ISO/TR 9272:2005
(Main)Rubber and rubber products — Determination of precision for test method standards
Rubber and rubber products — Determination of precision for test method standards
ISO/TR 9272:2005 presents guidelines for determining, by means of interlaboratory test programmes (ITPs), precision for test method standards used in the rubber manufacturing and the carbon black industries. It uses the basic one-way analysis of variance calculation algorithms of ISO 5725 and as many of the terms and definitions of ISO 5725 as possible that do not conflict with the past history and procedures for precision determination in these two industries. Although bias is not determined in this Technical Report, it is an essential concept in understanding precision determination. The ISO 5725 concepts of accuracy and trueness are not determined in this Technical Report. Two precision determination methods are given that are described as 'robust' statistical procedures that attempt to eliminate or substantially decrease the influence of outliers. The first is a 'level 1 precision' procedure intended for all test methods in the rubber manufacturing industry and the second is a specific variation of the general precision procedure, designated 'level 2 precision', that applies to carbon black testing. Both of these use the same uniform level experimental design and the Mandel h and k statistics to review the precision database for potential outliers. However, they use slight modifications in the procedure for rejecting incompatible data values as outliers. The 'level 2 precision' procedure is specific as to the number of replicates per database cell or material-laboratory combination.
Caoutchouc et produits en caoutchouc — Évaluation de la fidélité des méthodes d'essai normalisées
General Information
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Standards Content (Sample)
TECHNICAL ISO/TR
REPORT 9272
Second edition
2005-07-15
Rubber and rubber products —
Determination of precision for test
method standards
Caoutchouc et produits en caoutchouc — Évaluation de la fidélité des
méthodes d'essai normalisées
Reference number
ISO/TR 9272:2005(E)
ISO 2005
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ISO/TR 9272:2005(E)
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ISO/TR 9272:2005(E)
Contents Page
Foreword............................................................................................................................................................. v
Introduction ....................................................................................................................................................... vi
1 Scope ..................................................................................................................................................... 1
2 Normative references ........................................................................................................................... 1
3 Terms and definitions........................................................................................................................... 1
3.1 General................................................................................................................................................... 1
3.2 ISO 5725 terms ...................................................................................................................................... 2
3.3 Required terms not in ISO 5725 .......................................................................................................... 4
4 Field of application ............................................................................................................................... 6
4.1 General background............................................................................................................................. 6
4.2 Defining repeatability and reproducibility.......................................................................................... 7
5 Precision determination: Level 1 precision and level 2 precision................................................... 8
5.1 Level 1 precision................................................................................................................................... 8
5.2 Level 2 precision................................................................................................................................... 8
5.3 Types of level 1 and level 2 precision................................................................................................. 8
6 Steps in organizing an interlaboratory test programme................................................................... 9
7 Overview of level 1 precision analysis procedure .......................................................................... 11
7.1 Analysis operation sequence ............................................................................................................ 11
7.2 Background on outliers...................................................................................................................... 12
7.3 Outlier appearance patterns .............................................................................................................. 12
7.4 Sequential review of outliers ............................................................................................................. 12
8 Level 1 precision: Analysis step 1 .................................................................................................... 13
8.1 Preliminary numerical and graphical data review ........................................................................... 13
8.2 Graphical review of cell values ......................................................................................................... 13
8.3 Calculation of precision for original database ................................................................................ 14
8.4 Detection of outliers at the 5 % significance level using h and k statistics ................................. 14
8.5 Generation of revision 1 database using outlier option 1 or 2 ...................................................... 15
8.6 Revision 1 (R1) database tables........................................................................................................ 15
9 Level 1 precision: Analysis step 2 .................................................................................................... 15
9.1 Detection of outliers at the 2 % significance level using h and k statistics ................................. 15
9.2 Generation of revision 2 database using outlier option 1 or 2 ...................................................... 15
10 Level 1 precision: Analysis step 3 — Final precision results ........................................................ 16
11 Level 2 precision: Analysis of results obtained when testing carbon blacks.............................. 16
11.1 Background on level 2 precision ...................................................................................................... 16
11.2 Data review and calculations............................................................................................................. 17
11.3 Expressing the precision determined for carbon black testing .................................................... 17
12 Format for level 1 and level 2 precision-data table and precision clause in test method
standards............................................................................................................................................. 18
12.1 Precision-data table............................................................................................................................ 18
12.2 Precision clause.................................................................................................................................. 18
12.3 Report on the precision determination ITP...................................................................................... 20
Annex A (normative) Calculating the h and k consistency statistics......................................................... 25
A.1 General background........................................................................................................................... 25
A.2 Defining and calculating the h statistic............................................................................................ 25
A.3 Defining and calculating the k-statistic............................................................................................ 26
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ISO/TR 9272:2005(E)
A.4 Identification of outliers using the critical h and k values.............................................................. 27
Annex B (normative) Spreadsheet calculation formulae for precision parameters —Recommended spreadsheet table layout and data calculation sequence ................................... 29
B.1 Calculation formulae........................................................................................................................... 29
B.2 Table layout for spreadsheet calculations .......................................................................................30
B.3 Sequence of database calculations for precision ........................................................................... 33
Annex C (normative) Procedure for calculating replacement values for deleted outliers........................ 35
C.1 Introduction ......................................................................................................................................... 35
C.2 The replacement procedure............................................................................................................... 35
C.3 Outlier replacement categories ......................................................................................................... 36
C.4 PRs for outliers at 5 % significance level ......................................................................................... 36
C.5 DRs for outliers at 5 % significance level......................................................................................... 37
C.6 PRs for outliers at 2 % significance level ......................................................................................... 37
C.7 DRs for outliers at 2 % significance level......................................................................................... 38
Annex D (normative) An example of general precision determination — Mooney viscosity testing ..... 39
D.1 Introduction ......................................................................................................................................... 39
D.2 Organization of the Mooney example precision determination ..................................................... 40
D.3 Part 1: Level 1 analysis — Option 2: Outlier replacement .............................................................. 40
D.4 Part 2: Level 1 precision analysis — Option 1: Outlier deletion .................................................... 49
Annex E (informative) Background on ISO 5725 and new developments in precisiondetermination....................................................................................................................................... 76
E.1 Elements of ISO 5725.......................................................................................................................... 76
E.2 Elements of this TC 45 precision standard ...................................................................................... 76
Bibliography ..................................................................................................................................................... 78
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ISO/TR 9272:2005(E)
Foreword
ISO (the International Organization for Standardization) is a worldwide federation of national standards bodies
ISO (the International Organization for Standardization) is a worldwide federation of national standards bodies
(ISO member bodies). The work of preparing International Standards is normally carried out through ISO
technical committees. Each member body interested in a subject for which a technical committee has been
established has the right to be represented on that committee. International organizations, governmental and
non-governmental, in liaison with ISO, also take part in the work. ISO collaborates closely with the
International Electrotechnical Commission (IEC) on all matters of electrotechnical standardization.
International Standards are drafted in accordance with the rules given in the ISO/IEC Directives, Part 2.
The main task of technical committees is to prepare International Standards. Draft International Standards
adopted by the technical committees are circulated to the member bodies for voting. Publication as an
International Standard requires approval by at least 75 % of the member bodies casting a vote.
In exceptional circumstances, when a technical committee has collected data of a different kind from that
which is normally published as an International Standard (“state of the art”, for example), it may decide by a
simple majority vote of its participating members to publish a Technical Report. A Technical Report is entirely
informative in nature and does not have to be reviewed until the data it provides are considered to be no
longer valid or useful.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.
ISO/TR 9272 was prepared by Technical Committee ISO/TC 45, Rubber and rubber products, Subcommittee
SC 2, Testing and analysis.This second edition cancels and replaces the first edition (ISO/TR 9272:1986), which has been technically
revised.© ISO 2005 – All rights reserved v
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ISO/TR 9272:2005(E)
Introduction
The primary precision standard for ISO test method standards is ISO 5725, a generic standard that presents
the fundamental statistical approach and calculation algorithms for determining repeatability and
reproducibility precision as well as accuracy and a concept related to bias called trueness. However there are
certain parts of ISO 5725 that are not compatible with precision determination in the rubber manufacturing and
carbon black industries over the past four decades.two major problems exist:
a) strict adherence to ISO 5725 conflicts with the operational procedures and the past history of testing as
conducted in these two industries andb) ISO 5725 does not address certain requirements that are unique to rubber and carbon black testing.
Thus although ISO 5725 is necessary as a foundation document for this Technical Report and is used as such,
it is not sufficient for the needs of TC 45.This Technical Report replaces ISO/TR 9272, an interim document that has been used for guidance on
precision determination since 1986. This new edition of the Technical Report has a more comprehensive
approach to the overriding issue with precision determination over the past several decades — the discovery
that the reproducibility (between-laboratory variation) of many test methods is quite large. The existence of
very poor between-laboratory agreement for many fundamental test methods in the industry has been the
subject of much discussion and consternation. Experience has shown that poor reproducibility is most often
caused by only a small number (percentage) of the laboratories that may be designated outlier laboratories.
This new edition of ISO/TR 9272 describes a “robust” analysis approach that eliminates or substantially
reduces the influence of outliers. See Annex E for a more detailed discussion of these issues and additional
background on ISO 5725.Five annexes are presented. These serve as supplements to the main body of the Technical Report. They are
in addition to the terminology section proper. Annex A defines the Mandel h and k statistics, illustrates how they are calculated and gives tables of
critical h and k values. Annex B lists the calculation formulae for repeatability and reproducibility. It also describes how to
generate and use six tables that are required for a spreadsheet precision analysis.
Annex C outlines the procedure for calculating replacement values for outliers that have been rejected by
h and k value analysis. Outlier replacement rather than deletion is an option that may be used for
precision determination with a minimum number of laboratories and/or materials. Annex D is an example of a typical general precision determination programme for Mooney viscosity
testing. It shows how a precision database is reviewed for outliers, using both the h and the k statistics,
and illustrates some of the problems with outlier identification and removal as described in ISO 5725-2.
Annex E presents some background on ISO 5725, robust analysis and other issues related to precision
determination.Annex E is given mainly as background information that is important for a full understanding of precision
determination. Annexes A, B, and C contain detailed instructions and procedures needed to perform the
operations called for in various parts of this Technical Report. The use of these annexes in this capacity
avoids long sections of involved instruction in the main body of the Technical Report, thus allowing better
understanding of the concepts involved in the determination of precision.vi © ISO 2005 – All rights reserved
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TECHNICAL REPORT ISO/TR 9272:2005(E)
Rubber and rubber products — Determination of precision for
test method standards
1 Scope
This Technical Report presents guidelines for determining, by means of interlaboratory test programmes
(ITPs), precision for test method standards used in the rubber manufacturing and the carbon black industries.
It uses the basic one-way analysis of variance calculation algorithms of ISO 5725 and as many of the terms
and definitions of ISO 5725 as possible that do not conflict with the past history and procedures for precision
determination in these two industries. Although bias is not determined in this Technical Report, it is an
essential concept in understanding precision determination. The ISO 5725 concepts of accuracy and trueness
are not determined in this Technical Report.Two precision determination methods are given that are described as “robust” statistical procedures that
attempt to eliminate or substantially decrease the influence of outliers. The first is a “level 1 precision”
procedure intended for all test methods in the rubber manufacturing industry and the second is a specific
variation of the general precision procedure, designated “level 2 precision”, that applies to carbon black testing.
Both of these use the same uniform level experimental design and the Mandel h and k statistics to review the
precision database for potential outliers. However, they use slight modifications in the procedure for rejecting
incompatible data values as outliers. The “level 2 precision” procedure is specific as to the number of
replicates per database cell or material-laboratory combination.2 Normative references
The following referenced documents are indispensable for the application 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 3534-1, Statistics — Vocabulary and symbols — Part 1: Probability and general statistical terms
ISO 5725 (all parts), Accuracy (trueness and precision) of measurement methods and results
3 Terms and definitions3.1 General
For the purposes of this document, the terms and definitions given in 3.3 apply, together with those in
ISO 5725 with modifications in 3.2.Additional terms concerning certain types of precision can be found in 5.3. Better understanding can be
gained by giving these definitions, which relate to the nature of the material to be tested, in that subclause.
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ISO/TR 9272:2005(E)
3.2 ISO 5725 terms
Terms defined in ISO 5725, usually those from ISO 3534-1, are used when:
a) their definition does not conflict with the procedures required for a comprehensive treatment of precision
determination for TC 45 test method standards, andb) when they are adequate to the task of giving definitions that are informative and promote understanding.
In this subclause, some additional notes have been added to the ISO 5725 term definitions to give greater
insight into precision determination for TC 45 test methods.3.2.1
accepted reference value
value that serves as an agreed-upon reference for comparison and which is derived as:
a) a theoretical or established value, based on scientific principles;b) an assigned or certified value, based on experimental work of some national or international organization;
c) a consensus or certified value, based on collaborative experimental work under the auspices of a
scientific or engineering group;d) when a), b) and c) are not available, the expectation of the (measured) quantity, i.e. the mean of a
specified population of measurements.3.2.2
test result
value of a characteristic obtained by carrying out a specified test method
NOTE The test method should specify that one or a number of individual measurements, determinations or
observations be made and their average or another appropriate function (median or other) be reported as the test result. It
may also require standard corrections to be applied, such as correction of gas volumes, etc.
3.2.3accuracy
closeness of agreement between a test result and the accepted reference value
NOTE The term accuracy, when applied to a set of test results, involves a combination of random components and a
common systematic error or bias component.3.2.4
bias
difference between the expectation of the test results and an accepted reference value
NOTE Bias is the total systematic error (deviation) as contrasted to random error. There may be one or more
systematic error components contributing to bias. A larger systematic difference from the accepted reference value is
reflected by a larger bias.3.2.5
laboratory bias
difference between the expectation of the test results from a particular laboratory and an accepted reference
value2 © ISO 2005 – All rights reserved
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3.2.6
precision
closeness of agreement between independent test results obtained under stipulated conditions
NOTE 1 Precision (for within-laboratory conditions or repeatability) depends on the distribution of random errors and
does not relate to the true value (accepted reference value) or the specified value. For a global testing domain (between-
laboratory conditions), see 3.3.1 below, the between-laboratory precision (reproducibility) is influenced by laboratory bias
as well as the random variations inherent in such a global testing domain.NOTE 2 The measure of precision is usually expressed in terms of the imprecision and computed as a standard
deviation of the test results. Less precision is reflected by a larger standard deviation.
NOTE 3 The term “independent test results” is defined as a set of results where the measurement of each value (of the
set) has no influence on the magnitude of any other test result in the set.NOTE 4 Quantitative measures of precision depend critically on the stipulated conditions (the type of test domain).
Repeatability and reproducibility conditions are particular sets of extreme conditions.
NOTE 5 Alternatively, precision may be defined as a “figure of merit” concept. It is proportional to the inverse of the
dispersion of independent replicate (test or observed) values, as estimated by the standard deviation, for a specified
testing domain.3.2.7
repeatability conditions
conditions where independent test results are obtained with the same method on identical test items (or
elements) in the same laboratory by the same operator using the same equipment within short intervals of
timeNOTE As defined in 3.3.1, a “local test domain” is the locale or environment (in a particular laboratory) under which
repeatability tests are conducted. The word “identical” should be interpreted as “nominally identical”, i.e. no intentional
differences among the items. The “intervals of time” between repeat measurement of test results may be selected by the
consensus of a particular testing community. For TC 45 and the international rubber manufacturing industry, the time
interval between repeat tests is of the order of one to seven days.3.2.8
repeatability
precision under repeatability conditions
NOTE 1 Repeatability, defined by the symbol r, is expressed in terms of an interval or range that is a multiple of the
standard deviation; this interval should (on the basis of a 95 % probability) encompass duplicate independent test results
obtained under the defined local testing domain.NOTE 2 Relative repeatability, (r), is expressed in terms of an interval (a multiple of the standard deviation) that is a
percentage of the mean level of the measured property; this interval should (on the basis of a 95 % probability)
encompass duplicate independent test results (on a percentage basis) obtained for a defined local testing domain.
NOTE 3 Repeatability may be dependent on the magnitude or level of the measured property and is usually reported
for particular property levels or materials or element classes (that determine the level).
NOTE 4 Although repeatability as defined above applies to a local testing domain, it can be obtained in two different
ways and the term repeatability can be used in two different contexts. It can pertain to a common community value,
obtained as an average (or pooled) value from all laboratories in an ITP among N different laboratories. This can be
referred to as a universal or global repeatability, that applies to a “typical laboratory”, that stands as a representative of all
laboratories that are part of a global testing domain. It can also pertain to the long-term or established value for a
“particular laboratory” as derived from ongoing testing in that laboratory, not related to any ITP. The second use can be
referred to as a local repeatability, i.e. repeatability obtained in and for one laboratory.
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ISO/TR 9272:2005(E)
3.2.9
reproducibility conditions
conditions where test results are obtained with the same method on identical test items (or elements) in
different laboratories with different operators using different equipmentNOTE 1 Each laboratory (or location) in the global testing domain, see 3.3.1.5, conducts n repeatability tests on a
material (target material) and reproducibility is determined based on the mean values (of the n local domain tests) for the N
laboratories for that material. Reproducibility may also depend on the level of the measured property or on the materials
tested and it is also usually reported for particular levels or materials.NOTE 2 The term “different equipment” should be interpreted as different realizations of an accepted and standard test
device, i.e. all of the test devices are nominally identical but they are located in different laboratories.
3.2.10reproducibility
precision obtained under reproducibility conditions
NOTE 1 Reproducibility, R, (for a defined global testing domain) is obtained by way of independent tests conducted in
N laboratories (with n replicates each) on nominally identical test items or elements, expressed in terms of an interval or
range that is a multiple of the standard deviation; this interval should (on basis of a 95 % probability) encompass duplicate
test results, each obtained in different laboratories for a defined global testing domain.
NOTE 2 Relative reproducibility, (R), is expressed in terms of an interval (a multiple of the standard deviation) that is a
percentage of the mean level of the measured property; this interval should (on the basis of a 95 % probability)
encompass duplicate independent test results (on a percentage basis) each obtained in different laboratories for a defined
global testing domain.NOTE 3 Reproducibility may also depend on the level of the measured property or on the materials tested and it is also
usually reported for particular levels or materials. Reproducibility usually does not have the dual interpretation or use as
discussed above for repeatability, since it is a “group characteristic” that only applies across a number of laboratories in a
global testing domain.NOTE 4 As indicated in Note 1 in the definition of precision above, reproducibility is determined by the magnitude of
random variations in the global testing domain as well as the distribution of bias components in this same global domain.
Laboratories that have good agreement with either a reference value or an overall mean value for the ITP, have either
zero or a very small bias. Laboratories that do not have good mean value agreement have substantial biases and,
although the bias magnitude is relatively constant for each laboratory, it differs among the biased laboratories, i.e. it has
the characteristics of a distribution.3.2.11
outlier
member of a set of values which is inconsistent with the other members of that set
NOTE This TC 45 standard defines a “set” as a “class of elements” that are subjected to measurement. See element
and element class defined in 3.3.1 below.3.3 Required terms not in ISO 5725
A number of specialized terms are defined here in a systematic sequential order
...
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