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)

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.

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

Status
Published
Public Enquiry End Date
30-Mar-2016
Publication Date
09-Jan-2018
Current Stage
6060 - National Implementation/Publication (Adopted Project)
Start Date
20-Dec-2017
Due Date
24-Feb-2018
Completion Date
10-Jan-2018

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SLOVENSKI STANDARD
SIST EN ISO 4259-1:2018
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
SIST EN ISO 4259-1:2018 en,fr,de

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

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SIST EN ISO 4259-1:2018
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SIST EN ISO 4259-1:2018
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.
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SIST EN ISO 4259-1:2018
EN ISO 4259-1:2017 (E)
Contents Page

European foreword ....................................................................................................................................................... 3

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SIST EN ISO 4259-1:2018
EN ISO 4259-1:2017 (E)
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.
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SIST EN ISO 4259-1:2018
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SIST EN ISO 4259-1:2018
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
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SIST EN ISO 4259-1:2018
ISO 4259-1:2017(E)
COPYRIGHT PROTECTED DOCUMENT
© 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
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SIST EN ISO 4259-1:2018
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 2017 – All rights reserved iii
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SIST EN ISO 4259-1:2018
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
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SIST EN ISO 4259-1:2018
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 2017 – All rights reserved v
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SIST EN ISO 4259-1:2018
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
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SIST EN ISO 4259-1:2018
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 2017 – All rights reserved 1
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SIST EN ISO 4259-1:2018
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
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SIST EN ISO 4259-1:2018
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 2017 – All rights reserved 3
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SIST EN ISO 4259-1:2018
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
...

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