SIST EN ISO 4259-1:2026

• Abstract:

  This document specifies the methodology for the design, planning, and execution 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,; it specifies the procedures to be adopted in the planning and execution of an ILS to determine the precision of a test method, and; it specifies the method of calculating the precision from the results of such a study.; 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.

• Status: Published
• Public Enquiry End Date: 29-Jun-2025
• Publication Date: 15-Jul-2026
• ICS: 75.080 - Petroleum products in general
• ICS: 75.180.30 - Volumetric equipment and measurements
• Technical Committee: NAD - Petroleum products, lubricants and related products
• Current Stage: 6060 - National Implementation/Publication (Adopted Project)
• Start Date: 01-Jul-2026
• Due Date: 05-Sep-2026
• Completion Date: 16-Jul-2026
• Ref Project: EN ISO 4259-1:2026 - Petroleum and related products - Precision of measurement methods and results - Part 1: Determination of precision data in relation to methods of test (ISO 4259‑1:2026)

• Replaces: SIST EN ISO 4259-1:2018/A2:2021 - Petroleum and related products - Precision of measurement methods and results - Part 1:Determination of precision data in relation to methods of test - AMENDMENT 2 (ISO 4259-1:2017/Amd 2:2020)
• Effective Date: 01-Sep-2026
• Replaces: SIST EN ISO 4259-1:2018/A1:2019 - Petroleum and related products - Precision of measurement methods and results - Part 1: Determination of precision data in relation to methods of test - Amendment 1 (ISO 4259-1:2017/Amd 1:2019)
• Effective Date: 01-Sep-2026
• Replaces: SIST EN ISO 4259-1:2018 - 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)
• Effective Date: 01-Sep-2026
• Referred By: SIST EN 16136:2015 - Automotive fuels - Determination of manganese and iron content in unleaded petrol - Inductively coupled plasma optical emission spectrometry (ICP OES) method
• Effective Date: 24-Jun-2026
• Referred By: SIST EN 14023:2010 - Bitumen and bituminous binders - Specification framework for polymer modified bitumens
• Effective Date: 24-Jun-2026
• Referred By: SIST EN 14214:2012+A2:2019 - Liquid petroleum products - Fatty acid methyl esters (FAME) for use in diesel engines and heating applications - Requirements and test methods
• Effective Date: 24-Jun-2026
• Referred By: SIST EN 12591:2009 - Bitumen and bituminous binders - Specifications for paving grade bitumens
• Effective Date: 24-Jun-2026
• Referred By: SIST EN 17306:2019 - Liquid petroleum products - Determination of distillation characteristics at atmospheric pressure - Micro-distillation
• Effective Date: 24-Jun-2026
• Referred By: SIST EN 13924-2:2014 - Bitumen and bituminous binders - Specification framework for special paving grade bitumen - Part 2: Multigrade paving grade bitumens
• Effective Date: 24-Jun-2026
• Referred By: SIST EN 15293:2011 - Automotive fuels - Ethanol (E85) automotive fuel - Requirements and test methods
• Effective Date: 24-Jun-2026
• Referred By: SIST EN 228:2025 - Automotive fuels - Unleaded petrol - Requirements and test methods
• Effective Date: 24-Jun-2026
• Referred By: SIST EN 14274:2013 - Automotive fuels - Assessment of petrol and diesel quality - Fuel quality monitoring system (FQMS)
• Effective Date: 24-Jun-2026
• Referred By: SIST EN 16900:2017 - Fast pyrolysis bio-oils for industrial boilers - Requirements and test methods
• Effective Date: 24-Jun-2026
• Referred By: SIST-TP CEN/TR 15745:2009 - Liquid petroleum products - Determination of hydrocarbon types and oxygenates via multidimensional gas chromatography method - Round Robin research report
• Effective Date: 24-Jun-2026
• Referred By: SIST-TP CEN/TR 15745:2015 - Liquid petroleum products - Determination of hydrocarbon types and oxygenates via multidimensional gas chromatography method - Round Robin research report
• Effective Date: 24-Jun-2026

Overview

SIST EN ISO 4259-1:2026 is an international standard that establishes a systematic framework for determining the precision of measurement methods for petroleum and related products. Developed by the Slovenian Institute for Standardization (SIST) and aligning with ISO 4259-1:2026, this document details the procedures for planning, conducting, and evaluating interlaboratory studies (ILS) to assess the repeatability and reproducibility of test methods. While tailored primarily for homogeneous petroleum products, the standard’s methodology is applicable to other homogeneous substances, supporting quality control, regulatory compliance, and industry best practices.

Key Topics

• Definition of Statistical Terms: The standard provides clear, internationally recognized definitions of key statistical and measurement concepts such as repeatability, reproducibility, bias, variance, and more.
• Planning Interlaboratory Studies (ILS):
  • Steps for preparing draft test methods and conducting pilot studies
  • Criteria for selecting participating laboratories and test samples
  • Recommendations for ensuring sample homogeneity and blind coding
• Execution of ILS:
  • Standardized protocols for distributing test instructions and samples
  • Procedures for sample handling, test order assignment, and reporting results
  • Guidelines for maintaining operator consistency and minimizing bias
• Statistical Data Treatment:
  • Techniques for pre-screening data and identifying outliers
  • Approaches for statistical analysis, including ANOVA (Analysis of Variance)
  • Detailed calculation of repeatability and reproducibility limits
  • Requirements for minimum numbers of samples, laboratories, and degrees of freedom
• Reporting Precision Data: Instructions and formats for presenting precision estimates and relevant statistical details in test method documentation.

Applications

SIST EN ISO 4259-1:2026 offers practical value for a range of stakeholders in the petroleum industry and beyond:

• Test Method Validation: Laboratories, product manufacturers, and method developers use the standard to ensure that new or modified test methods deliver reliable and consistent results.
• Quality Control and Compliance: Petroleum refineries, chemical plants, and related enterprises rely on precision data to monitor product quality, demonstrate compliance with industry specifications, and meet regulatory requirements.
• Interlaboratory Collaboration: The standardized ILS protocol allows organizations across regions to align their measurement procedures and compare results effectively.
• International Trade: Reliable precision data help eliminate disputes over test results, facilitating fair trade and acceptance of products across borders.
• Broader Industrial Use: Beyond petroleum, any sector dealing with homogeneous products-such as chemicals, lubricants, or pharmaceuticals-can apply the principles from this standard.

Related Standards

The methodologies and definitions in SIST EN ISO 4259-1:2026 align with and complement several important international standards:

• ISO 5725-2 - Accuracy (trueness and precision) of measurement methods and results - Basic method for the determination of repeatability and reproducibility
• ISO 3534-2 - Statistics - Vocabulary and symbols - Part 2: Applied statistics
• ASTM D6300 - Standard practice for determining precision data for test methods for petroleum products and lubricants
• ISO 4259-2 - Petroleum and related products - Application of precision data in relation to methods of test

By following SIST EN ISO 4259-1:2026, organizations can improve confidence in test results, streamline method validation, and support the international harmonization of measurement procedures in petroleum product analysis. This ensures greater consistency, operational efficiency, and market acceptance in a globally interconnected industry.

SLOVENSKI STANDARD
01-september-2026
Nadomešča:
SIST EN ISO 4259-1:2018
SIST EN ISO 4259-1:2018/A1:2019
SIST EN ISO 4259-1:2018/A2:2021
Nafta in sorodni proizvodi - Natančnost merilnih metod in rezultatov - 1. del:
Določanje natančnosti podatkov preskusnih metod (ISO 4259-1:2026)
Petroleum and related products - Precision of measurement methods and results - Part
1: Determination of precision data in relation to methods of test (ISO 4259‑1:2026)
Mineralöl und verwandte Produkte - Präzision von Messverfahren und Ergebnissen - Teil
1: Bestimmung der Präzisionsdaten von Prüfverfahren (ISO 4259-1:2026)
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-
1:2026)
Ta slovenski standard je istoveten z: EN ISO 4259-1:2026
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
June 2026
EUROPÄISCHE NORM
ICS 75.080 Supersedes EN ISO 4259-1:2017, EN ISO 4259-
1:2017/A1:2019, EN ISO 4259-1:2017/A2:2020
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-
1:2026)
Produits pétroliers et connexes - Fidélité des méthodes Mineralöl und verwandte Produkte - Präzision von
de mesure et de leurs résultats - Partie 1: Messverfahren und Ergebnissen - Teil 1: Bestimmung
Détermination des valeurs de fidélité relatives aux der Präzisionsdaten von Prüfverfahren (ISO 4259-
méthodes d'essai (ISO 4259-1:2026) 1:2026)
This European Standard was approved by CEN on 31 May 2026.

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, France, Germany, Greece, Hungary, Iceland, Ireland, Italy, Latvia, Lithuania, Luxembourg, Malta, Netherlands, Norway,
Poland, Portugal, Republic of North Macedonia, Romania, Serbia, Slovakia, Slovenia, Spain, Sweden, Switzerland, Türkiye 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
© 2026 CEN All rights of exploitation in any form and by any means reserved Ref. No. EN ISO 4259-1:2026 E
worldwide for CEN national Members.

Contents Page
European foreword . 3

European foreword
This document (EN ISO 4259-1:2026) 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 December 2026, and conflicting national standards
shall be withdrawn at the latest by December 2026.
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 4259-1:2017.
Any feedback and questions on this document should be directed to the users’ national standards
body/national committee. A complete listing of these bodies can be found on the CEN website.
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, France, Germany, Greece, Hungary, Iceland,
Ireland, Italy, Latvia, Lithuania, Luxembourg, Malta, Netherlands, Norway, Poland, Portugal, Republic of
North Macedonia, Romania, Serbia, Slovakia, Slovenia, Spain, Sweden, Switzerland, Türkiye and the
United Kingdom.
Endorsement notice
The text of ISO 4259-1:2026 has been approved by CEN as EN ISO 4259-1:2026 without any
modification.
International
Standard
ISO 4259-1
Second edition
Petroleum and related products —
2026-06
Precision of measurement methods
and results —
Part 1:
Determination of precision data in
relation to methods of test
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
Reference number
ISO 4259-1:2026(en) © ISO 2026

ISO 4259-1:2026(en)
© ISO 2026
All rights reserved. Unless otherwise specified, or required in the context of its implementation, 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
CP 401 • Ch. de Blandonnet 8
CH-1214 Vernier, Geneva
Phone: [phone]
Email: [e-mail]
Website: www.iso.org
Published in Switzerland
ii
ISO 4259-1:2026(en)
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 .4
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 .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 multiplied by 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
6.6 Reporting limits instruction for the test method . 20
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 the Bromine Number and
statistical tables .30

iii
ISO 4259-1:2026(en)
Annex E (normative) Types of dependence and corresponding transformations .50
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 .63
Annex I (informative) Glossary .71
Bibliography .75

iv
ISO 4259-1:2026(en)
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 document 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).
ISO draws attention to the possibility that the implementation of this document may involve the use of (a)
patent(s). ISO takes no position concerning the evidence, validity or applicability of any claimed patent
rights in respect thereof. As of the date of publication of this document, ISO had not received notice of (a)
patent(s) which may be required to implement this document. However, implementers are cautioned that
this may not represent the latest information, which may be obtained from the patent database available at
www.iso.org/patents. ISO shall not be held responsible for identifying any or all such patent rights.
Any trade name used in this document is information given for the convenience of users and does not
constitute an endorsement.
For an explanation of 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 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, in collaboration with the European Committee for Standardization
(CEN) Technical Committee CEN/TC 19, Gaseous and liquid fuels, lubricants and related products of petroleum,
synthetic and biological origin, in accordance with the Agreement on technical cooperation between ISO and
CEN (Vienna Agreement).
This second edition cancels and replaces the first edition (ISO 4259-1:2017), which has been technically
revised. It also incorporates the Amendments ISO 4259-1:2017/Amd 1:2019 and ISO 4259-1:2017/Amd
2:2020.
The main changes are as follows:
— in 4.4, the sufficient number of samples in the ILS has been modified to at least six;
— in 4.4, Formula (2) has been modified to ensure that no sample has a leverage exceeding 4/n ;
t
— in Annex B, the explanation for choosing 30 as minimum degrees of freedom has been improved.
A list of all parts in the ISO 4259 series can be found on the ISO website.
Any feedback or questions on this document should be directed to the user’s national standards body. A
complete listing of these bodies can be found at www.iso.org/members.html.

v
ISO 4259-1:2026(en)
Introduction
For purposes of quality control and to check conformity 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.
The ISO 4259 series encompasses both the derivation of precision estimates and the application of precision
[4]
data. The ISO 4259 series combines 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.
Careful investigations should be carried out before applying this document to products for which the
assumption of homogeneity can be questioned.
[1]
A glossary of the variables used in this document and ISO 4259-2 is included for information as Annex I.

vi
International Standard ISO 4259-1:2026(en)
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, planning, and execution 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,
— it specifies the procedures to be adopted in the planning and execution of an ILS to determine the
precision of a test method, and
— it specifies the method of calculating the precision from the results of such a study.
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.
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 terminology databases for use in standardization at the following addresses:
— ISO Online browsing platform: available at https:// www .iso .org/ obp
— IEC Electropedia: available at https:// www .electropedia .org/
3.1
analysis of variance
technique that enables the total variance of a method to be broken down into its component factors
3.2
accepted reference value
agreed-upon reference value for a specific property of a material determined using an accepted reference
method and protocol, e.g. derived from an interlaboratory study (3.8)

ISO 4259-1:2026(en)
3.3
between laboratory variance
component of the total variance (3.23) attributable to the difference between the means (3.10) 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
of a test method> difference between the population mean of test results (3.19) 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 (3.2) for the property where this is available
Note 1 to entry: See Note 1 to entry in 3.12 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 (3.13)
3.6
degrees of freedom
divisor used in the calculation of variance (3.23)
Note 1 to entry: This definition applies strictly only in the simplest cases. Definitions for more complex cases are
beyond the scope of this document.
3.7
determination
process of carrying out the series of operations specified in a test method, whereby a single value is obtained
3.8
interlaboratory study
ILS
study specifically designed to estimate the repeatability and reproducibility of a test method achieved
at a fixed point in time by multiple laboratories through the statistical analysis of their test results (3.19)
obtained on aliquots prepared from multiple materials
3.9
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.
3.10
mean
sum of a set of results (3.19) divided by the number of results
3.11
mean square
sum of squares (3.21) divided by the degrees of freedom (3.6)

ISO 4259-1:2026(en)
3.12
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 
 
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 (3.10), or true
value (3.22) of the property as determined by a specific test method; σ is the standard deviation (3.20) 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).
3.13
operator
person who normally and regularly carries out a particular test
3.14
outlier
result (3.19) far enough in magnitude from other results to be considered not a part of the set
3.15
precision
closeness of agreement between the results (3.19) 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.
3.16
random error
component of measurement error that in replicate measurements varies in an unpredictable manner
3.17
repeatability
quantitative expression for the random error (3.16) associated with the difference between two independent
results (3.19) obtained under repeatability conditions in the normal and correct operation of the same
method, that is expected to be exceeded with an approximate probability of 5 %
Note 1 to entry: The representative parameter for the dispersion of the population that can be associated with these
results is repeatability standard deviation (3.20) or repeatability variance (3.23). 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 2 to entry: The term “repeatability” is not to be confused with the terms “between repeats” or “repeats”.
Note 3 to entry: The conditions where independent test results (3.19) are obtained using the same method for test
material are considered to be the same in the same laboratory by the same operator (3.13) using the same equipment
with short intervals of time. This is also known as the repeatability conditions.
3.18
reproducibility
quantitative expression for the random error (3.16) associated with the difference between two independent
results (3.19) obtained under reproducibility conditions in the normal and correct operation of the same
method, that is expected to be exceeded with an approximate probability of 5 %
Note 1 to entry: The representative parameter of the dispersion of the population that can be associated with these
results (3.19) is reproducibility standard deviation (3.20) or reproducibility variance (3.23). Reproducibility refers to
the maximum difference attributable to random variation between two results obtained under the state of maximum
random variability.
ISO 4259-1:2026(en)
Note 2 to entry: The conditions where independent test results (3.19) are obtained using the same method for test
material are considered to be the same in different laboratories. A different laboratory means a different operator
(3.13), different equipment, different geographic location, and under different supervisory control. This is also known
as the reproducibility conditions.
3.19
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.
3.20
standard deviation
measure of the dispersion of a series of results (3.19) around their mean (3.10), equal to the positive square
root of the variance (3.23) and estimated by the positive square root of the mean square (3.11)
3.21
sum of squares
differences between a series of results (3.19) and their mean (3.10)
3.22
true value
for practical purposes, value towards which the average of single results (3.19) 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.
[2]
Note 2 to entry: A different and idealized definition is given in ISO 3534-2:2006, 3.2.5 .
3.23
variance
mean of the squares of the deviation of a random variable from its mean (3.10), estimated by the mean square
(3.11)
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 (see 4.2);
b) planning a pilot study with at least two laboratories if necessary (see 4.3);
c) planning the ILS (see 4.4);
d) executing the ILS (see 4.5).
4.2 Preparing a draft method of test
The draft method of test 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 in the draft.
The ILS shall be designed so that it covers the intended range of the test method (see also 6.5). At this stage,
a clause on precision is included in the draft method of the test only as a heading.

ISO 4259-1:2026(en)
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 shall be applied, to cover the range of the property measured at approximately equidistant
intervals, and to give reliability to the precision estimates. At least six 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) based on either its known value, or a single test result. No sample shall have a
leverage exceeding 4/n . See Table D.11 for an example of leverage calculation (second column from the right
t
under heading "lev ").
i
1 ()xix
lev  (2)
i
n
n 2
t
t
()xx

k
k1
where
lev is leverage of sample i;
i
n is total number of planned samples;
t
x is Napierian logarithm, ln (p ), with p being the planned property level for sample i;
i i i
x is grand average of all x .
i
In any event, it is necessary to obtain at least 30 degrees of freedom for both repeatability and reproducibility
(see Annex B for additional information). For repeatability, this means obtaining a total of at least 30 pairs of
results in the ILS.
For reproducibility, Table A.1 shall be used for 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.

ISO 4259-1:2026(en)
In the absence of pilot study information to permit the use of Table A.1, the number of samples shall be at
least six, 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 shall 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, the repeat results shall be 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 shall 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 shall 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.
[5] [4]
NOTE For additional guidance on the planning and execution of an ILS, consult ASTM D7778 and ASTM D6300 .

ISO 4259-1:2026(en)
5 Statistical treatment of ILS results
5.1 General
Although the procedures described in Clauses 5 and 6 are in a form suitable for hand calculation, it is
recommended 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 recommended that these procedures be carried out under the guidance of a statistician.
[14]
NOTE D2PP software was historically used for precision evaluation calculations, however this software's
capability does not meet the requirements of this document, as it does not execute the generalized extreme studentized
deviation (GESD) or Cook’s Distance.
In 5.2 to 5.7, 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 specified in Annex C.
Illustration of the procedures is provided in Annex D.
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 [7] for a statistical test on normality.
5.2 Pre-screen using GESD technique
Prior to executing the steps specified in 5.3 to 5.7, examine all information returned by ILS participants
to determine conformity 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 the steps 1 to 10, to the results received for each ILS sample to identify unusual or
extreme results. Investigation for causes associated with unusual results shall be conducted. If acceptable
causes are 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. See Annex H and
Tables H.1 to H.9 for illustration of the GESD technique execution.
An overall summary of this GESD pre-screening technique is outlined below.
For each ILS sample, execute the following steps.
1) Calculate the sample median 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 median 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).

ISO 4259-1:2026(en)
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
...