SIST EN ISO 4259-1:2018
(Main)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)
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)
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.
Mineralölerzeugnisse - Präzision von Messverfahren und Ergebnissen - Teil 1: Bestimmung der Werte für die Präzision von Prüfverfahren (ISO 4259-1:2017)
Diese Internationale Norm umfasst die Methodik für die Auslegung einer Laborvergleichsuntersuchung (ILS, en: Interlaboratory Study) und die Berechnung von Schätzwerten für die Präzision eines durch die Untersuchung festgelegten Prüfverfahrens. Insbesondere enthält sie Definitionen für wichtige statistische Begriffe (siehe Abschnitt 3), die zu ergreifenden Maßnahmen für die Planung von ILS zur Bestimmung der Präzision eines Prüfverfahrens (siehe Abschnitt 4) und die Methodik zur Berechnung der Präzision aus den Ergebnissen einer derartigen Untersuchung (Abschnitte 5 und 6).
Die Verfahren in dieser Internationalen Norm wurden speziell für Mineralölerzeugnisse und verwandte Produkte entwickelt, die im Allgemeinen homogene Produkte sind. Die in dieser Internationalen Norm beschriebenen Verfahren können jedoch auch auf andere Arten von homogenen Erzeugnissen angewendet werden. Vor der Anwendung dieser Internationalen Norm auf andere Erzeugnisse, bei denen die Ausnahme der Homogenität hinterfragt werden kann, sind sorgfältige Untersuchungen hinsichtlich der Anwendbarkeit erforderlich.
Produits pétroliers - Fidélité des méthodes de mesure et des résultats - Partie 1: Détermination des valeurs de fidélité relatives aux méthodes d'essai (ISO 4259-1:2017)
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.
Nafta in sorodni proizvodi - Natančnost merilnih metod in rezultatov - 1. del: Določevanje natančnosti preskusnih metod (ISO 4259-1:2017)
Ta dokument opredeljuje metodologijo za načrtovanje medlaboratorijske študije (ILS) in izračun stopnje natančnosti preskusne metode, ki jo je določila študija. Še zlasti določa ustrezne statistične izraze (točka 3), postopke za načrtovanje medlaboratorijske študije za določitev natančnosti preskusne metode (točka 4) in metodo za izračun natančnosti na podlagi rezultatov take študije (točki 5 in 6).
Postopki v tem dokumentu so bili zasnovani posebej za nafto in sorodne
proizvode, ki se običajno obravnavajo kot homogeni. Kljub temu pa se postopke, opisane v tem
dokumentu, lahko uporablja tudi za druge vrste homogenih proizvodov. Pred uporabo tega dokumenta za proizvode, pri katerih je predpostavka o homogenosti lahko vprašljiva, so potrebne
temeljite preiskave.
General Information
Relations
Standards Content (Sample)
SLOVENSKI STANDARD
01-februar-2018
1DGRPHãþD
SIST EN ISO 4259:2006
1DIWDLQVRURGQLSURL]YRGL1DWDQþQRVWPHULOQLKPHWRGLQUH]XOWDWRYGHO
'RORþHYDQMHQDWDQþQRVWLSUHVNXVQLKPHWRG ,62
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)
Mineralölerzeugnisse - Präzision von Messverfahren und Ergebnissen - Teil 1:
Bestimmung der Werte für die Präzision von Prüfverfahren (ISO 4259-1:2017)
Produits pétroliers - Fidélité des méthodes de mesure et des résultats - Partie 1:
Détermination des valeurs de fidélité relatives aux méthodes d'essai (ISO 4259-1:2017)
Ta slovenski standard je istoveten z: EN ISO 4259-1:2017
ICS:
75.080 Naftni proizvodi na splošno Petroleum products in
general
75.180.30 Oprema za merjenje Volumetric equipment and
prostornine in merjenje measurements
2003-01.Slovenski inštitut za standardizacijo. Razmnoževanje celote ali delov tega standarda ni dovoljeno.
EN ISO 4259-1
EUROPEAN STANDARD
NORME EUROPÉENNE
December 2017
EUROPÄISCHE NORM
ICS 75.080 Supersedes EN ISO 4259:2006
English Version
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)
Produits pétroliers et connexes - Fidélité des méthodes Mineralölerzeugnisse - Präzision von Messverfahren
de mesure et de leurs résultats - Partie 1: und Ergebnissen - Teil 1: Bestimmung der Werte für
Détermination des valeurs de fidélité relatives aux die Präzision von Prüfverfahren (ISO 4259-1:2017)
méthodes d'essai (ISO 4259-1:2017)
This European Standard was approved by CEN on 27 October 2017.
CEN members are bound to comply with the CEN/CENELEC Internal Regulations which stipulate the conditions for giving this
European Standard the status of a national standard without any alteration. Up-to-date lists and bibliographical references
concerning such national standards may be obtained on application to the CEN-CENELEC Management Centre or to any CEN
member.
This European Standard exists in three official versions (English, French, German). A version in any other language made by
translation under the responsibility of a CEN member into its own language and notified to the CEN-CENELEC Management
Centre has the same status as the official versions.
CEN members are the national standards bodies of Austria, Belgium, Bulgaria, Croatia, Cyprus, Czech Republic, Denmark, Estonia,
Finland, Former Yugoslav Republic of Macedonia, France, Germany, Greece, Hungary, Iceland, Ireland, Italy, Latvia, Lithuania,
Luxembourg, Malta, Netherlands, Norway, Poland, Portugal, Romania, Serbia, Slovakia, Slovenia, Spain, Sweden, Switzerland,
Turkey and United Kingdom.
EUROPEAN COMMITTEE FOR STANDARDIZATION
COMITÉ EUROPÉEN DE NORMALISATION
EUROPÄISCHES KOMITEE FÜR NORMUNG
CEN-CENELEC Management Centre: Rue de la Science 23, B-1040 Brussels
© 2017 CEN All rights of exploitation in any form and by any means reserved Ref. No. EN ISO 4259-1:2017 E
worldwide for CEN national Members.
Contents Page
European foreword . 3
European foreword
This document (EN ISO 4259-1:2017) has been prepared by Technical Committee ISO/TC 28
"Petroleum and related products, fuels and lubricants from natural or synthetic sources" in
collaboration with Technical Committee CEN/TC 19 “Gaseous and liquid fuels, lubricants and related
products of petroleum, synthetic and biological origin” the secretariat of which is held by NEN.
This European Standard shall be given the status of a national standard, either by publication of an
identical text or by endorsement, at the latest by June 2018, and conflicting national standards shall be
withdrawn at the latest by June 2018.
Attention is drawn to the possibility that some of the elements of this document may be the subject of
patent rights. CEN shall not be held responsible for identifying any or all such patent rights.
This document supersedes EN ISO 4259:2006.
According to the CEN-CENELEC Internal Regulations, the national standards organizations of the
following countries are bound to implement this European Standard: Austria, Belgium, Bulgaria,
Croatia, Cyprus, Czech Republic, Denmark, Estonia, Finland, Former Yugoslav Republic of Macedonia,
France, Germany, Greece, Hungary, Iceland, Ireland, Italy, Latvia, Lithuania, Luxembourg, Malta,
Netherlands, Norway, Poland, Portugal, Romania, Serbia, Slovakia, Slovenia, Spain, Sweden, Switzerland,
Turkey and the United Kingdom.
Endorsement notice
The text of ISO 4259-1:2017 has been approved by CEN as EN ISO 4259-1:2017 without any
modification.
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 4259-1:2017(E)
©
ISO 2017
ISO 4259-1:2017(E)
© 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
CH-1214 Vernier, Geneva, Switzerland
Tel. +41 22 749 01 11
Fax +41 22 749 09 47
copyright@iso.org
www.iso.org
ii © ISO 2017 – All rights reserved
ISO 4259-1:2017(E)
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
ISO 4259-1:2017(E)
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
ISO 4259-1:2017(E)
Foreword
ISO (the International Organization for Standardization) is a worldwide federation of national standards
bodies (ISO member bodies). The work of preparing International Standards is normally carried out
through ISO technical committees. Each member body interested in a subject for which a technical
committee has been established has the right to be represented on that committee. International
organizations, governmental and non-governmental, in liaison with ISO, also take part in the work.
ISO collaborates closely with the International Electrotechnical Commission (IEC) on all matters of
electrotechnical standardization.
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.
ISO 4259-1:2017(E)
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
ISO 4259-1:2017(E)
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
ISO 4259-1:2017(E)
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”.
ISO 4259-1:2017(E)
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
ISO 4259-1:2017(E)
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
ISO 4259-1:2017(E)
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
ISO 4259-1:2017(E)
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
ISO 4259-1:2017(E)
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
ISO 4259-1:2017(E)
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 app
...
Questions, Comments and Discussion
Ask us and Technical Secretary will try to provide an answer. You can facilitate discussion about the standard in here.
Loading comments...