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STANDARD 4259
Second edition
1992-12-15
Petroleum products - Determination and
application of precision data in relation to
methods of test
Produits p6 troliers - D6termina tion et application des valeurs de fidblit6
relatives aux m6 thodes d ‘essai
Reference number
IS0 42597 992(E)
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IS0 4259:1992(E)
Page
CONTENTS
1
Introduction .
2
Scope .
2
Normative Reference .
Definitions . 2
Stages in planning of an inter-laboratory test programme for the determination of the precision of a test method . 3
4.1 Preparing a draft method of test . 3
4.2 Planning a pilot programme with at least two laboratories . 3
4.3 Planning the inter-laboratory programme . 4
4.4 Executing the inter-laboratory programme . 4
5 Inspection of inter-laboratory results for uniformity and for outliers . 4
5.1 Transformation of data . 4
5.2 Tests for outliers . 5
5.3 Rejection of complete data from a sample . 6
5.4 Estimating missing or rejected values . 7
5.5 Rejection test for outlying laboratories . 8
8
5.6 Confirmation of selected transformation .
8
6 Analysis of variance and calculation of precision estimates .
8
6.1 Analysis of variance .
Expectation of mean squares and calculation of precision estimates . 10
6.2
Precision clause of a method of test . 12
6.3
7 . 12
Significance of repeatability r and reproducibility R as discussed in earlier clauses
12
7.1 Repeatability r .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
7.2 Reproducibility R
8 Specifications . 13
8.1 Aim of specifications . 13
8.2 Construction of specifications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
9 Quality control against specifications . 14
14
9.1 Testing margin at the supplier .
Testing margin at the recipient . 14
9.2
................................................................................................................ 14
10 Acceptance and rejection rules in case of dispute
Annexes
A (Normative) Determination of number of samples required . 16
B (Informative) Derivation of formula for calculating the number of samples required . 17
C (Normative) Notation and tests . 18
Example results of test for determination of bromine number and statistical tables . 22
D (Normative)
Types of dependence and corresponding transformations . 29
E (Normative)
32
F (Normative) Weighted linear regression analysis .
37
G (Normative) Rules for rounding off results .
38
H (Informative) Explanation of formulae in clause 7 .
Specifications which relate to a specified degree of criticality . 40
J (Informative)
,,.,.,.,.,.,.,.,.,.,. 42
Bibliography
0 IS0 1992
All rights reserved. No part of this publication may be reproduced or utilized in any form or
by any means, electronic or mechanical, including photocopying and microfilm, without per-
mission in writing from the publisher.
International Organization for Standardization
Case Postale 56 l CH-1211 Geneve 20 l Switzerland
Printed in Switzerland
ii
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IS0 4259: 1992(E)
Foreword
IS0 (the International Organization for Standardization) is a worldwide
federation of national standards bodies (IS0 member bodies). The work
of preparing International Standards is normally carried out through IS0
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. IS0
collaborates closely with the International Electrotechnical Commission
(IEC) on all matters of electrotechnical standardization.
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.
International Standard IS0 4259 was prepared by Technical Committee
ISOTTC 28, Petroleum products and lubricants.
This second edition cancels and replaces the first edition
(IS0 4259:1979), of which it constitutes a technical revision.
Significant changes from the first edition include:
Independence of repeated results (subclause 3.17)
Blind coding in relation to repeated results (subclauses 3.4, 4.4)
Probability level for precision (subclauses 3.17, 3.19, 6.2.3)
Transformation procedure (subclause 5.1, annex E, annex F)
Hawkins’ outlier test (subclauses 5.2.2, 5.5, clause C.5)
Rejection criteria for complete data from a sample (subclause 5.3)
Variance ratio test/bias between laboratories (subclauses 6.1.4, 6.2.3.2,
clause C.6)
Formula for acceptability of results/confidence limits (clause 7, annex H)
Specifications which include a stated degree of criticality (subclause 8. ‘l,
annex J)
IS0 4259 makes reference to IS0 3534, Statistics - Vocabulary and
symbols, which gives a different definition of “true value” (see subclause
3.24). IS0 4259 also refers to IS0 5725, Precision of test methods -
Determination of repeatability and reproducibility for a standard test
method by inter-laboratory tests. The latter will be required in particular
and unusual circumstances (see subclause 5.1) for the purpose of esti-
mating precision.
Annexes form an integral part of this International
A, C, D, E, F and G
r information only.
Standard. Annexes B, H and J are fo
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IS0 4259:1992(E)
INTERNATIONAL STANDARD
Petroleum products - Determination and application
of precision data in relation to methods of test
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 any given test method do 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 to be expected between two or more results obtained in specified circumstances.
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1 SCOPE 3.5 check sample : A sample taken at the place where the
product is exchanged, i.e. where the responsibility for the
This International Standard covers the calculation of product quality passes from the supplier to the recipient.
precision estimates and their application to specifications.
In particular, it contains definitions of relevant statistical
3.6 degrees of freedom : The divisor used in the
terms ( clause 3), the procedures to be adopted in the
calculation of variance; one less than the number of
planning of an inter-laboratory test programme to determine
independent results.
the precision of a test method (clause 4), the method of
calculating the precision from the results of such a
NOTE - The definition applies strictly only in the simplest
programme (clauses 5 and 6), and the procedure to be
cases. Complete deLfiniti0n.s are beyond the scope of this
followed in the interpretation of laboratory results in relation
International Standard.
both to precision of the methods and to the limits laid down
in specifications (clauses 7 to 10).
3.7 determination : The process of carrying out the series
of operations specified in the test method, whereby a single
It is emphasised that the procedures in this International
value is obtained.
Standard are designed to cover methods of test for petroleum
products only. The latter are, in general, homogeneous
products with which serious sampling problems do not 3.8 known val ue : The actual quantitative value implied by
normally arise. It would not be appropriate, therefore, to the preparation of the sample.
consider the procedures to be necessarily of wider
application, for example to heterogeneous solids. NOTE - The known value does not always exist, for example
for empirical tests such asjlash point.
2 NORMATIVE REFERENCE
3.9 mean; arithmetic mean; average : For a given set of
The following standard contains provisions which, through
results, the sum of the results divided by their number.
reference in this text, constitutes provisions of this
International Standard. At the time of publication, the
3.10 mean square : The sum of squares divided by the
edition indicated was valid. All standards are subject to
degrees of freedom.
revision, and parties to agreements based on this
International Standard are encouraged to investigate the
possibility of applying the most recent edition of the standard 3.11 normal distribution : The probability distribution of
listed below. Members of IEC and IS0 maintain registers a continuous random variable X such that, if x is any real
of currently valid International Standards. number, the probability density is
IS0 5725: “Precision of Test Methods - Determination of
-Lp[ -;( q] . .(l)
Repeatability and Reproducibility for a Standard Test
AX) diF
Method by Interlaboratory Tests ”.
-= NOTE - ~1 is the true value and o is the standard deviation
3 DEFINITIONS of the normal distribution (CJ > 0).
For the purposes of this International Standard, the following
3.12 operator : A person who normally and regularly
definitions apply :
carries out a particular test.
3.1 analysis of variance : A technique which enables the
3.13 outlier : A result far enough in magnitude from other
total variance of a method to be broken down into its
results to be considered not a part of the set.
component factors.
3.2 between-laboratory variance : When results obtained 3.14 precision : The closeness of agreement between the
by more than one laboratory are compared, the scatter is results obtained by applying the experimental procedure
usually wider than when the same number of tests are carried several times on identical materials and under prescribed
out by a single laboratory, and there is some variation conditions. The smaller the random part of the experimental
between means obtained by different laboratories. These error, the more precise is the procedure.
give rise to the between-laboratory variance which is that
component of the overall variance due to the difference in
3.15 random error : The chance variation encountered in
the mean values obtained by different laboratories. (There
all test work despite the closest control of variables.
is a corresponding definition for between-operator variance.)
3.16 recipient : Any individual or organization who
The term “between-laboratory” is often shortened to
receives or accepts the product delivered by the supplier.
“laboratory” when used to qualify representative parameters
of the d&&ion of the popilatkn of results, for example as
“laboratoAq variance ”. * * 3.17 repeatability :
a) Qualitatively
3.3 bias : The difference between the true value (related to
the method of test) (see 3.24) and the known value (see 3X),
The closeness of agreement between independent results
where this is available.
obtained in the normal and correct operation of the same
method on identical test material, in a short interval of
3.4 blind coding : The assignment of a different number to
time, and under the same test conditions (same operator,
each sample. No other identification or information on any
sample is given to the operator. same apparatus, same laboratory).
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IS0 4259:1992(E)
me representative parameters of the dispersion of the 3.23 supplier : Any individual or organization responsible
population which may be associated with the results are for the quality of a product just before it is taken over by the
qualified by the term “repeatability ”, for example recipient.
repeatability standard deviation, repeatability variance.
The term “repeatability” shall not be confused with the 3.24 true value : For practical purposes, the value towards
terms “between repeats” or “repeats” when used in this which the average of single results obtained by n laboratories
tends, as n tends towards infinity; consequently, such a true
way (see 3.18). Repeatability refers to the state of
minimum random variability of results. The period of value is associated with the particular method of test.
time during which repeated results are to be obtained
shall therefore be short enough to exclude time - NOTE - A d@ierent and idealized definition is given in
dependent errors, for example, environmental and IS0 3534, Statistics - Vocabulary and symbols.
calibration errors.
3.25 variance : The mean of the squares of the deviation of
b) Quuntitatively a random variable from its mean, estimated by the mean
square.
The value equal to or below which the absolute difference
between two single test results obtained in the above
conditions may be expected to lie with a probability of 4 STAGES IN PLANNING OF AN INTER-
LABORATORY TEST PROGRAMME FOR THE
95 %.
DETERMINATION OF THE PRECISION OF A
TEST METHOD
3.18 replication : The execution of a test method more than
once so as to improve precision and to obtain a better
The stages in planning an inter-laboratory test programme
estimation of testing error. Replication shall be
are as follows :
distinguished from repetition in that the former implies that
repeated experiments are carried out at one place and, as far
as possible, one period of time. The representative
a) Preparing a draft method of test.
parameters of the dispersion of the population which may be
associated with repeated experiments are qualified by the
b) Planning a pilot programme with at least two
term “between repeats ”, or in shortened form “repeats ”, for
laboratories.
example “repeats standard deviation ”.
c) Planning the inter-laboratory programme.
3.19 reproducibility :
d) Executing the inter-laboratory programme.
a) Qualitatively
The four stages are described in turn.
The closeness of agreement between individual results
obtained in the normal and correct operation of the same
4.1 Preparing a draft method of test
method on identical test material but under different test
conditions (different operators, different apparatus and
This shall contain all the necessary details for carrying out
different laboratories).
the test and reporting the results. Any condition which could
alter the results shall be specified.
The representative parameters of the dispersion of the
population which may be associated with the results are
The clause on precision will be included at this stage only
qualified by the term “reproducibility ”, for example
as a heading.
reproducibility standard deviation, reproducibility
variance.
4.2 Planning a pilot programme with at least two
laboratories
b) Quantitatively
A pilot programme is necessary for the following reasons :
The value equal to or below which the absolute difference
between two single test results on identical material
obtained by opera;ors in different laboratories, using the
a) to verify the details in the operation of the test;
standardized test method, may be expected to lie with a
probability of 95 %.
b) to find out how well operators can follow the
instructions of the method;
3.20 result : The final value obtained by following the
complete set of instructions in the test method; it may be
c) to check the precautions regarding samples;
obtained from a single determination or from several
determinations depending on the instructions in the method.
d) to estimate roughly the precision of the test.
(It is assumed that the result is rounded off according to the
procedure specified in annex G.)
At least two samples are required, covering the range of
results to which the test is intended to apply; however, at
3.21 standard deviation : A measure of the dispersion of
least 12 laboratory/sample combinations shall be included.
a series of results around their mean, equal to the positive
Each sample is tested twice by each laboratory under
square root of the variance and estimated by the positive
repeatability conditions. If any omissions or inaccuracies in
square root of the mean square.
the draft method are revealed, they shall now be corrected.
The results shall be analysed for bias and precision : if either
3.22 sum of squares : The sum of squares of the is considered to be too large, then alterations to the method
differences between a series of results and their mean. shall be considered.
3
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IS0 4259:1992(E)
4.3 Planning the inter-laboratory programme f) a blank form for reporting the results. For each
sample, there shall be space for the date of testing, the
two results, and any unusual occurrences. The unit of
There shall be at least five participating laboratories, but it
is preferable to exceed this number in order to reduce the accuracy for reporting the results shall be specified;
number of samples required.
g) a statement that the test shall be carried out under
The number of samples shall be sufficient to cover the range normal conditions, using operators with good experience
but not exceptional knowledge; and that the duration of
of the property measured, and to give reliability to the
precision estimates. If any variation of precision with level the test shall be the same as normal.
was observed in the results of the pilot programme, then at
least five samples shall be used in the inter-laboratory The pilot programme operators may take part in the
inter-laboratory programme. If their extra experience in
programme. In any case, it is necessary to obtain at least 30
degrees of freedom in both repeatability and reproducibility. testing a few more samples produces a noticeable effect,
For repeatability, this means obtaining a total of at least 30 it will serve as a warning that the method is not
pairs of results in the programme. satisfactory. ‘Ihey shall be identified in the report of the
results so that any effect may be noted.
For reproducibility, table 11 (annex A) gives the minimum
number of samples required in terms of L, P and Q, where
L is the number of participating laboratories and P and Q are
5 INSPECTION OF INTER-LABORATORY
the ratios of variance component estimates obtained from
RESULTS FOR UNIFORMITY AND FOR
Specifically, P is the ratio of the
the pilot programme.
OUTLlERS
interaction component to the repeats component, and Q is
the ratio of the laboratories component to the repeats
This clause specifies procedures for examining the results
component. Annex B gives the derivation of the formula
reported in a statistically designed inter-laboratory
used. If Q is much larger than P, then 30 degrees of freedom
programme (see clause 4) to establish
cannot be achieved; the blank entries in table 11 correspond
to this situation or the approach of it (i.e. when more than
a) the independence or dependence of precision and the
20 samples are required). For these cases, there is likely to
level of results;
be a significant bias between laboratories.
b) the uniformity of precision from laboratory to
4.4 Executing the inter-laboratory programme
laboratory, and to detect the presence of outliers.
One person shall be responsible for the entire programme,
The procedures are described in mathematical terms based
from the distribution of the texts and samples, to the final
on the notation of annex C and illustrated with reference to
appraisal of the results. He shall be familiar with the method,
the example data (calculation of bromine number) set out in
but shall not personally take part in the tests.
annex D.
The text of the method shall be distributed to all the
Throughout this clause (and clause 6), the procedures to be
laboratories in time to raise any queries before the tests begin.
used are first specified and then illustrated by a worked
If any laboratory wants to practice the method in advance,
example using data given in annex D.
this shall be done with samples other than those used in the
programme.
It is assumed throughout this clause that all the results are
either from a single\ormal distribution or capable of being
The samples shall be accumulated, subdivided and
transformed into-such a distribution (see 5.1). Other cases
distributed by the organizer, who shall also keep a reserve
(which are rare) would require different treatment which is
of each sample for emergencies. It is most important that
beyond the scope of this International Standard. See
the individual laboratory portions be homogeneous. They
reference [8] for a statistical test on normality.
shall be blind coded before distribution, and the following
instructions shall be sent with them :
Although the procedures shown here are in a form suitable
for hand calculation, it is strongly advised that an electronic
a) the agreed draft method of test;
computer be used to store and analyse inter-laboratory test
results, based on the procedures of this standard.
requirements for the
b) the handling and storage
samples;
5.1 Transformation of data
be tested
c) the order in which the samples are to
(a
In many test methods the precision depends on the 1 eve1 of
different random order for each laboratory)
the test result, and thus the variability of the reported results
is different from sample to sample. -? ‘he method of analysis
d) the statement that two results are to be obtained
outlined in this International Standard requires that this shall
consecutively on each sample by the same operator with
not be so and the position is rectified, if necessary, by a
thesameapparatus. Forstatisticalreasonsitisimperative
transformation.
that the two results are obtained independently of each
other, that is that the second result is not biased by
knowledge of the first. If this is regarded as impossible The laboratories standard deviations Dj, and the repeats
to achieve with the operator concerned, then the pairs of standard deviations ! ‘j (see annex C) are calculated and
results shall be obtained in a blind fashion, but ensuring plotted separately agamst the sample means mj. If the points
that they are carried out in a short period of time; so plotted may be considered as lying about a pair of lines
parallel to the m-axis, then no transformation is necessary.
If, however, the plotted points describe non-horizontal
e) the period of time during which repeated results are
to be obtained and the period of time during which all straight lines or curves of the form D = fi(m) and d = f2(m),
then a transformation will be necessary.
the samples are to be tested;
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IS0 4259:1992(E)
Inspection of the figures in table 1 shows that both D and d
The relationships D = fi(m) and d --h(m) will not in general
be identical. The statistical procedures of this International increase with m, the rate of increase diminishing as m
increases. A plot of these figures on log-log paper (i.e. a
Standard require, however, that the same transformation be
graph of log D and log d against log m) shows that the points
applicable both for repeatability and for reproducibility. For
may reasonably be considered as lying about two straight
this reason the two relationships are combined into a single
lines (see figure F. 1 in annex F). From the example
dependency relationship D = f(m) (where D now includes
calculations given in annex F.4, the gradients of these lines
d) by including a dummy variable T. This will take account
are shown to be the same, with an estimated value of 0,638.
of the difference between the relationships, if one exists, and
will provide a means of testing for this difference (see Bearing in mind the errors in this estimated value, the
annex F.l). gradient may for convenience be taken as 2/s.
Hence, the same transformation is appropriate both for
The single relationship D = f(m) is best estimated by
repeatability and reproducibility, and is given by the formula
weighted linear regression analysis. Strictly speaking, an
iteratively weighted regression should be used, but in most
cases even an unweighted regression will give a satisfactory
x-$& = 3x’
. . .
(3)
The derivation of weights is described in
approximation.
I
annex F.2, and the computational procedure for the
regression analysis is described in annex F.3. Typical forms
Since the constant multiplier may be ignored, the
of dependence D = f(m) are given in annex E. 1. These are
transformation thus reduces to that of taking the cube roots
of a single transformation
all expressed in terms
of the reported results (bromine numbers). This yields the
parameter B.
transformed data shown in table 16 (annex D), in which the
cu
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