reproducibility
limiting value for the difference between two independent results obtained in the normal and correct
operation of the same method, for test material considered to be the same, under different test
conditions, that is expected to be exceeded with a probability of 5 % due to random variation
Note 1 to entry: Different test conditions are to be considered as different operator, different apparatus, different
calibration, and different laboratory.
Note 2 to entry: The representative parameter of the dispersion of the population that can be associated with
these results is reproducibility standard deviation or reproducibility variance. Reproducibility refers to the
maximum difference attributable to random variation between two results obtained under the state of maximum
random variability.
3.20
result
final value obtained by following the complete set of instructions in a test method
Note 1 to entry: It is assumed that the result is rounded off according to the procedure specified in Annex G.
3.21
standard deviation
measure of the dispersion of a series of results around their mean, equal to the positive square root of
the variance and estimated by the positive square root of the mean square
3.22
sum of squares
sum of squares of the differences between a series of results and their mean
3.23
true value
for practical purposes, the value towards which the average of single results obtained by n laboratories
tends, as n tends towards infinity
Note 1 to entry: Such a true value is associated with the particular method of test.
[1]
Note 2 to entry: A different and idealized definition is given in ISO 3534‐2 .
3.24
variance
mean of the squares of the deviation of a random variable from its mean, estimated by the mean square
4 Stages in the planning of an interlaboratory study for the determination of the
precision of a test method
4.1 General
The stages in planning an interlaboratory study (ILS) are as follows:
a) preparing a draft method of test;
© ISO 2017 – All rights reserved
lxxiii
b) planning a pilot study with at least two laboratories;
c) planning the ILS;
d) executing the ILS.
The four stages are described in turn in 4.2 to 4.5.
4.2 Preparing a draft method of test
This shall contain all the necessary details for carrying out the test and reporting the results. Any
condition that could alter the results shall be specified.
The ILS shall be designed so that it covers the intended range of the test method (see also 6.5). A clause
on precision is included in the draft method of the test at this stage only as a heading.
4.3 Planning a pilot study with at least two laboratories
A pilot study is necessary for the following reasons:
a) to verify the details in the operation of the test;
b) to find out how well operators can follow the instructions of the method, and thus of the ILS;
c) to check the precautions regarding samples;
d) to estimate approximately the precision of the test.
At least two samples are required, covering the range of results to which the test method is intended to
apply; however, at least 12 laboratory/sample combinations shall be included. Each sample is tested
twice by each laboratory under repeatability conditions. The samples should be equally distributed
across the test method range, and should include major product groups covered in the test method
scope. If any omissions or inaccuracies in the draft test method are revealed, they shall now be
corrected. The results shall be analysed for precision, and bias for sample(s) with accepted reference
values. If either is considered to be too large, then alterations to the test method shall be considered.
4.4 Planning the ILS
There shall be at least six participating laboratories, but it is recommended this number be increased to
eight or more in order to ensure the final precision is based on at least six laboratories and to ensure
the precision statement is more representative of the user population.
The number of samples shall be sufficient to adequately represent the types of materials to which the
test method is to be applied, to cover the range of the property measured at approximately equidistant
intervals, and to give reliability to the precision estimates. If precision is found to vary with the level of
results in the pilot study, then at least five samples shall be used in the ILS. In order to correctly
estimate precision versus level relationship, it is important that the choice of samples evenly covers the
range and materials for the property measured, so that an estimated relationship is not too dependent
upon the leverage of a sample with extreme property value.
It is strongly recommended that the leverage of each planned sample in the sample set design, lev be
i,
assessed using Formula (2). No sample shall have a leverage exceeding 0,5. See Table D.11 for an
example of leverage calculation (second column from the right under heading 'levi').
© ISO 2017 – All rights reserved
lxxiv
()xx
i
lev (2)
i
n
n
()xx
 k
k1
where
lev is leverage of sample i;
i
n is total number of planned samples;
xi is Napierian logarithm, ln (pi), with pi being the planned property level for sample i;
x is grand average of all xi.
In any event, it is necessary to obtain at least 30 degrees of freedom for both repeatability and
reproducibility (see Annex B for the corresponding rationale). For repeatability, this means obtaining a
total of at least 30 pairs of results in the ILS.
For reproducibility, Annex A, Table A.1 gives the minimum number of samples required in terms of L, P
and Q, where L is the number of participating laboratories, and P and Q are the ratios of variance
component estimates obtained from the pilot study. Specifically, P is the ratio of the interaction
component to the repeats component and Q is the ratio of the laboratories component to the repeats
component. Annex B gives the derivation of the formula used. If Q is much larger than P, then
30 degrees of freedom cannot be achieved; the blank entries in Table A.1 correspond to this situation
(i.e. when more than 20 samples are required). For these cases, there is likely to be a significant bias
between laboratories.
In the absence of pilot test program information to permit the use of Table A.1, the number of samples
shall be greater than five, and chosen such that the number of laboratories times the number of samples
is greater than or equal to 42.
When it is known or suspected that different types of materials exhibit different precision functional
forms when tested by the test method, consideration should be given to conducting separate ILS for
each type of material.
4.5 Executing the ILS
One person shall be responsible for the entire ILS, from the distribution of the texts of the test method
and samples to the final appraisal of the results. This person shall be familiar with the test method, but
shall not personally take part in the tests.
The text of the test method shall be distributed to all the laboratories in time to allow any queries to be
raised before the tests begin. If any laboratory wants to practice the method in advance, than this shall
be carried out with samples other than those used in the ILS.
The samples shall be accumulated, subdivided and distributed by the coordinator, who shall also keep a
reserve of each sample for emergencies. It is most important that the individual laboratory portions be
homogeneous and stable for the property of interest throughout the entire duration of the ILS. Prior to
distribution, the ILS sample set shall be blind coded in a manner that preserves the anonymity of the
nature of the test material and the expected value of the property. The following information shall be
sent with the ILS sample set.
a) Agreed (draft) method of test.
b) Handling and storage requirements for the samples.
© ISO 2017 – All rights reserved
lxxv
c) Order in which the samples are to be tested. A different random order for each laboratory is highly
recommended. For large number of laboratories, several unique test orders may be randomly
assigned to groups of laboratories, with no more than 4 laboratories per group.
d) For statistical reasons, it is imperative that the repeat results are obtained independently of each
other, i.e. that the second result is not biased by knowledge of the first. This is achieved by blind
coding where the repeat for each material in the ILS design is included in the test set sent to ILS
participants without disclosing that it is a repeat, with an accompanying statement that a single
result is to be obtained on each sample in the test set, in the specified testing order, by the same
operator with the same apparatus within a short time. If this blind coding is regarded as infeasible
to achieve, then the statement shall state that a pair of results associated with a sample shall be
obtained by the same operator with the same apparatus within a short time, without disclosing the
nature of the sample.
e) Period of time within which all the samples are to be tested.
f) Blank form for reporting the results. For each sample, there shall be space for the date of testing,
the test results, and any unusual occurrences. The unit of accuracy for reporting the results shall be
specified.
g) Statement that the test shall be carried out under normal conditions, using qualified operators who
carry out this kind of test routinely and that the duration of the test shall be the same as normal.
h) A questionnaire requesting information on the conditions used in the application of the test
method, e.g. apparatus details, reagents and materials, calibration and verification procedures,
quality control procedure, any deviations from either the test method or the instructions supplied,
observations and suggestions for future improvement of the test method.
Operators that participated in the pilot study may also participate in the ILS. If their extra experience in
testing a few more samples produces a noticeable effect, it serves as a warning that the test method is
not satisfactory. They shall be identified in the report of the results so that any effect can be noted.
[4]
NOTE For additional guidance on the planning and execution of an ILS, consult ASTM D7778 and
[2]
ASTM D6300 .
5 Statistical treatment of ILS results
5.1 General recommendation
Although the procedures described in Clauses 5 and 6 of this document are in a form suitable for hand
calculation, it is strongly advised that these procedures be carried out using an electronic computer
with appropriately validated software designed specifically to store and analyse ILS test results based
on the procedures of this document. It is also highly recommended that these procedures be carried out
under the guidance of a statistician.
[13]
NOTE A software package extensively used in the ISO and ASTM community is D2PP . That software
package does not include GESD or Cook's Distance assessment in line with this document.
In the clauses to follow, procedures are specified to achieve the following:
a) pre‐screen the results as reported from the ILS on a sample‐by‐sample basis for grossly discordant
results (outliers);
b) assess independence or dependence of precision and the level of results after pre‐screening;
© ISO 2017 – All rights reserved
lxxvi
c) assess uniformity of precision from laboratory to laboratory by detecting the presence (or absence)
of additional outliers using the detection power from the entire data set.
The procedures are described in mathematical terms based on the notation of Annex C.
Illustration of the procedures is provided in referenced Annexes.
For all the procedures, it is assumed that the results are either from a single normal distribution or
capable of being transformed into such a distribution (see 5.3). Other cases (which are rare) require a
different treatment that is beyond the scope of this document. See Reference [6] for a statistical test on
normality.
5.2 Pre-screen using GESD technique
Prior to execution of 5.3 to 5.7, examine all information returned by ILS participants to determine
compliance with agreed‐upon test protocol and method of test. If the investigation disclosed no clerical,
sampling or procedural errors, apply the Generalized Extreme Studentized Deviation (GESD) technique
as outlined in this clause to results received for each ILS sample to identify unusual or extreme results.
Investigation for causes associated with unusual results shall be conducted. If acceptable cause(s) is
found during the investigation, the unusual results shall be either corrected, replaced, or rejected.
Correction or replacement of the unusual results with a new set of results shall be approved by the ILS
coordinator in consultation with the ILS statistician. If no acceptable cause is found, the unusual or
extreme results as identified by the GESD technique at the 99 % confidence level shall be rejected.
An overall summary of this GESD pre‐screening technique is outlined below.
For each ILS sample, execute the following steps.
1) Calculate the sample mean using all results received for the sample.
2) Calculate difference for each pair of results as received from laboratories that have reported both
results.
3) Identify outlier(s) in the data set of differences obtained from step 2) by following the methodology
outlined in Annex H.
4) For each outlying difference identified, remove the member from the pair that is farthest from the
sample mean calculated in 1) and replace it with the value of the remaining result.
5) For laboratories that have only reported one result, i.e. the other result is missing, assign the value
of the single reported result to the missing result before proceeding to step 6).
6) Calculate the sum of the pair of the results for each lab. For laboratories that have reported both
results and neither result has been rejected, this will be the sum of both reported results. In the
case where one of the pair of results is missing (not reported) or rejected from step 4), this sum will
be twice the single reported result since the missing result is assigned the same value as the
reported result.
7) Identify outlier(s) in data set of sums as obtained from step 6) by following the methodology
outlined in Annex H.
8) For each outlying sum of results, exclude both results from further statistical analysis.
9) For the pairs of results with sums that have not been rejected, retain both reported results for
analysis if both results are as originally received from the laboratories. If one of the two results of
© ISO 2017 – All rights reserved
lxxvii
the pair is an assigned value from step 4) or step 5), retain the reported result from the laboratories
for analysis, and treat the other result as “missing”.
10) The data set remaining after completion of step 9) then constitutes the data set to be further
analysed as per 5.3 to 5.7.
5.3 Transformation of data and outlier tests
5.3.1 General
In many test methods, the precision depends on the level of the test result, and thus the variability of
the reported results is different from sample to sample. The method of analysis outlined in this
document requires that this shall not be so and the position is rectified, if necessary, by a
transformation.
The laboratories standard deviations, D, and the repeats standard deviations, d, for sample j (see
j j
Annex C for notation explanation) are calculated and plotted separately against the sample means, mj, in
accordance with Annexes D and E). If the points so plotted can be considered as lying about a pair of
lines parallel to the m‐axis, then no transformation is necessary. If, however, the plotted points describe
non‐horizontal straight lines or curves of the form D = f(m) and d = f(m), then a transformation is
1 2
necessary.
The relationships D = f(m) and d = f(m) are not, in general, identical. The statistical procedures of this
1 2
document require, however, that the same transformation be applicable both for repeatability and for
reproducibility. For this reason, the two relationships are combined into a single dependency
relationship D = f(m) (where D now includes d) by including a dummy variable, T. This takes account of
the difference between the relationships, if one exists, and provides a means of testing for this
difference (see F.1).
The single relationship D = f(m) is best estimated by a weighted linear regression analysis, even though
in most cases an unweighted regression gives a satisfactory approximation. The derivation of weights is
described in F.2, and the computational procedure for the regression analysis is described in F.3.
Typical forms of dependence D = f(m) are given in E.1. These are all expressed in terms of
transformation parameters B and B.
The estimation of B and B0, and the transformation procedure which follows, are summarized in E.2.
This includes statistical tests for the significance of the regression (i.e. is the relationship D = f(m)
parallel to the m‐axis), and for the difference between the repeatability and reproducibility
relationships, based at the 5 % significance level. If such a difference is found to exist, or if no suitable
common transformation exists, then the alternative sample by sample procedures of ISO 5725‐2 shall
be used. In such an event, it is not possible to test for laboratory bias over all samples (see 5.6) or
separately estimate the interaction component of variance (see 6.2).
If it has been shown at the 5 % significance level that there is a significant regression of the form
D = f(m), then the appropriate transformation y = F(x), where x is the reported result, is given by
Formula (3):
dx
Fx K (3)


fx

where K is a constant.
In that event, all results shall be transformed accordingly and the remainder of the analysis carried out
in terms of the transformed results. Typical transformations are given in E.1.
It is difficult to make the choice of transformation the subject of formalized rules. Qualified statistical
assistance can be required in particular cases. The presence of outliers can affect judgement as to the
© ISO 2017 – All rights reserved
lxxviii
type of transformation required, if any (see 5.7). That is why extremely discordant results shall be
removed as described in 5.1 above prior to making a judgement on transformation(s).
The transformation and outlier procedure is described in the form of a flow chart in Figure 1. Note that
the transformation process is an iterative procedure, requiring confirmation of the choice of
transformation if outliers have been rejected. If the original transformation is found to be inadequate
after outliers have been removed, then a different transformation will be required.
© ISO 2017 – All rights reserved
lxxix
Figure 1 — Transformation and outlier procedure
© ISO 2017 – All rights reserved
lxxx
5.3.2 Outlier identification after pre-screening
The pre‐screened results, or if it has been decided that a transformation is necessary, the pre‐screened
and transformed results, shall be further tested statistically for outliers. These are the values that are so
different from the remaining data that it can only be concluded that they have arisen from some fault in
the application of the test method or from testing a wrong sample. Many possible tests may be used and
the associated significance levels can be varied, but those that are given below have been found to be
appropriate for this document. These outlier tests all assume a normal distribution of errors (see 5.1).
5.3.3 Uniformity of repeatability
The first outlier test is concerned with detecting a discordant result for the absolute difference between
[7] 2
a pair of repeat results. This test involves calculating the e ij over all the laboratory/sample
combinations. Cochran's criterion at the 1 % significance level is then used to test the ratio of the
largest of these e values over their sum (see C.5). If its value exceeds the value given in Table D.14,
ij
corresponding to one degree of freedom, n being the number of pairs available for comparison, then
r
the member of the pair farthest from the sample mean shall be rejected and the process repeated,
reducing n by 1, until no more rejections are called for. In certain cases, this test “snowballs” and leads
r
to an unacceptably large proportion of rejections (say more than 10 %). If this is so, this rejection test
shall be abandoned and some or all of the rejected results shall be retained. An arbitrary decision based
on judgement is necessary in this case. See D.3 for an illustration.
5.3.4 Uniformity of reproducibility
The following outlier test, Hawkins' test, see also D.4, is concerned with establishing uniformity in the
reproducibility estimate. It is designed to detect a discordant pair of results from a laboratory on a
particular sample. It involves, for each sample, forming the ratio of the largest absolute deviation of
laboratory mean from the overall sample mean to the square root of certain sums of squares (see C.6).
The ratio corresponding to the largest absolute deviation shall be compared with the critical 1 % values
given in Table D.15, where n is the number of laboratory cells in the sample concerned and where ν is
R
the degrees of freedom for the sum of squares, which is additional to that corresponding to the sample
in question. That is, for this test, ν refers to the degrees of freedom from other samples (i.e. excludes
R
the sample being tested).
If a significant value is encountered, the corresponding extreme value shall be omitted and the process
repeated.
If the test “snowballs”, leading to an unacceptably large proportion of rejections (say more than 10 %),
then this rejection test shall be abandoned and some or all of the rejected results shall be retained. An
arbitrary decision based on judgement is necessary in this case.
5.4 Rejection of complete data (from all laboratories) for a sample
The laboratories standard deviation and repeats standard deviation shall be examined for any outlying
samples. If a transformation has been carried out or any rejection made, new standard deviations shall
be calculated. See D.5 for further illustration.
If the standard deviation for any sample is excessively large, it shall be examined with a view to
rejecting the results from that sample.
Cochran's criterion at the 1 % level can be used when the standard deviations are based on the same
number of degrees of freedom. This involves calculating the ratio of the largest of the corresponding
sums of squares (laboratories or repeats, as appropriate) to their total (see C.5). If the ratio exceeds the
critical value given in Table D.14, with n as the number of samples and ν the degrees of freedom, then all
the results from the sample in question shall be rejected. In such an event, care should be taken that the
extreme standard deviation is not due to the application of an inappropriate transformation (see 5.3),
or undetected outliers.
© ISO 2017 – All rights reserved
lxxxi
There is no optimal test when standard deviations are based on different degrees of freedom. However,
the variance ratio (i.e. the ratio of largest variance to that pooled from the remaining samples) follows
an F‐distribution with ν and ν degrees of freedom (see C.7). Here ν is the degrees of freedom of the
1 2 1
variance in question and ν is the degrees of freedom for the remaining samples. If the ratio is greater
than the critical value given in Tables D.17 to D.20, corresponding to a significance level of 0,01/S,
where S is the number of samples, then results from the sample in question shall be rejected.
5.5 Estimating missing or rejected values
5.5.1 One of the two repeat values missing or rejected
If one of a pair of repeats (x or x for un‐transformed results, y or y for transformed results) is
ij1 ij2 ij1 ij2
missing or rejected, this shall be considered to have the same value as the other repeat in accordance
with the least squares method.
5.5.2 Both repeat values missing or rejected
If both the repeat values are missing, estimates of aij [(xij1 + xij2) for un‐transformed results, or (yij1 + yij2)
for transformed results] shall be made by forming the laboratories × samples interaction sum of
squares, including the missing values of the totals of the laboratories/samples pairs of results as
unknown variables. Any laboratory or sample from which all the results were rejected shall be ignored
and new values of L and S used. The estimates of the missing or rejected values shall then be found by
forming the partial derivatives of this sum of squares with respect to each variable in turn and equating
these to zero to solve as a set of simultaneous formulae.
Deleted: 5
Formula (4) may be used where only one pair sum has to be estimated. If more estimates are to be
made, the technique of successive approximation can be used. In this, each pair sum is estimated in turn
from Formula (4), using L, S and T values which contain the latest estimates of the other missing Deleted: 5
1 1 1
pairs. Initial values for estimates can be based on the appropriate sample mean, and the process usually
converges to the required level of accuracy within three complete iterations. See Reference [9] for
details.
If the value of one pair sum, a , has to be estimated, the estimate is given by Formula (4):
Deleted: 5
ij
aLLS
Deleted: 
4259‐1_ed1fig2.EPSaLLSST (4) ij 1

ij 111
lS11
 
LS11
 
(5)¶
Field Code Changed
where
S′ is S minus the number of samples rejected in 5.4;
L1 is the total of remaining pairs in the ith laboratory;
S1 is the total of remaining pairs in the jth sample;
T is the total of all pairs except a .
ij
See illustration in D.6 for estimating a single pair of missing values.
5.6 Rejection test for outlying laboratories
At this stage, one further rejection test remains to be carried out. This determines whether it is
necessary to reject the complete set of results from any particular laboratory (i.e. a discordant set of
results from a laboratory on all samples). It cannot be carried out at an earlier stage, except in the case
where no individual results or pairs are missing or rejected. The procedure again consists of Hawkins'
test (see 5.3.4), applied to the laboratory averages over all samples. If any laboratories are rejected on
all samples, new estimates shall be calculated for any remaining missing values (see 5.5).
© ISO 2017 – All rights reserved
lxxxii
This test involves identifying and forming the ratio of the largest absolute deviation of laboratory‐
average‐over‐all samples versus the overall mean to the square root of certain sums of squares (see
C.6).
For this test, n is the total number of laboratories, ν is zero. See illustration in D.7.
5.7 Confirmation of selected transformation
5.7.1 General
At this stage, it is necessary to check that the rejections carried out have not invalidated the
transformation used. If necessary, the procedure given in 5.3 shall be repeated with the outliers deleted,
and if a new transformation is selected, outlier tests shall be reapplied. See also D.8.
5.7.2 Identification of excessively influential sample(s)
The last step prior to proceeding with analysis of variance and calculation of precision estimates in
Clause 6 is to determine if the selection of transformation function is excessively influenced by one or
more samples. Cook's Distance is the recommended statistic for this evaluation. Cook’s Distance is
calculated for every sample in the unweighted linear regression of ln(D) versus ln(m) using the
i i
untransformed ILS results excluding the outliers identified in 5.2 to 5.6. Cook's Distance is a metric
which combines the leverage (lev, see 4.4) of a sample along with the degree of fit with and without use
i
of this sample in the regression. This will determine if the regression relationship is overly dependent
on the sample. A sample with Cook's Distance exceeding 1 constitutes a highly influential sample, and is
a candidate for exclusion. The ILS coordinator shall be notified of any sample with Cook's Distance
exceeding 1. Exclusion of samples based on Cook's Distance shall be discussed with the ILS coordinator,
who shall make the final decision after consultation with all stakeholders and the statistician.
Cook's Distance is calculated as follows:
2 Deleted: 6
rlev
ii
Cook's Distance (5)
p 1 lev

i
where
p = 2 (for regression with slope and intercept);
lev is leverage of sample i [see Formula (2)];
i
Deleted: 7
r is studentized residual of sample i [see Formula (6)].
i
Deleted: 7

i
ri = (6)
s()il1ev
i
where
ε is the residual of sample i;
i
s(i) is the residual mean square obtained from regression with the
...

NORME ISO
INTERNATIONALE 4259-1
Première édition
2017-11
Produits pétroliers et connexes —
Fidélité des méthodes de mesure et de
leurs résultats —
Partie 1:
Détermination des valeurs de fidélité
relatives aux méthodes d'essai
Petroleum and related products — Precision of measurement
methods and results —
Part 1: Determination of precision data in relation to methods of test
Numéro de référence
©
ISO 2017
DOCUMENT PROTÉGÉ PAR COPYRIGHT
© ISO 2017, Publié en Suisse
Droits de reproduction réservés. Sauf indication contraire, 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, l’affichage sur
l’internet ou sur un Intranet, sans autorisation écrite préalable. Les demandes d’autorisation peuvent être adressées à l’ISO à
l’adresse ci-après ou au comité membre de l’ISO dans le pays du demandeur.
ISO copyright office
Ch. de Blandonnet 8 • CP 401
CH-1214 Vernier, Geneva, Switzerland
Tel. [phone]
Fax [phone]
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www.iso.org
ii © ISO 2017 – Tous droits réservés

Sommaire Page
Avant-propos .v
Introduction .vi
1 Domaine d'application . 1
2 Références normatives . 1
3 Termes et définitions . 1
4 Étapes de l'organisation d'un essai interlaboratoires pour la détermination de la
fidélité d'une méthode d'essai . 4
4.1 Généralités . 4
4.2 Préparation d'un projet de méthode d'essai . 5
4.3 Organisation d'un ILS pilote avec au moins deux laboratoires . 5
4.4 Organisation de l’ILS . 5
4.5 Exécution de l’ILS . 6
5 Traitement statistique des résultats de l’ILS. 7
5.1 Recommandation . 7
5.2 Prévisualisation selon la technique GESD . 8
5.3 Transformation des données et recherche des valeurs aberrantes . 9
5.3.1 Généralités . 9
5.3.2 Identification des valeurs aberrantes après prévisualisation .11
5.3.3 Uniformité de la répétabilité .11
5.3.4 Uniformité de la reproductibilité .11
5.4 Rejet de tous les résultats (de tous les laboratoires) concernant un échantillon .11
5.5 Estimation des valeurs manquantes ou rejetées .12
5.5.1 L'une des valeurs d'une paire de résultats répétés est manquante ou rejetée .12
5.5.2 Les deux valeurs répétées sont manquantes ou rejetées .12
5.6 Test de rejet des résultats des laboratoires aberrants .13
5.7 Confirmation de la transformation sélectionnée .13
5.7.1 Généralités .13
5.7.2 Identification du ou des échantillon(s) excessivement influents .13
6 Analyse de la variance, calcul et expression des estimations de fidélité .14
6.1 Généralités .14
6.2 Analyse de la variance .14
6.2.1 Calcul des sommes des carrés pour la somme des carrés de l'interaction
laboratoires/échantillons .14
6.2.2 Calcul de la somme des carrés pour l'analyse exacte de la variance .15
6.2.3 Degrés de liberté .15
6.2.4 Carrés moyens et analyse de variance .15
6.3 Espérance des carrés moyens et calcul des estimations de fidélité .16
6.3.1 Espérance des carrés moyens sans valeurs estimées .16
6.3.2 Espérance des carrés moyens lorsqu'il y a des valeurs estimées .16
6.3.3 Calcul des estimations de fidélité .17
6.4 Expression de l’estimation de la fidélité dans une méthode d'essai .19
6.5 Spécification du domaine d’application pour la méthode d’essai .20
7 Ratio R/r .20
Annexe A (normative) Détermination du nombre d'échantillons requis .22
Annexe B (informative) Établissement de la formule d’estimation du nombre de
laboratoires et d'échantillons requis pour atteindre les 30 degrés de liberté minimum .24
Annexe C (normative) Notation et essais .26
Annexe D (normative) Représentation des procédures utilisant les résultats de l'ILS pour
l’indice de brome et les tableaux statistiques de brome .31
Annexe E (normative) Types de dépendance et transformations correspondantes .50
Annexe F (normative) Analyse de régression linéaire pondérée .56
Annexe G (normative) Règles d'arrondissage des résultats .63
Annexe H (normative) Technique GESD pour identifier simultanément plusieurs valeurs
aberrantes d’un jeu de donnée .65
Annexe I (informative) Glossaire .74
Bibliographie .78
iv © ISO 2017 – Tous droits réservés

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 (IEC) en ce qui
concerne la normalisation électrotechnique.
Les procédures utilisées pour élaborer le présent document et celles destinées à sa mise à jour sont
décrites dans les Directives ISO/IEC, Partie 1. Il convient, en particulier de prendre note des différents
critères d'approbation requis pour les différents types de documents ISO. Le présent document a été
rédigé conformément aux règles de rédaction données dans les Directives ISO/IEC, Partie 2 (voir www.
iso.org/directives).
L'attention est attirée sur le fait que certains des éléments du présent document 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. Les détails concernant
les références aux droits de propriété intellectuelle ou autres droits analogues identifiés lors de
l'élaboration du document sont indiqués dans l'Introduction et/ou dans la liste des déclarations de
brevets reçues par l'ISO (voir www.iso.org/brevets).
Les appellations commerciales éventuellement mentionnées dans le présent document sont données
pour information, par souci de commodité, à l’intention des utilisateurs et ne sauraient constituer un
engagement.
Pour une explication de la nature volontaire des normes, la signification des termes et expressions
spécifiques de l'ISO liés à l'évaluation de la conformité, ou pour toute information au sujet de l'adhésion
de l'ISO aux principes de l’Organisation mondiale du commerce (OMC) concernant les obstacles
techniques au commerce (OTC), voir le lien suivant: www.iso.org/avant-propos.
Le présent document a été élaboré par le comité technique ISO/TC 28, Produits pétroliers et connexes,
carburants et lubrifiants d'origine naturelle ou synthétique.
Cette édition de l’ISO 4259-1 annule et remplace, avec l’ISO 4259-2, l’ISO 4259 qui a fait l'objet d'une
révision technique.
Une liste de toutes les parties de la série ISO 4259 se trouve sur le site web de l’ISO.
Introduction
Pour les besoins de contrôle de qualité et pour vérifier leur conformité aux spécifications, les
caractéristiques des produits pétroliers commerciaux sont contrôlées au moyen de méthodes d'essai
normalisées de laboratoire. Deux ou plusieurs déterminations de la même caractéristique d'un
échantillon donné, selon une méthode d'essai spécifique ou selon des méthodes d’essai différentes qui
ont pour objet de mesurer la même caractéristique, ne donneront généralement pas exactement le même
résultat. Il est donc nécessaire de tenir compte correctement de ce fait, en parvenant à des estimations
fondées sur les statistiques de la fidélité d'une méthode, qui constituent une mesure objective du degré
de concordance attendu entre deux ou plusieurs résultats obtenus dans des conditions données.
[1]
L’ISO 4259-1 fait référence à l’ISO 3534-2, qui donne une définition différente de la valeur vraie
(voir 3.23). Ce document fait également référence à l’ISO 5725-2. Cette dernière est nécessaire pour
l’estimation de la fidélité dans des circonstances particulières et inhabituelles (voir 5.3.1).
Les deux parties de l’ISO 4259 regroupent toutes deux l’établissement d’évaluations de la fidélité et
[2]
l’application des données de fidélité. Elles combinent les informations de l’ASTM D6300 concernant la
[3]
détermination d’évaluations de la fidélité et les informations de l’ASTM D3244 pour l’utilisation des
données d’essai.
Un glossaire des variables utilisées dans ce document et dans l'ISO 4259-2 est inclus dans l'Annexe I de
ce document.
vi © ISO 2017 – Tous droits réservés

NORME INTERNATIONALE ISO 4259-1:2017(F)
Produits pétroliers et connexes — Fidélité des méthodes
de mesure et de leurs résultats —
Partie 1:
Détermination des valeurs de fidélité relatives aux
méthodes d'essai
1 Domaine d'application
Le présent document spécifié la méthodologie pour la conception d’un essai interlaboratoires (ILS) et
pour le calcul des estimations de fidélité d’une méthode d’essai spécifié par cet ILS. En particulier, il
définit les termes statistiques concernés (Article 3), les procédures à suivre dans l'organisation d'un ILS
destiné à déterminer la fidélité d'une méthode d'essai (Article 4) et la méthode de calcul de la fidélité à
partir des résultats d'un tel ILS (Articles 5 et 6).
Les procédures du présent document ont été conçues spécifiquement pour les produits pétroliers et
leurs produits connexes qui sont normalement considérés homogènes. Les procédures décrites dans
le présent document peuvent cependant aussi s’appliquer à d’autres types de produits homogènes. Il
est nécessaire de procéder à des contrôles attentifs avant d’appliquer ce document à des produits pour
lesquels la présomption d’homogénéité peut être mise en question.
2 Références normatives
Le document suivant est mentionné afin que la totalité ou une partie de son contenu constitue
des exigences de ce document. Pour les références datées, seule l'édition citée s'applique. Pour les
références non datées, la dernière édition du document de référence s'applique (y compris les éventuels
amendements).
ISO 5725-2, Exactitude (justesse et fidélité) des résultats et méthodes de mesure — Partie 2: Méthode de
base pour la détermination de la répétabilité et de la reproductibilité d’une méthode de mesure normalisée
3 Termes et définitions
Pour les besoins du présent document, les termes et définitions suivants s'appliquent.
L'ISO et la CEI tiennent à jour des bases de données terminologiques pour la normalisation aux adresses
suivantes:
— ISO Online browsing platform: disponible à l’adresse https://www.iso.org/obp
— IEC Electropedia: disponible à l’adresse http://www.electropedia.org/
3.1
analyse de variance
ANOVA
technique qui permet de décomposer la variance totale d'une méthode en ses différents facteurs
composants
3.2
valeur de référence acceptée
ARV
valeur de référence convenue pour une propriété spécifique d'un produit déterminé en suivant une
méthode et un protocole de référence acceptés, c'est-à-dire provenant d’un ILS
3.3
variance «interlaboratoires»
constituant d’une variance totale attribuable à la différence entre les moyennes des différents
laboratoires
Note 1 à l'article: Lorsque des résultats obtenus par plus d'un laboratoire sont comparés, la dispersion est
normalement plus importante que lorsque le même nombre d'essais est effectué par un seul laboratoire, et il y
a des écarts entre les moyennes obtenues par les différents laboratoires. Ces écarts donnent lieu à la variance
«interlaboratoire» qui est l'élément de la variance totale dû aux différences entre les moyennes des différents
laboratoires.
Note 2 à l'article: Il existe une définition correspondante pour la variance entre opérateurs)
Note 3 à l'article: Le terme «interlaboratoire» est souvent abrégé en «laboratoire» lorsqu'il est utilisé pour
qualifier des paramètres représentatifs de la dispersion de la population de résultats, par exemple sous forme de
«variance de laboratoire».
3.4
biais
(d’une méthode d’essai) différence entre la moyenne des résultats d’essai d’une population à partir
d’un très large nombre de laboratoires différents pour la détermination d’une caractéristique d’un
produit obtenue suivant une méthode d’essai spécifique et la valeur de référence acceptée de cette
caractéristique, lorsque celle-ci est disponible
Note 1 à l'article: Voir la note en 3.13 pour une interprétation de «moyenne des résultats d’essai d’une population»
3.5
codage aveugle
attribution d'un numéro différent pour chaque échantillon, afin qu'aucune autre identification ou
information sur les échantillons ne soit donnée à l'opérateur
3.6
échantillon de contrôle
échantillon prélevé au lieu où un produit est échangé, c'est-à-dire où la responsabilité de la qualité du
produit passe du fournisseur au réceptionnaire
3.7
degrés de liberté
diviseur utilisé dans le calcul de la variance
Note 1 à l'article: La définition n'est strictement applicable que dans les cas les plus simples. Des définitions pour
des cas plus complexes sont en dehors de l'objet du présent document.
3.8
détermination
exécution de la série d'opérations prescrites dans une méthode d'essai et permettant d'obtenir une
seule valeur
3.9
essai interlaboratoires
ILS
étude spécifiquement conçue pour évaluer la répétabilité et la reproductibilité d'une méthode d’essai
normalisée réalisée à un moment fixé par de multiples laboratoires au moyen de l'analyse statistique de
leurs résultats obtenus sur des échantillons préparés à partir de multiples produits
2 © ISO 2017 – Tous droits réservés

3.10
valeur connue
valeur quantitative pour une caractéristique qui peut théoriquement être établie ou calculée à partir de
la préparation de l'échantillon
Note 1 à l'article: La valeur connue n'existe pas toujours, par exemple dans le cas d'essais empiriques tels que la
détermination du point d'éclair.
3.11
moyenne
somme d’une série de résultats divisée par leur nombre
3.12
moyenne des carrés
somme des carrés divisée par le nombre de degrés de liberté
3.13
distribution normale
distribution de probabilité d'une variable aléatoire continue x, telle que si x est un nombre réel
quelconque, la densité de probabilité est telle que donnée dans la Formule (1):
 
1 1 x−μ 
 
fx()=−exp,−∞<  
2 σ
 
σ 2À  
 
Note 1 à l'article: Dans le cadre d’une modélisation d’une distribution des résultats de l’essai, μ est la moyenne
de la population ou valeur vraie (voir 3.23) de la caractéristique telle que déterminée par une méthode d’essai
spécifique; σ est l'écart-type de la distribution normale utilisé pour décrire la distribution d'un nombre infini de
résultats d’essai obtenus suivant la même méthode d’essai pratiquée par un nombre infini de laboratoires (σ > 0).
3.14
opérateur
personne qui effectue normalement et régulièrement un essai particulier
3.15
valeur aberrante
résultat dont la valeur est suffisamment éloignée des autres résultats pour qu'il ne soit pas considéré
comme faisant partie de l'ensemble des résultats
3.16
fidélité
étroitesse de l'accord entre les résultats obtenus en appliquant la même procédure d’essai à plusieurs
reprises sur essentiellement les mêmes produits et dans des conditions déterminées
Note 1 à l'article: Le procédé est d'autant plus fidèle que la partie aléatoire des erreurs expérimentales qui
affectent les résultats est moindre.
3.17
erreur aléatoire
composante de l'erreur de mesure qui dans des mesures dupliquées varie de manière imprédictible
3.18
répétabilité
valeur limitante pour la différence entre deux résultats indépendants obtenus dans l'exécution normale
et correcte de la même méthode sur un produit soumis à l'essai, considéré comme identique, sur un
court intervalle de temps dans les mêmes conditions, qui devrait être dépassée avec une probabilité de
5% en raison d'une variation aléatoire
Note 1 à l'article: On considère les conditions identiques quand l’opérateur est le même, l’appareillage est le même,
l’étalonnage et le laboratoire sont les mêmes.
Note 2 à l'article: Le paramètre représentatif de la dispersion de la population qui peut être associée à ces
résultats est l’écart-type de répétabilité ou variance de répétabilité. La répétabilité se réfère à la différence
maximale attribuable à la variation aléatoire entre deux résultats obtenus sous l'état de variabilité aléatoire
minimale. Par conséquent, le temps pendant lequel des résultats répétés doivent être obtenus sera suffisamment
court pour exclure les écarts qui dépendent du temps, par exemple, variations causées par des changements
d’environnement ou par des étalonnages multiples.
Note 3 à l'article: Le terme «répétabilité» ne soit pas confondu avec les termes «entre répétitions» ou «répétitions».
3.19
reproductibilité
valeur limitante pour la différence entre deux résultats indépendants obtenus dans l'exécution normale
et correcte de la même méthode sur un produit soumis à l'essai considéré comme étant le même, dans
des conditions opératoires différentes, qui devrait être dépassée avec une probabilité de 5% en raison
d'une variation aléatoire
Note 1 à l'article: On considère des conditions opératoires différentes lorsque les opérateurs sont différents, les
appareillages différents, les étalonnages différents et les laboratoires différents
Note 2 à l'article: Le paramètre représentatif de la dispersion de la population qui peut être associé à ces résultats
est l’écart-type de reproductibilité ou variance de reproductibilité. La reproductibilité se réfère à la différence
maximale attribuable à la variation aléatoire entre deux résultats obtenus sous l'état de variabilité aléatoire
maximale.
3.20
résultat
valeur finale obtenue en suivant le mode opératoire complet d’une méthode d'essai
Note 1 à l'article: Il est admis que le résultat est arrondi conformément à la procédure spécifiée dans l'Annexe G
3.21
écart-type
mesure de la dispersion d'une série de résultats autour de leur moyenne, égale à la racine carrée positive
de la variance et estimée par la racine carrée positive de la moyenne des carrés
3.22
somme des carrés
somme des carrés de la différence entre une série de résultats et leur moyenne
3.23
valeur vraie
pour les besoins pratiques, valeur vers laquelle tend la moyenne des résultats individuels obtenus par n
laboratoires, lorsque n tend vers l'infini
Note 1 à l'article: Une valeur vraie ainsi définie est associée à chaque méthode d'essai particulière
[11]
Note 2 à l'article: Une définition différente et idéalisée est donnée dans l'ISO 3534-2 .
3.24
variance
moyenne des carrés de l'écart d'une variable aléatoire par rapport à sa moyenne, estimée par la
moyenne des carrés
4 Étapes de l'organisation d'un essai interlaboratoires pour la détermination de
la fidélité d'une méthode d'essai
4.1 Généralités
Les étapes de l'organisation d'un essai interlaboratoires (ILS) sont les suivantes:
a) préparation d'un projet de méthode d'essai;
4 © ISO 2017 – Tous droits réservés

b) organisation d'un ILS pilote avec au moins deux laboratoires;
c) organisation de l’ILS;
d) exécution de l’ILS.
Les quatre étapes sont décrites successivement de 4.2 à 4.5.
4.2 Préparation d'un projet de méthode d'essai
Celui-ci doit contenir tous les détails nécessaires pour l'exécution de l'essai et l'expression des résultats.
Toute condition susceptible d'avoir une influence sur les résultats doit être spécifiée.
L'ILS doit être conçu de manière à couvrir la gamme prévue de la méthode d'essai (voir aussi 6.5). à ce
stade, concernant l'article relatif à la fidélité, seul son titre sera inclus dans le projet de méthode d’essai.
4.3 Organisation d'un ILS pilote avec au moins deux laboratoires
Un programme pilote est nécessaire pour les raisons suivantes:
a) pour vérifier les détails de l'exécution de l'essai;
b) pour déterminer dans quelle mesure les opérateurs peuvent observer correctement les instructions
de la méthode, et par suite de l’ILS;
c) pour contrôler les instructions concernant les échantillons;
d) pour estimer grossièrement la fidélité de l'essai.
Au moins deux échantillons sont nécessaires, couvrant la plage de résultats pour laquelle la méthode
d'essai est conçue. Cependant, au moins 12 combinaisons laboratoire/échantillon doivent être incluses.
Chaque échantillon est essayé deux fois par chaque laboratoire dans les conditions de répétabilité. Il
convient que les échantillons soient également distribués sur l’ensemble de l’intervalle de la méthode
d’essai et qu’y soient inclus les groupes de produits majoritaires couverts dans le domaine d’application
de la méthode. Si des omissions ou des imprécisions dans le projet de méthode d’essai sont révélées,
elles doivent alors être corrigées. Les résultats doivent être analysés sous l'angle du biais et de la fidélité
pour des échantillons avec des valeurs de référence acceptées. Si l'un ou l'autre paraît trop important,
des modifications à la méthode d’essai doivent être envisagées.
4.4 Organisation de l’ILS
Celui-ci doit recueillir la participation d'au moins six laboratoires, mais il est recommandé que ce
soit plutôt huit laboratoires ou plus pour s’assurer que la fidélité finale est établie sur au moins six
laboratoires et assurer une meilleure représentativité de la population des utilisateurs.
Le nombre d'échantillons doit être suffisant pour représenter convenablement les types de produits
auxquels la méthode d’essai est appliquée, pour couvrir la plage de la caractéristique à des intervalles
équivalents mesurée et rendre sûres les estimations de fidélité. S’il est déterminé que la fidélité varie
avec le niveau de résultats dans l’étude pilote, alors au moins cinq échantillons doivent être utilisés
dans l’ILS. Afin d’évaluer correctement la relation de la fidélité et du niveau, il est important que le choix
des échantillons couvre à intervalle régulier la gamme et les produits pour la caractéristique mesurée,
de sorte qu’une relation estimée ne dépende pas trop de l’influence d’un échantillon ayant une valeur
extrême.
Il est fortement recommandé que l’influence de chaque échantillon planifié dans la conception de
l'ensemble des échantillons, lev , soit évaluée en utilisant la Formule (2). Aucun échantillon ne doit avoir
i
une influence excédant 0,5. Voir le Tableau D.11 pour un exemple de calcul d’influence (la deuxième
colonne de droite sous 'lev '.
i
()xx−
i
lev =+ (2)
i
n
n
()xx−
∑ k
k=1
où
lev est l’influence de l’échantillon i;
i
n est le nombre total d’échantillons planifiés;
x est le logarithme népérien, ln (p ), où p est le niveau de la caractéristique planifié pour
i i i
l’échantillon i;
est la grande moyenne de tous les x .
i
x
Dans tous les cas, il est nécessaire d'obtenir au moins 30 degrés de liberté tant pour la répétabilité que
pour la reproductibilité (voir l'Annexe B pour la justification correspondante). Pour la répétabilité, cela
implique d'obtenir un total d'au moins 30 paires de résultats dans l'ILS.
Pour la reproductibilité, le Tableau A.1 de l’Annexe A donne le nombre minimal d'échantillons requis
en fonction de L, P et Q, où L est le nombre de laboratoires participants et P et Q sont les rapports
des estimations des composantes de variance obtenues dans l’étude pilote. Spécifiquement, P est le
rapport de la composante interaction à la composante répétitions et Q est le rapport de la composante
laboratoires à la composante répétitions. L'Annexe B donne le calcul de la formule utilisée. Si Q est
beaucoup plus grand que P, les 30 degrés de liberté ne peuvent être atteints; les entrées vides dans
le Tableau A.1 correspondent à cette situation (c'est-à-dire lorsque plus de 20 échantillons sont
nécessaires). Dans ces cas, il y a vraisemblablement un biais significatif entre laboratoires.
En absence d'informations sur le programme d’essai pilote pour permettre l'utilisation du Tableau A.1,
le nombre d'échantillons doit être supérieur à cinq et choisi tel que le nombre de laboratoires multiplié
par le nombre d'échantillons est supérieur ou égal à 42.
Quand il est connu ou suspecté que les différents types de produits présentent différentes formes
fonctionnelles de fidélité avec la méthode d’essai, il est recommandé de considérer l’organisation d’ILS
séparés pour chaque type de produits.
4.5 Exécution de l’ILS
Une personne doit être responsable de l’ILS entier, depuis la distribution des textes de la méthode
d’essai et des échantillons jusqu'à l'évaluation finale des résultats. Elle doit bien connaître la méthode
d’essai, mais ne doit pas prendre part personnellement aux essais.
Le texte de la méthode d’essai doit être diffusé à tous les laboratoires pour leur permettre de soulever
d'éventuelles questions avant le début des essais. Si un laboratoire désire pratiquer la méthode à
l'avance, cela doit alors être fait sur des échantillons autres que ceux utilisés dans l’ILS.
Les échantillons doivent être réunis, divisés et distribués par le coordinateur, qui doit également
conserver une réserve de chaque échantillon pour les cas urgents. Il est de la plus haute importance
que les parties fractionnées pour chaque laboratoire soient homogènes et stables en ce qui concerne
la caractéristique évaluée sur l’ensemble de la durée du programme de l’ILS. Avant la distribution,
l'ensemble des échantillons de l'ILS doivent être codés à l’aveugle de telle manière que l'anonymat
de la nature du produit de l’essai soit préservé ainsi que la valeur attendue de la caractéristique. Les
informations suivantes doivent accompagner l’envoi des échantillons:
a) le (projet de) méthode choisi pour les essais;
b) les instructions pour la manipulation et le stockage des échantillons;
6 © ISO 2017 – Tous droits réservés

c) l'ordre dans lequel les échantillons doivent être soumis à essai. Un ordre aléatoire différent pour
chaque laboratoire est fortement recommandé. Pour un grand nombre de laboratoires, plusieurs
ordres d'essai uniques peuvent être assignés au hasard à des groupes de laboratoires, avec pas plus
de 4 laboratoires par groupe;
d) pour des raisons statistiques, il est impératif que les résultats de la répétition soient obtenus
indépendamment l'un de l'autre, c'est-à-dire que le second résultat ne soit pas influencé par
la connaissance du premier. Cela est réalisé au moyen d’un codage à l’aveugle où la répétition
pour chaque produit dans la conception de l’ILS est incluse dans l’ensemble de l’essai envoyé
aux participants de l’ILS, sans divulguer qu’il s’agit d’une répétition, avec une déclaration jointe
précisant qu'un seul résultat doit être obtenu sur chaque échantillon dans l'ensemble de l’essai, dans
l'ordre de l’essai spécifié, par le même opérateur avec le même appareil sur un court laps de temps.
Si ce codage à l’aveugle est considéré comme impossible à atteindre, alors l’indication doit préciser
qu'une paire de résultats associés à un échantillon doit être obtenue par le même opérateur avec le
même appareillage dans un court laps de temps, sans divulguer la nature de l'échantillon;
e) la période durant laquelle tous les échantillons doivent être soumis à essai;
f) un formulaire en blanc pour le report des résultats. Pour chaque échantillon, il doit être prévu la
date de l'essai, les résultats de l’essai et toute circonstance inhabituelle. Le degré d'exactitude pour
l'expression des résultats doit être spécifié;
g) l'indication que l'essai doit être exécuté dans des conditions normales, par des opérateurs qualifiés
qui pratiquent ce type d’essai quotidiennement; et que la durée de l'essai doit être conforme à ce
qui se fait normalement.
h) un questionnaire demandant des informations sur les conditions dans lesquelles la méthode d’essai
est appliquée, par exemple des précisions sur l’appareillage, les produits et réactifs, les procédures
d’étalonnage et de vérification, la procédure de contrôle qualité, tout écart à la méthode d’essai
ou aux instructions fournies, des observations et des suggestions pour l'amélioration future de la
méthode d’essai.
Les opérateurs qui ont participé à l’ILS pilote peuvent aussi prendre part à l’ILS. Si le surcroît
d'expérience qu'ils ont acquis lors de l'essai de quelques échantillons supplémentaires produit un effet
notable, cela sert d'avertissement sur le fait que la méthode d’essais n'est pas satisfaisante. Ils doivent
être identifiés dans le compte rendu des résultats de sorte que tout effet puisse être noté.
[4]
NOTE Pour des directives supplémentaires sur le planning et l’exécution d’un ILS, consulter l’ASTM D7778
[2]
et l’ASTM D6300 .
5 Traitement statistique des résultats de l’ILS
5.1 Recommandation
Bien que les procédures définies dans les Articles 5 et 6 de ce document soient appropriées pour le
calcul manuel, il est fortement conseillé de les effectuer par ordinateur avec un logiciel convenablement
validé et conçu spécifiquement pour stocker et analyser des résultats d’essais d'ILS basés sur les
procédures de ce document. Il est aussi fortement recommandé que ces procédures soient effectuées
sous la direction d'un statisticien.
[13]
Note Le logiciel D2PP est largement utilisé dans la communauté ISO et ASTM. Ce logiciel ne comprend
pas l'évaluation GESD ou Distance de Cook en conformité avec ce document.
Dans les articles à suivre, les procédures sont spécifiées pour réaliser les actions suivantes:
a) prévisualiser les résultats obtenus de l'ILS sur le principe d’un échantillon par un échantillon pour
des résultats particulièrement discordants (valeurs aberrantes);
b) évaluer l'indépendance ou la dépendance de la fidélité et le niveau des résultats après la
prévisualisation;
c) évaluer l'uniformité de la fidélité d'un laboratoire à un autre en détectant la présence (ou l'absence)
de valeurs aberrantes supplémentaires en utilisant le pouvoir de détection sur l'ensemble des
données.
Les procédures sont décrites en termes mathématiques en fonction de la notation de l'Annexe C.
L'illustration des procédures est fournie dans les annexes référencées.
Pour toutes les procédures, il est supposé que tous les résultats, soit appartiennent à une distribution
normale unique, soit sont susceptibles d'être transformés en une telle distribution (voir 5.3). Les autres
cas (qui sont rares), nécessitent un traitement différent qui n'est pas dans l'objet du présent document.
Se reporter à la Référence [6] pour l'essai statistique de normalité.
5.2 Prévisualisation selon la technique GESD
Avant l'exécution des Articles 5.3 à 5.7, examiner toutes les informations fournies par les participants de
l'ILS pour déterminer la conformité entre le protocole d’essai convenu et la méthode d’essai. Si l’examen
n'a révélé aucune erreur d’écriture, d’échantillonnage ou de procédures, appliquer la technique de
l’écart studentisé généralisé extrême (Generalized Extreme Studentized Deviation, GESD) telle qu’elle
est décrite dans cet article aux résultats reçus pour chaque échantillon de l’ILS pour identifier les
résultats insolites ou extrêmes. L’examen pour des causes associées à des résultats insolites doit être
conduit. Si une ou des causes acceptables sont trouvées pendant l’examen, les résultats insolites doivent
être ou corrigés, remplacés, ou rejetés. La correction ou le remplacement des résultats insolites par un
nouvel ensemble de résultats doivent être approuvés par le coordinateur de l’ILS en consultation avec
le statisticien de l’ILS. Si aucune cause acceptable n'est trouvée, les résultats insolites ou extrêmes tels
qu’identifiés selon la technique GESD à un niveau de confiance de 99 % doivent être rejetés.
Une présentation globale de cette technique de prévisualisation de GESD est décrite ci-dessous.
Pour chaque échantillon de l’ILS, exécuter les étapes suivantes:
1) Calculer la moyenne de l’échantillon en utilisant tous les résultats reçus pour l'échantillon.
2) Calculer la différence pour chaque paire de résultats tels que reçus des laboratoires qui ont reporté
les deux résultats.
3) Identifier la ou les valeur(s) aberrante(s) dans l'ensemble des différences calculées à l'étape 2) en
suivant la méthodologie décrite dans l'Annexe H.
4) Pour chaque différence aberrante identifiée, retirer le résultat de la paire qui est le plus éloigné de
la moyenne de l'échantillon calculée en 1) et le remplacer par la valeur du résultat restant.
5) Pour les laboratoires qui n’ont reporté qu’un seul résultat, c'est-à-dire que l'autre résultat manque,
attribuer la valeur de l’unique résultat reporté au résultat manquant avant de procéder à l’étape 6).
6) Calculer la somme de la paire des résultats pour chaque laboratoire. Pour les laboratoires qui
ont rapporté les deux résultats et pour lesquels aucun n’a été rejeté, il s’agira de la somme des
deux résultats rapportés. Pour les laboratoires dont un des résultats manque, soit qu’il n’a pas
été reporté soit qu’il a été rejeté à l’étape 4), cette somme consistera en le double de la valeur de
l’unique résultat reporté étant donné que la même valeur que le résultat rapporté est assignée au
résultat manquant.
7) Identifier la ou les valeur(s) aberrante(s) dans l'ensemble des sommes calculées à l'étape 6) en
suivant la méthodologie décrite dans l'Annexe H.
8) Pour chaque somme de résultats aberrante, exclure les deux résultats pour la suite de l'analyse
statistique.
9) Pour les paires de résultats dont les sommes n'ont pas été rejetées, retenir les deux résultats
reportés pour l’analyse si les deux résultats sont tels que reçus à l’origine des laboratoires. Si un des
8 © ISO 2017 – Tous droits réservés

deux résultats de la paire est une valeur attribuée aux étapes 4) ou 5), retenir le résultat rapporté
des laboratoires pour l'analyse, et traiter l'autre résultat comme «manquant».
10) L'ensemble des données qui reste après l’exécution de l'étape 9) constitue alors l'ensemble des
données qui doivent être analysées suivant la procédure donnée de 5.3 à 5.7.
5.3 Transformation des données et recherche des valeurs aberrantes
5.3.1 Généralités
Dans de nombreuses méthodes d'essai, la fidélité dépend du niveau du résultat de l'essai, en sorte que
la dispersion des résultats diffère d'un échantillon à un autre. La méthode d'analyse décrite dans le
présent document suppose qu'il n'en est pas ainsi, et la situation est corrigée, si nécessaire, par une
transformation.
Les écarts-types D des laboratoires, et les écarts-types d des répétitions, pour l’échantillon j, (voir
j j
l’Annexe C pour une explication de l’annotation) sont calculés et leurs variations par rapport aux
moyennes, m des échantillons sont reportés graphiquement conformément aux Annexes D et E. Si les
j
courbes ainsi obtenues correspondent approximativement à deux droites parallèles à l'axe m, il n'est
pas nécessaire de procéder à une transformation. Mais si les points sont disposés approximativement
suivant des courbes de la forme D = f (m) et d = f (m), il faut procéder à une transformation.
1 2
Les relations D = f (m) et d = f (m) ne sont généralement pas identiques. Les procédures statistiques
1 2
du présent document exigent toutefois que la même transformation soit applicable en même temps à
la répétabilité et à la reproductibilité. Pour cette raison, les deux relations sont combinées dans une
relation de dépendance unique D = f(m) (où D inclut à présent d) en introduisant une variable fictive
T. Cela tient compte de la différence entre les relations, s'il en est, et fournit un moyen de soumettre à
essai cette différence (voir F.1).
La relation simple D = f(m) est évaluée au mieux par une analyse de régression linéaire pondérée, même
si dans la plupart des cas, une régression non pondérée constitue une approximation suffisante. La
dérivation des pondérations est décrite en F.2 et la procédure de calcul pour l'analyse de régression
est décrite dans l'Article F.3. Des formes types de dépendance D = f(m) sont données en E.1. Elles sont
toutes exprimées en fonction de paramètres de transformation B et B .
L'estimation de B et B et la procédure de transformation qui suit sont résumées en E.2. Celui-ci comporte
les essais statistiques pour la signification de la régression (c'est-à-dire, savoir si la relation D = f(m) est
parallèle à l'axe m) et pour la différence entre les relations de répétabilité et de reproductibilité basées
sur une probabilité à 95 %. Si une telle différence est constatée, ou si aucune transformation courante
appropriée n'existe, les procédures alternatives échantillon par échantillon de l'ISO 5725-2 doivent être
utilisées. En pareil cas, il n’est pas possible de soumettre à essai les biais de laboratoire de tous les
échantillons (voir 5.6) ni d'évaluer la composante d'interaction de variance (voir 6.2).
S'il apparaît, avec une probabilité de 95 %, qu'il existe une régression significative de la forme D = f(m),
la transformation adéquate y = F(x), où x est le résultat noté, est donnée par la Formule (3):
dx
Fx =K (3)
()
∫
fx()
où K est une constante. Dans ce cas, tous les résultats doivent être transformés en conséquence et
le reste de l'analyse exécuté en fonction des résultats transformés. Des transformations types sont
données en E.1.
Le choix d'une transformation est difficile et ne peut faire l'objet de règles formelles. Une assistance
statistique qualifiée peut être nécessaire dans certains cas particuliers. La présence de valeurs
aberrantes peut influencer le jugement quant au type de transformation nécessaire éventuellement
(voir 5.7). C'est pourquoi des résultats extrêmement discordants doivent être retirés comme décrit en
5.1 ci-dessus avant de faire un jugement sur la ou les transformation(s).
La transformation et la procédure pour les valeurs aberrantes sont décrites au moyen d'un
organigramme à la Figure 1. Noter que le procédé de transformation se constitue en une procédure
itérative, exigeant la confirmation du
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