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

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Withdrawn
Publication Date
04-Aug-2005
Withdrawal Date
04-Aug-2005
Current Stage
6060 - International Standard published
Start Date
20-Dec-2004
Completion Date
05-Aug-2005
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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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ii © ISO 2005 – All rights reserved
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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 precision

determination....................................................................................................................................... 76

E.1 Elements of ISO 5725.......................................................................................................................... 76

E.2 Elements of this TC 45 precision standard ...................................................................................... 76

Bibliography ..................................................................................................................................................... 78

iv © ISO 2005 – All rights reserved
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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 and

b) 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 definitions
3.1 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, and

b) 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.

3.2.3
accuracy
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

value
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ISO/TR 9272:2005(E)
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

time

NOTE 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 equipment

NOTE 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.

3.2.10
reproducibility
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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