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Disclosure to Promote the Right To Information
Whereas the Parliament of India has set out to provide a
practical regime of right to information for citizens to secure
access to information under the control of public authorities, in
order to promote transparency and accountability in the working of
every public authority, and whereas the attached publication of the
Bureau of Indian Standards is of particular interest to the public,
particularly disadvantaged communities and those engaged in the
pursuit of education and knowledge, the attached public safety
standard is made available to promote the timely dissemination of
this information in an accurate manner to the public.
इंटरनेट मानक
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“Step Out From the Old to the New”
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Sangathan
“The Right to Information, The Right to Live”
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है”Bhartṛhari—Nītiśatakam
“Knowledge is such a treasure which cannot be stolen”
“Invent a New India Using Knowledge”
है”ह”ह
IS 15393-1 (2003): Accuracy ( Trueness and Precision )
ofMeasurement Methods and Results, Part 1: General Principlesand
Definitions [PGD 25: Engineering Metrology]
-
IS 15393 (Part 1) :2003ISO 5725-1:1994
ml wFrt-=4fkG-la@TRJn@
Indian Standard
ACCURACY ( TRUENESS AND PRECISION ) OFMEASUREMENT METHODS AND
RESULTS
PART 1 GENERAL PRINCIPLES AND DEFINITIONS
ICS 17.020; 03.120.30
0 131S2003
BUREAU OF INDIAN STANDARDSMANAK BHAVAN, 9 BAHADUR SHAH ZAFAR
MARG
NEW DELHI 110002
September 2003 Price Group 8
-
Engineering Metrology Sectional Committee, BP 25
NATIONAL FOREWORD
This Indian Standard ( Part 1 ) which is identical with ISO
5725-1 :1994 ‘Accuracy ( trueness andprecision ) of measurement
methods and results — Part 1 : General principles and definitions’
issued
by the International Organization for Standardization ( ISO )
was adopted by the Bureau of IndianStandards on the recommendations
of the Engineering Metrology Sectional Committee and approval ofthe
Basic and Production Engineering Division Council.
This Indian Standard specifies the general principles and
definitions of accuracy of measurement methodsand results. This
document uses two terms ‘trueness’ and ‘precision’ to describe the
accuracy ofmeasurement method.
The text of the ISO Standard has been approved as suitable for
publication as an Indian Standardwithout deviations. In this
adopted standard certain conventions are, however, not identical to
thoseused in Indian Standards. Attention is particularly drawnlo
the following:
a) Wherever the words ‘International Standard’ appear referring
to this standard, they should beread as ‘Indian Standard’.
b) Comma ( , ) has been used as a decimal marker in the
International Standards, while in IndianStandards, the current
practice is to use a point ( . ) as the decimal marker.
In the adopted standard, reference appears to the following
International Standards for which IndianStandards also exists. The
corresponding Indian Standards which are to be substituted in their
placeare listed below along with their degree of equivalence for
the editions indicated:
international Standard
ISO 5725-2:1994
ISO 5725-3:1994
ISO 5725-4:1994
ISO 5725-5:1994
ISO 5725-6:1994
Corresponding Indian Standard Degree of Equivalence
IS 15393 ( Part 2 ) :2003 Accuracy ( trueness Identicaland
precision ) of measurement methods andresults : Part 2 Basic method
for thedetermination of repeatability and reproducibilityof a
standard measurement method
IS 15393 ( Part 3 ) :2003 Accuracy ( truenessand precision ) of
measurement methods andresults : Part 3 Intermediate measures of
theprecision of a standard measurement method
IS 15393 ( Part 4 ) :2003 Accuracy ( truenessand precision ) of
measurement methods andresults : Part 4 Basic methods for
thedetermination of the trueness of a standardmeasurement
method
IS 15393 ( Part 5 ) :2003 Accuracy ( truenessand precision ) of
measurement methods andresults : Part 5 Alternative methods for
thedetermination of the precision of a standardmeasurement
method
IS 15393 ( Part 6 ) :2003 Accuracy ( truenessand precision ) of
measurement methods andresults : Part 6 Use in practice of
accuracyvalues
do
do
do
do
( Continued on third cover)
-
IS 15393 (Part 1) :2003
ISO 5725-1 : 1994
Introduction
O.~ ISO 5725 uses two terms “trueness” and “precision” to
describethe accuracy of a measurement method. “Trueness” refers to
the close-ness of agreement between the arithmetic mean of a large
number of testresults and the true or accepted reference value.
“Precision” refers to thecloseness of agreement between test
results.
0.2 The need to consider “precision” arises because tests
performedon presumably identical materials in presumably identical
circumstancesdo not, in general, yield identical results. This is
attributed to unavoidablerandom errors inherent in evety
measurement procedure; the factors thatinfluence the outcome of a
measurement cannot all be completelycontrolled. In the practical
interpretation of measurement data, this vari-ability has to be
taken into account. For instance, the difference betweena test
result and some specified value may be within the scope of
un-avoidable random errors, in which case a real deviation from
such aspecified vatue has not been established. Similarly,
comparing test resultsfrom two batches of material will not
indicate a fundamental quality dif-ference if the difference
between them can be attributed to the inherentvariation in the
measurement procedure.
0.3 Many different factors (apart from variations between
supposedlyidentical specimens) may contribute to the variability of
results from ameasurement method, including:
a) the operator;
b) the equipment used;
c) the calibration of the equipment;
d) the environment (temperature, humidity, air pollution,
etc.);
e) the time elapsed between measurements.
The variability between measurements performed by different
operatorsand/or with different equipment will usually be greater
than the variabilitybetween measurements carried out within a short
interval of time by asingle operator using the same equipment.
0.4 The general term for variability between repeated
measurements isprecision. Two conditions of precision, termed
repeatability and reproduc-ibility conditions, have been found
necessa~ and, for many practicalcases, useful for describing the
variability of a measurement method. Un-der repeatability
conditions, factors a) to e) listed above are considered
i.
-
IS 15393 (Part 1) :2003ISO 5725-1 :1994
constants and do not contribute to the variability, while under
reproduc-ibility conditions they vary and do contribute to the
variability of the testresults. Thus repeatability and
reproducibility are the two extremes ofprecision, the first
describing the minimum and the second the maximumvariability in
results. Other intermediate conditions between these twoextreme
conditions of precision are also conceivable, when one or moreof
factors a) to e) are allowed to vary, and are used in certain
specifiedcircumstances. Precision is normally expressed in terms of
standard devi-ations.
0.5 The “trueness” of a measurement method is of interest when
it ispossible to conceive of a true value for the property being
measured. Al-though, for some measurement methods, the true value
cannot be knownexactly, it may be possible to have an accepted
reference value for theproperty being measured; for example, if
suitable reference materials areavailable, or if the accepted
reference value can be established by refer-ence to another
measurement method or by preparation of a knownsample. The trueness
of the measurement method can be investigatedby comparing the
accepted reference value with the level of the resultsgiven by the
measurement method. Trueness is normally expressed interms of bias.
Bias can arise, for example, in chemical analysis if themeasurement
method fails to extract all of an element, or if the presenceof one
element interferes with the determination of another.
0.6 The general term accuracy is used in ISO 5725 to refer to
bothtrueness and precision.
The term accuracy was at one time used to cover only the one
componentnow named trueness, but it became clear that to many
persons it shouldimply the total displacement of a result from a
reference value, due torandom as well as systematic effects.
The term bias has been in use for statistical matters for a very
long time,but because it caused certain philosophical objections
among membersof some professions (such as medical and legal
practitioners), the positiveaspect has been emphasized by the
invention of the term trueness.
il
-
IS 15393 (Part l): 2003ISO 5725-1 :1994
Indian Standard
ACCURACY ( TRUENESS AND PRECISION ) OFMEASUREMENT METHODS AND
RESULTS
PART 1 GENERAL PRINCIPLES AND DEFINITIONS
1 Scope
1.1 The purpose .of ISO 5725 is as follows:
a)
b)
c)
d)
e)
f)
to outline the general principles to be understoodwhen assessing
accuracy (trueness and precision)of measurement methods and
results, and in ap-plications, and to establish practical
estimationsof the various measures by experiment(ISO 5725-l);
to provide a basic method for estimating the twoextreme measures
of the precision of measure-ment methods by experiment (!S0
5725-2);
to provide a procedure for obtaining intermediatemeasures of
precision, giving the circumstancesin which they apply and methods
for estimatingthem (ISO 5725-3);
to provide basic methods for the determinationof the trueness of
a measurement method(ISO 5725-4);
to provide some alternatives to the basic meth-ods, given in ISO
5725-2 and ISO 5725-4, for de-termining the precision and trueness
ofmeasurement methods for use under certain cir-cumstances (ISO
5725-5);
to present some practical applications of thesemeasures of
trueness and precision (ISO 5725-6).
1.2 This part of 1S0 5725 is concerned exclusivelywith
measurement methods which yield measure-ments on a continuous scale
and give a single valueas the test result, although this single
value may bethe outcome of a calculation from a set of
observa-tions.
It defines values which describe, in quantitativeterms, the
ability of a measurement method to givea cortect result (trueness)
or to replicate a given result(precision). Thus there is an
implication that exactlythe same thing is being measured, in
exactly thesame way, and that the measurement process is un-der
control.
This part of ISO 5725 may be applied to a very widerange of
materials, including liquids, powders andsolid objects,
manufactured or naturally occurring,provided that due consideration
is given to anyheterogeneity of the material.
2 Normative references
The following standards contain provisions which,through
reference in this text, constitute provisionsof this part of ISO
5725. At the time of publication, theeditions indicated were valid.
All=standards are subjectto revision, and parties to agreements
based on thispart of ISO 5725 are encouraged to investigate
thepossibility of applying the most recent editions of thestandards
indicatedmaintain registersStandards.
below. Members of IEC and ISOof currently valid
International
1
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IS 15393 (Part 1) :2003ISO 5725-1 :1994
ISO 3534-1:1993, Statistics — Vocabulary and sym-bols — Part 1:
Probability and general statisticalterms.
ISO 572!5-2: 1994, Accuracy (trueness and precision)of
measurement methods and results — Part 2: Basicmethod for the
determination of repeatability and re-producibility of a standard
measurement method.
ISO !5725-3: 1994, Accuracy (trueness and precision)of
measurement methods and results — Part 3:Intermediate measures of
the precision of a standardmeasurement method.
ISO 5725-4:1994, Accuracy (trueness and precision)of measurement
methods and results — Part 4.. Basicmethods for the determination
of the trueness of astandard measurement pethod.
3 Definitions
For the purposes of ISO 5725, the following -defi-nitions
apply.
Some definitions are taken from ISO 3534-1.
The symbols used in ISO 5725 are given in annex A.
3.1 observed value The value of a characteristicobtained as the
result of a single observation.
[1s0 3534-1]
3.2 test result: The value of a characteristic ob-tained by
carrying out a specified test method.
NOTE 1 The test method should specify that one or anumber of
individual observations be made, and their aver-age or another
appropriate function (such as the median orthe standard deviation)
be reported as the test result. It mayalso require standard
corrections to be applied, such ascorrection of gas volumes to
standard temperature andpressura. Thus a test result can be a
result calculated fromseveral observed values. In the simple case,
the test resultis the observed value itself.
[1s0 3534-1]
3.3 level of the test in a precision experiment:The general
average of the test results from all lab-oratories for one
particular material or specimentested.
3.4 cell in a precision experiment: The test resultsat a single
level obtained by one laboratory.
3.5 accepted reference value: A value that servesas an
agreed-upon reference for comparison, andwhich is derived as:
a)
b)
c)
d)
a theoretical or established value, based onscientific
principles;
an assigned or certified value, based on exper-imental work of
some national or international or-ganization;
a consensus or certified value, based on collabor-ative
experimental work under the auspices of ascientific or engineering
group;
when a), b) and c) are not available, the expec-tation of the
(measurable) quantity, i.e. the meanof a specified population of
measurements.
[1s0 3534-1]
3.6 accuracy:The closeness of agreement betweena test result and
the accepted reference value.
NOTE 2 The term accuracy, when applied to a set of testresults,
involves a combination of random components anda common systematic
error or bias component.
[1s0 3534-1]
3.7 trueness The closeness of agreement betweenthe average value
obtained from a large series of testresults and an accepted
reference value.
NOTES
3 The measure of trueness is usually expressed in termsof
bias.
4 Trueness has been referred to as “accuracy of themean”. This
usage is not recommended.
[1s0 3534-1]
3.8 bias The difference between the expectationof the test
results and an accepted reference value.
NOTE 5 Bias is the total systematic error as contrastedto random
error. There may be one or more systematic errorcomponents
contributing to the bias. A larger systematicdifference from the
accepted reference value is reflectedby a larger bias value.
[1s0 3534-1]
3.9 laboratory bias The difference between theexpectation of the
test results from a particular lab-oratory and an accepted
reference value.
2
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IS 15393 (Part l) :2003ISO 5725-1 :1994
3.10 bias of the measurement method: The dif-ference between the
expectation of test results ob-tained from all laboratories using
that method and anaccepted reference value.
NOTE 6 One example of this in operation would bewhere a method
purporting to measure the sulfur contentof a compound consistently
fails to extract all the sulfur,giving a negative bias to the
measurement method. Thebias of the measurement method is measured
by the dis-placement of the average of results from a large
numberof different laboratories all using the same method. The
biasof a measurement method may be different at
differentlevels.
3.11 laboratory component of bias: The differencebetween the
laboratory bias and the bias of themeasurement method.
NOTES
7 The laboratory component of bias is specific to a
givenlaboratory and the conditions of measurement within
thelaborato~, and also it may be different at different levels
ofthe test.
8 The laboratory component of bias is relative tooverall average
result, not the true or reference value.
3.12 precision: The closeness of agreement
the
be-tween ‘independent test results obtained under stipu-lated
conditions.
NOTES
9 Precision depends only on the distribution of randomerrors and
does not relate to the true value or the specifiedvalue,
10 The measure of precision is usually expressed in termsof
imprecision and computed as a standard deviation of thetest
results. Less precision is ;eflected by a larger
standarddeviation.
11 “Independent test results” means results obtained ina manner
not influenced by any previous result on the sameor similar test
object. Quantitative measures of precisiondepend critically on the
stipulated conditions. Repeatabilityand reproducibility conditions
are particular sets of extremeconditions.
[1s0 3534-l-J
3.13 repeatability: Precision under repeatabilityconditions.
[1s0 3534-1]
3.14 repeatability conditions: Conditions whereindependent test
results are obtained withmethod on identical test items in the
same
the samelaboratory
by the same operator using the same equipmentwithin short
intervals of time.
[1s0 3534-1]
3.15 repeatability standard deviation: The stan-dard deviation
of test results obtained under repeat-ability conditions.
NOTES
12 It is a measure of dispersion of the distribution of
testresults under repeatability conditions.
13 Similarly “repeatability variance” and “repeatability
co-efficient of variation” could be defined and used as meas-ures
of the dispersion of test results under
repeatabilityconditions.
“[ISO 3534-1]
3.16 repeatability limit The value less than orequal to which
the absolute difference between twotest results obtained under
repeatability conditionsmay be expected to be with a probability of
95 ‘?/o.
NOTE 14 The symbol used is r.
[1s0 3534-1]
3.17 reproducibility Precision under
reproducibilityconditions.
[1s0 3534-1]
3.18 reproducibility conditions Conditions wheretest results are
obtained with the same method onidentical test items in different
laboratories with dif-ferent operators using different
equipment.
[1s0 3534-1]
3.19 reproducibility standard deviation The stan-dard deviation
of test results obtained under repro-ducibility conditiorw.
NOTES
15 It is a measure of the dispersion of the distribution oftest
results under reproducibility conditions.
16 Similarly “reproducibility variance” and “
reproducibilitycoefficient of variation” could be defined and used
asmeasures of the dispersion of test results under reproduc-ibility
conditions.
[1s0 3534-1]
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IS 15393 (Part 1) :2003ISO 5725-1 :1994
3.20 reproducibility limit: The value less than orequal to which
the absolute difference between twotest results obtained under
reproducibility conditionsmay be expected to be with .a probability
of 95 Yo.
NOTE 17 The symbol used is R.
[1s0 3534-1]
3.21 outlier: A member of a set of values which isinconsktent
with the other members of that set.
NOTE 18 ISO 5725-2 specifies Ihe statistical tests andthe
significance level to be used to identify outliers intrueness and
precision experiments.
3.22 collaborative assessment experiment Aninterlaboratory
experiment in which the performanceof each laborato~ is assessed
using the same stan-dard measurement method on identical
material.
NOTES
19 The definitions given in 3.16 and 3.20 apply to resultsthat
vary on a continuous scale. If the test result is discreteor
rounded off, the repeatability limit and the reproducibilitylimit
as defined above are each the minimum value equal toor below which
the absolute difference between two singletest results is expected
to lie with a probability of not lessthan 95 %.
20 The definitions given in 3.8 to 3.11, 3.15, 3.16, 3.19
and3.20 refer to theoretical values which in reality remain
un-known. The values for reproducibility and repeatability
stan-dard deviations and bias actually determined by experiment
(as described in ISO 5725-2 and ISO 5725-4) are, in stat-istical
terms, estimates ot these values, and as such aresubject to errors.
Consequently, for example, the probabilitylevels associated with
the limits r and R will not be exactly95 Y., They will approximate
to 95 Y. when many labora-tories have taken part in the precision
experiment, but maybe considerably different from .95 ‘?’. when
fewer than 30laboratories have participated. This is unavoidable
but doesnot seriously detract from their practical utility as they
areprimarily designed to serve as tools for judging whether
thedifference between results could be ascribed to
randomuncertainties inheFent in the measurement method or
not.Differences larger than the repeatability limit r or the
repro-ducibility limit R are suspect.
21 The symbols r and R are already in general use forother
purposes; in ISO 3534-1 r is recommended for thecorrelation
coefficient and R (or W) for the range of a singleseries of
observations. However, there should be no con-fusion if the full
wordings repeatability limit r and reproduc-ibility limit R are
used whenever there is a possibility ofmisunderstanding,
particularly when they are quoted instandards.
4 Practicalimplications of the definitionsfor
accuracyexperiments
4.1 Standard measurement meth’od
4.1.1 In order that the measurements are made inthe same way,
the measurement method shall havebeen standardized. All
measurements shall be carriedout according to that standard method.
This meansthat there has to be a written document that laysdown in
full detail how the measurement shall becarried out, preferably
including a description as tohow the measurement specimen should be
obtainedand prepared.
4.1.2 The existence of a documented measurementmethod implies
the existence of an organization re-sponsible for the establishment
of the measurementmethod under study.
NOTE 22 The standard measurement method is dis-cussed more fully
in 6.2.
4.2 Accuracy experiment
4.2.1 The accuracy (trueness and precision) meas-ures should be
determined from a series of test re-sults reported by the
participating laboratories,organized under a panel of experts
established spe-cifically for that purpose.
Such an interlaboratory experiment is called an “ac-curacy
experiment”. The accuracy experiment mayalso be called a
“precision” or “trueness exper-iment” according to its limited
purpose. If the purposeis to determine trueness,’then a precision
experimentshall either have been completed previously or shalloccur
simultaneously.
The estimates of accuracy derived from such an ex-periment
should always be quoted as being valid onlyfor tests carried out
according to the standardmeasurement method.
4.2,2 An accuracy experiment can often be consid-ered to be a
practical test of the adequacy of thestandard measurement method.
One of the mainpurposes of standardization is to eliminate
differencesbetween users (laboratories) as far as possible, andthe
data provided by an accuracy experiment will re-veal how
effectively this purpose has been achieved.Pronouncedantes
(seemeans may
differences in the within-laboratory vari-clause 7) or between
the laboratory
indicate that the standard measurement
4
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IS 15393 (Part l) :2003ISO 5725-1 :1994
method is not yet sufficiently detailed and can poss-ibly be
improved. If so, this should be reported to thestandardizing body
with a request for further investi-gation.
4.3 Identical test items
4.3.1 In an accuracy experiment, samples of a spe-cific material
or specimens of a specific product aresent from a central point to
a number of laboratoriesin different places, different countries,
or even in dif-ferent continents. The definition of repeatability
con-ditions (3.1 4) stating that the measurements in
theselaboratories shall be performed on identical test itemsrefers
to the moment when these measurements areactually carried out. To
achieve this, two differentconditions have to be satisfied:
a)
b)
the samples have to be identical when dispatchedto the
laboratories;
they have to remain identical during transport andduring the
different time intervals that may elapsebefore the measurements are
actually performed.
In organizing accuracy experiments, both conditionsshall be
carefully observed.
NOTE 23 The selection of material is discussed morefully in
6.4.
4.4 Short intervals of time
4.4.1 According to the definition of repeatabilityconditions (3.
14), measurements for the determi-nation of repeatability have to
be made under con-stant operating conditions; i.e. during the
timecovered by the measurements, factors such as thoselisted in 0.3
should be constant. In particular, theequipment should not be
recalibrated between themeasurements unless this is an essential
part ofevery single measurement. In practice, tests
underrepeatability conditions should be conducted in asshort a time
as possible in order to minimize changesin those factors, such as
environmental, which cannotalways be guaranteed constant.
4.4.2 There is also a second” consideration whichmay affect the
interval elapsing between measure-ments, and that is that the test
results are assumedto be independent. If it is feared that previous
resultsmay influence subsequent test results (and so reducethe
estimate of repeatability variance), it may benecessary to provide
separate specimens coded insuch a way that an operator will not
know which aresupposedly identical. Instructions would be given
asto the order in which those specimens are to be
measured, and presumably that order will be ran-domized so that
all the “identical” items are notmeasured together. This might mean
that the timeinterval between repeated measurements may appearto
defeat the object of a short interval of time unlessthe
measurements are of such a nature that thewhole series of
measurements could all be completedwithin a short interval of time.
Common sense mustprevail.
4.5 Parth5pating laboratories
4.5.1 A basic assumption underlying this part ofISO 5725 is
that, for a standard measurementmethod, repeatability will be, at
least approximately,the same for all laboratories applying the
standardprocedure, so that it is permissible to establish onecommon
average repeatability standard deviationwhich will be applicable to
any laboratory. However,any laborato~ can, by carrying out a series
ofmeasurements under repeatability conditions, arriveat an estimate
of its own repeatability standard devi-ation for the measurement
method and check itagainst the common standard value. Such a
pro-cedure is dealt with in ISO 5725-6.
4.5.2 The quantities defined in 3.8 to 3.20 in theoryapply to
all laboratories which are likely to perform themeasurement method.
[n practice, they are deter-mined from a sample of this population
of labora-tories. Further details of the selection of this
sampleare given in 6.3. Provided the instructions given
thereregarding the number of laboratories to be includedand the
number of measurements that they carry outare followed, then the
resulting estimates of truenessand precision should suffice. If,
however, at some fu-ture date it should become evident that the
labora-tories participating were not, or are no longer,
trulyrepresentative of all those using the standardmeasurement
method, then the measurement shallbe repeated.
4.6 Observation conditions
4.6.1 The factors which contribute to the variabilityof the
observed values obtained within a laboratoryare listed in 0.3. They
may be given as time, operatorand equipment when observations at
different timesinclude the effects due to the change of
environ-mental conditions and the recalibration of equipmentbetween
observations. Under repeatability conditions,observations are
carried out with all these factorsconstant, and under
reproducibility conditions obser-vations are carried out at
different laboratories; i.e. notonly with all the other factors
varying but also withadditional effects due to the difference
between lab-
5
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IS 15393 (Part 1) :2003ISO 5725-1 :1994
oratories in management and maintenance of thelaboratory,
stability checking of the observations, etc.
4.6.2 It may be useful on occasion to considerintermediate
precision conditions, in which observa-tions are carried out in the
same laborato~ but oneor more of the factors time, operator or
equipment areallowed to vary. In establishing the precision of
ameasurement method, it is very important to definethe appropriate
observation conditions, i.e. whetherthe above three factors should
be constant or not.
Furthermore, the size of the variability arising from afactor
will depend on the measurement method. Forexample, in chemical
analysis, the factors “operator”and “time” may dominate; likewise
with microanaly-sis the factors “equipment” and “environment”,
andwith physical testing “equipment” and “calibration”may
dominate.
5 Statisticalmodel
5.1 Basic model
For estimating the accuracy (trueness and precision)
of a measurement method, it is useful to assume that
every test result, y, is the sum of three components:
y=m+ll+e . . . (1)
where, for the particular material tested,
m is the general mean (expectation);
B k the laboratory component of bias under re-peatability
conditions;
e is the random error occurring in everymeasurement under
repeatability conditions.
5.1.1 General mean, m
5.1.1.1 The general mean m is the level of the test;specimens of
different purities of a chemical, or dif-ferent materials (e.g.
different types of steel), willcorrespond to different levels. In
many technical situ-ations the level of the test is exclusively
defined bythe measurement method, and the notion of an inde-pendent
true value does not apply. However, in somesituations the concept
of a true value g of the testproperty may hold good, such as the
true concen-tration of a solution that is being titrated. The level
mis not necessarily equal to the true value p.
5.1.1.2 ‘When examining the difference betweentest results
obtained by the same measurementmethod, the bias of the measurement
method willhave no influence and can be ignored. However,
when comparing test results with a value specified ina contract
or a standard where the contract or speci-fication refers to the
true value (~) and not to the“level of the test” (m), or when
comparing resultsproduced using different measurement methods,
thebias of the measurement method will have to betaken into
account. If a true value exists and a satis-factory reference
material is available, the bias of themeasurement method should be
determined asshown in ISO 5725-4.
5.1.2 Term B
5.1.2.1 This term is considered to be constant dur-ing any
series of tests performed under repeatabilityconditions, but to
differ in value for tests carried outunder other conditions. When
test results are alwayscompared between the same two laboratories,
it isnecessa~ for them to determine their relative bias,either from
their individual bias values as determinedduring an accuracy
experiment, or by carrying out .aprivate trial between themselves.
However, in orderto make general statements regarding
differencesbetween two unspecified laboratories, or when mak-ing
comparisons between two laboratories that havenot determined their
own bias, then a general distri-bution of Iaboratoy components of
bias must beconsidered. This was the reasoning behind the con-cept
of reproducibility. The procedures given inISO 5725-2 were
developed assuming that the distri-bution of laborato~ components
of bias is approxi-mately normal, but in practice they work for
mostdistributions provided that they are unimodal.
5.1.2.2 The variance of B is called the between-Iaboratory
variance and is expressed as:
var (B) = at . . . (2)
where at includes the between-operator andbetween-equipment
variabilities.
In the basic precision experiment described inISO 5725-2, these
components are not separated.Methods are given in ISO 5725-3 for
measuring thesize of some of the random components of B.
5.1.2.3 In general, B can be considered as the sumof both random
and systematic components. No at-tempt is made to give here -an
exhaustive list of thefactors that contribute to B, but they
include differentclimatic conditions, variations of equipment
within themanufacturer’sthe techniquesferent places.
tolerances, and even differences inin which operators are
trained in dif-
6
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IS 15393 (Part 1) :2003ISO 5725-1 :1994
5.1.3 Error term e 5.3 Alternative models
5.1.3.1 This term represents a random error occur-ring in every
test result and the procedures giventhroughout this part of ISO
5725 were developed as-suming that the distribution of this error
variable wasapproximately normal, but in practice they work formost
distributions provided that they are unimodal.
5.1.3.2 Within a single laboratory, its variance
underrepeatability conditions is called the
within-laboratoryvariance and is expressed as:
var (e) = cT& . . . (3)
5.1.3.3 It may be expected that u& will have differ-ent
values in different laboratories due to differencessuch as in the
skills of the operators, but in this partof ISO 5725 it is assumed
that for a properly stan-dardized measurement method such
differences be-tween laboratories should be small and that it
isjustifiable to establish a common value of within-Iaboratoty
variance for all the laboratories using themeasurement method. This
common value, which isestimated by the arithmetic mean of the
within-laborato~ variances, is called the repeatability vari-ance
and is designated by:
f+’= var (e) = ~ . . . (4)
This arithmetic mean is taken over all those labora-
tories taking part in the accuracy experiment which
remain after outliers have been excluded.
5.2 Relationship between the basic modeland the precision
5.2.1 When the basic model in 5.1 is adopted, therepeatability
variance is measured directly as the vari-ance of the error term e,
but the reproducibility vari-ance depends on the sum of the
repeatability varianceand the between-laboratory variance mentioned
in5.1.2.2.
5.2.2 Two quantities are required as measures ofprecision, the
repeatability standard deviation
(5)
and the reproducibility standard deviation
,
Extensionspriate andISO 5725.
to the basic model areare described in the
used when appro-relevant parts of
6 Experimental design considerationswhen estimating accuracy
6.1 Planning of an accuracy experiment
6.1.1 The actual planning of an experiment to esti-mate the
precision and/or trueness of a standardmeasurement method should be
the task of a panelof experts familiar with the measurement method
andits application. At least one member of the panelshould have
experience in the statistical design andanalysis of
experiments.
6.1.2 The following questions should be consideredwhen planning
the experiment.
a)
b)
c)
d)
e)
f)
g)
h)
i)
j)
Is a satisfactory standard available for themeasurement
method?
How many laboratories should be recruited to co-operate in the
experiment?
How should the laboratories be recruited, andwhat requirements
should they satisfy?
What is tkte range of levels encountered in prac-tice?
How many levels should be used in the exper-iment?
What are suitable materials to represent theselevels and how
should they be prepared?
What number of replicates should be specified?
What time-frame should be specified for thecompletion of all the
measurements?
Is the-basic model of 5.1 appropriate, or should amodified one
be considered?
Are any special precautions needed to ensure thatidentical
materials are measured in the same statein all laboratories?
These questions are considered in 6.2 to 6.4.
,.
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ts 15393 (Part11:2003ISO 5725-1 :1994
6.2 Standard measurement method
As stated in 4.1, the measurement method under in-vestigation
shall be one that has been standardized.Such a method has to be
robust, i.e. small variationsin the procedure should not produce
unexpectedlylarge changes in the results. If this might
happen,there shall be adequate precautions or warnings. It isalso
desirable that in the process of developing astandard measurement
method every effort has beenmade to remove or reduce bias.
Similar experimental procedures may be used -tomeasure the
trueness and precision of both estab-lished measurement methods and
recently standard-ized measurement methods. In the latter case,
theresults obtained should be regarded as prelimina~estimates,
because the trueness and precision couldchange as laboratories gain
experience.
The document setting out the measurement methodshall be
unambiguous and complete. All essentialoperations concerning the
environment of the pro-cedure, the reagents and apparatus,
prelimina~checking of equipment, and the preparation of thetest
specimen should be included in the measure-ment method, possibly by
references to other writtenprocedures that are available to the
operators. Themanner of calculating and expressing the test
resultshould be precisely specified, including the numberof
significant figures to be reported.
6.3 Selection of laboratories for the accuracyexperiment
6.3.1 Choice of laboratories
From a statistical point of view, those
laboratoriesparticipating in any experiment to estimate
accuracyshould have been chosen at random from all the
lab-oratories using the measurement method. Volunteersmight not
rep&sent a realistic cross-section. How-ever, other practical
considerations, such as a re-quirement that the participating
laboratories bedistributed over different continents or Climatlc
re-gions, may affect the pattern of representation.
The participating laboratories should not consist ex-clusively
of those that have gained special experienceduring the process of
standardizing the method.Neither should they consist of
specialized“reference” laboratories in order to demonstrate the
accuracy to which the method can perform in experthands.
The number of laboratories to be recruited to partici-pate in a
cooperative interlaboratory experiment and
the number of test results required from each labora-tory at
each level of the test are interdependent. Aguide to deciding how
many there should be is givenin 6.3.2 to 6.3.4.
6.3.2 Number of laboratories required for anestimate of
precision
6.3.2.1 The various quantities represented by thesymbol a in
equations (2) to (6) of clause 5 are truestandard deviations whose
values are not known, anobject of a precision experiment being to
estimatethem. When an estimate (s) of a true standard devi-ation
(a) is to be made, conclusions can be drawn asto the range about u
within which the estimate (s) canbe expected to lie. This is a
well-understood statisticalproblem which is solved by the use of
the chi-squareddistribution and the number of results from which
theestimate ofs was based. One formula frequently usedis:
P[– A
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IS 15393 (Part 1) :2003ISO 5725-1 :1994
For reproducibility
‘=AR=l”~
. . . (lo)
NOTE 24 A sample variance which has v degrees offreedom and
expectation U2 may be assumed to have, ap-proximately, a normal
distribution with variance 2U4/V.Equations (9) and (1O) were
derived by making this as-sumption about the variances involved in
the estimation ofU, and UR.The adequacy of the approximation was
checkedby an exact calculation.
6.3.2.4 The value of y is not known, but often pre-liminary
estimates are available of the within-Iaboratory standard
deviations and the
between-laboratory standard deviations obtained dur-ing the
process of standardizing the measurementmethod. Exact values of the
uncertainty percentagesfor repeatability and reproducibility
standard devi-ations with different numbers of laboratories (p)
anddifferent numbers of results per laborato~ (n) aregiven in table
1 and are also plotted in chart form inannex B.
6.3.3 Number of laboratories required for theestimate of
bias
6.3.3.1 The biasmay be estimated
;=; –p
where
of the measurement method, 6,from:
. . . (11)
~ is the grand mean of all the test results ob-tained by all the
laboratories at a particularlevel of the experiment;
I.I is the accepted reference value.
The uncertainty of this estimate can be expressed bythe
equation:
P[6– AUR
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IS 15393 (Part l) :2003ISO 5725-1 : 1994
Table 2 — Values of A, the uncertainty of anestimate of the bias
of the measurement method
No. ofValueof A
laboratories ““y=o y=l
P all n n=z n=3 n=d
5 0,88 0,76 0,72 0,69
10 0,62 0,54 0,51 0,4915 0,51 0,44 0,41 0,40
20 0,44 0,38 0,36 0,35
25 0,39 0,34 0,32 0,31
30 0,36 0,31 0,29 0,28
35 0,33 0,29 0,27 0,2640 0,31 0,27 0,25 0,25
Table 3 — Values of Aw, the uncertainty of anestimate of the
within-laboratory bias
No. of test results Valueof Awn
5 0,8810 0,6215 0,5120 0,4425 0,3930 0,3635 0,3340 0,31
6.3.4 Implications in the choice of laboratories
The choice of the number of laboratories will be acompromise
between availability of resources and adesire to reduce the
uncertainty of the estimates toa satisfactory level. From figures
B.1 and B.2 inannex B it can be seen that estimates of the
repeat-ability and reproducibility standard deviations coulddiffer
substantially from their true values if only asmall number (p = 5)
of laboratories take part in aprecision experiment, and that
increasing the numberof the laboratories by 2 or 3 yields only
small re-ductions in the uncertainties of the estimates whenp is
greater than 20. It is common to choose a valueof p between 8 and
15. When CL is larger than a, (i.e.y is larger than 2), as is often
the case, little is to begained by obtaining more than n = 2 test
results perIaboratov per level.
6.4 Selection of materials to be used for anaccuracy
experiment
6.4.1 The materials to be used in an experiment todetermine the
accuracy of a measurement methodshould represent fully those to
which the measure-ment method is expected to be applied in normal
use.As a general rule, five different materials will usuallyprovide
a sufficiently wide range of levels to allow theaccuracy to be
established adequately. A smallernumber might be appropriate in the
first investigationof a recently developed measurement method
whenit is suspected that modifications to the method maybe
necessa~, followed by further accuracy exper-iments.
6.4.2 When the measurements have to be per-formed on discrete
objects that are not altered bymeasuring, they could, in principle
at least, be carriedout using the same set of objects in different
labora-tories. This, however, would necessitate circulatingthe same
set of objects around many laboratories of-ten situated far apart,
in different countries or conti-nents, with a considerable risk of
loss or damageduring transport. If different items are to be used
indifferent laboratories, then they shall be selected insuch a way
as to ensure that they can be presumedto be identical for practical
purposes.
6.4.3 In selecting the material to represent the dif-ferent
levels, it should be considered whether thematerial should be
specially homogenized before pre-paring the samples for dispatch,
or whether the effectof the heterogeneity of the material should be
in-cluded in the accuracy values.
6.4.4 When measurements have to be performedon solid materials
that cannot be homogenized (suchas metals, rubber or textile
fabrics) -and when themeasurements cannot be repeated on the same
testpiece, inhomogeneity in the test material will form anessential
component of the precision of themeasurement and the idea of
identical material nolonger holds good. Precision experiments can
still becarried out, but the values of precision may only bevalid
for the particular material used and should bequoted as such. A
more universal use of the precisionas determined will be acceptable
only if it can bedemonstrated that the values do not differ
signif-icantly between materials produced at different timesor by
different producers. This ‘would require a moreelaborate experiment
than has been considered inISO 5725.
-
IS 15393 (Part l) :2003ISO” 5725-1:1994
6.4.5 In general, where destructive testing is in-volved, the
contribution to the variability in the ‘testresults arising from
differences between the speci-mens on which the measurements are
performedshall either be negligible compared to the variabilityof
the measurement method itself, or else shall forman inherent part
of the variability of the measurementmethod, and thus be truly a
component of precision.
6.4.6 When the materials under measurement mightchange with
time, the overall time-scale of the ex-
periment should be chosen to take this into account.
It might be appropriate in some cases to specify the
times at which the samples are to be measured.
6,4.7 In all the above, reference is made to measur-ing in
different laboratories, with the implication oftransportation of
the test specimens to the Iaboratoty,but some test specimens are
not transportable, suchas an oil storage tank. In such cases,
measuring bydifferent laboratories means that different
operatorsare sent with their equipment to the test site. In
othercases, the quantity being measured may be transitoryor
variable, such as water flow in a river, when careshall be taken
that the different measurements -aremade under, as near as
possible, the same conditions.The guiding principle must always be
that the objec-tive is to determine the ability to repeat the
samemeasurement.
6.4.8 The establishment of precision values for ameasurement
method presupposes that the precisioneither is independent of the
material being tested, ordepends on the material in a predictable
manner. Withsome measurement methods it is possible to quotethe
precision only in relation to one or more definableclasses of test
material. Such data will be only a roughguide to the precision in
other applications. More of-ten it is found that the precision is
closely related tothe level of the test, and determination of the
pre-cision then includes the establishment of a relation-ship
between precision and level. Therefore, whenpublishing precision
values for a standard measure-ment method, it is recommended that
the materialused in the precision experiment should be
clearlyspecified along with the range of materials to whichthe
values can be expected 10 apply.
6.4.9 For the assessment of tru ess, at least one
zof the materials used should h, e an accepted reTer-ence value.
If it is likely that trueness varies with level,materials with
accepted reference values will beneeded at severs) levels.
7 Utilization of accuracydata
7.1 Publication of trueness and precisionvalues
7.1.1 When the aim of a precision experiment is toobtain
estimates of the repeatability and reproducibil-ity standard
deviations under the conditions definedin 3.14 and 3.18, then the
basic model of 5.1 shall beused. ISO 5725-2 then provides an
appropriatemethod of estimating these standard deviations, oran
alternative may be found in ISO 5725-5. When theaim is to obtain
estimates of intermediate measuresof precision, then the
alternative model and themethods given in ISO 5725-3 shall be
used.
7.1.2 Whenever the bias of the measurementmethod has been
determined, it should be publishedwith a statement regarding the
reference againstwhich that bias was determined. Where the
biasvaries with the level of the test, publication should bein the
form of a table giving the level, the bias as de-termined, and the
reference used in that determi-nation.
7.4.3 When an interlaboratory experiment has beenperformed for
estimating trueness or precision, eachparticipating laborato~
should be informed of its lab:orato~ component of bias relative to
the generalmean as determined from the experiment. This
infor-mation could be of value in the future if similar
ex-periments are performed, but should not be used forcalibration
purposes.
7.1.4 The repeatability and reproducibility standarddeviations
for any standard measurement methodshall be determined as laid down
in parts-2 to 4 ofISO 5725, and should be published as part of
thestandard measurement method under a section en-titled precision.
This section may also show the re-peatability and reproducibility
limits (r and R). Whenprecision does not vary with level, single
average fig-ures can be given in each case. Where precisionvaries
with the level of the test, publication should bein the form of a
table, such as table 4, and may alsobe expressed as a mathematical
relationshi~. inter-mediate measuresin a similar form.
of precision should be presented
11
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IS 15393 (Patt 1) :2003ISO 5725-1 :1994
Table 4 — Example of method of reportingstandard deviations
i 1 I tRepeatability Reproducibility
standard standardRangeor level deviation deviation
I I s, I 1.From to .......
From ....... to .......
From ....... to .......
7.1.5 The definitions of repeatability and reproduc-ibility
conditions (3.14 and 3.18) shall be given in theprecision clause.
When intermediate measures ofprecision are given, care should be
taken to statewhich of the factors, (time, operators,
equipment)have been allowed to vary. When the repeatability
andreproducibility limits are given, some statementshould be added
linking them to the difference be-tween two test results and the 95
Y. probability level.Suggested wordings are as follows.
The difference between two test results found onidentical test
material by one operator using thesame apparatus within the
shortest feasible timeintetial will exceed the repeatability limit
(r) onaverage not more than once in 20 cases in thenormal and
correct operation of the method.
Test results on identical test material reported bytwo
laboratories will differ by more than the re-producibility limit
(1?) on average not more thanonce in 20 cases in the normal and
correct oper-aticm of the method.
Ensure that the definition of a test result is clear,either by
quoting the clause numbers of themeasurement method standard that
have to be fol-lowed to obtain the test result or by other
means.
7.1.6 In general, a brief mention of the accuracy ex-periment
should be added at the end of this precisionsection. Suggested
wording is as follows.
The accuracy data were determined from an ex-periment organized
and analysed in accordancewith ISO 5725- (part) in (year) involving
(p) lab-oratories and (q) levels. Data from ( )
laboratoriescontained outliers. The outliers were not includedin
the calculation of the repeatability standard de-viation and the
reproducibility standard deviation.
A description of the materials used in the accuracyexperiment
should be ad?ed, especially when thetrueness or precision depend on
the materials.
7.2 Practicalapplicationsof truenessandprecisionvalues
Practical applications of trueness and precision valuesare
covered in detail in ISO 5725-6. Some examplesare as follows.
7.2.1 Checking the acceptability of test results
A product specification could require repeatedmeasurements to be
obtained under repeatabilityconditions. A repeatability standard
deviation may beused in these circumstances to check the
acceptabil-ity of the test results and to decide what action
shouldbe taken if they are not acceptable. When both asupplier and
a purchaser measure the same materialand their results differ,
repeatability and reproducibilitystandard deviations may be used to
decide if the dif-ference is of a size that is to be expected with
themeasurement method.
7.2.2 Stability of test results within a laboratory
By carrying out regular measurements on referencematerials, a
laboratory can check the stability of itsresults and produce
evidence to demonstrate itscompetence, with respect to both the
bias and therepeatability of its testing.
7.2.3 Assessing the performance of a laboratory
Laboratory accreditation schemes are becoming in-creasingly
widespread. Knowledge of the truenessand precision of a measurement
method allows thebias and repeatability of a candidate laboratory
to beassessed, either using reference materials or
aninterlaboratory experiment.
7.2.4 Comparing alternative measurementmethods
Two measurement methods may be available formeasuring the same
property, one being simpler andless expensive than the other but
less generally ap-plicable. Trueness and precision values may be
usedto justify the use of the less expensive method forsome
restricted range of materials.
12
-
IS 15393 (Part l-)~ISO 5725-1 :1994
Annex A(normative)
B
BO
B(l),B(z), etc.
c
c, c’, c“
Symbols and abbreviations
Intercept in the relationship
s=a+bm
Factor used to calculate the uncer-tainty of an estimate
Slope in the relationship
s=a+bm
Component in a test result repre-senting the deviation of a
laborato~from the general average (laboratorycomponent of bias)
Componer?t of B representing allfactors that do not change in
inter-mediate precision conditions
Components of B representing fac-tors that vary in intermediate
pre-cision conditions
Intercept in the relationship
Igs=c+dlgm
Te-st statistics
c C’Cr,t,cm, C“Ctit Critical values for statistical tests
CDP Critical difference for probability P
CRP Critical range for probability P
d Slope in the relationship
Igs=c+dlgm
e Component in a test result repre-senting the random error
occurringin every test result
f Critical range Iactor
FP(v1, V2) p-quantile of the F-distribution with
VI and V2 degrees of freedom
G Grubbs’ test statistic
h Mandel’-s between-laboratory con-sistency test statistic
k
LCL
m
M
N
n
P
P
q
r
R
RM
s
t
T
t
UCL
w
w
x
Y
used in ISO 5725
Mandel’s within-laboratory consistency teststatistic
Lower control limit (either action limit or warninglimit)
General mean of the test property; level
Number of factors considered in intermediateprecision
conditions
Number of iterations
Number of test results obtained in one labora-tory at one level
(i.e. per cell)
Number of laboratories participating in the inter-Iaboratofy
experiment
Probability
Number of levels of the test property in theinterlaboratory
experiment
Repeatability limit
Reproducibility limit
Reference material
Estimate of a standard deviation
Predicted standard deviation
Total or sum of some expression
Number of test objects or groups
Upper control limit (either action limit or warninglimit)
Weighting factor used in calculating a weightedregression
Range of a set of test results
Datum used for Grubbs’ teat
Test result
13
-
K- T5393 (Part 1) :2003ISO 5725-1 :1994
Arithmetic mean of test results
3rand mean of test results
Significance level
Type II error probability
Ratio of the reproducibility standard deviation tothe
repeatability standard deviation (a~/uJ
Laboratory bias
Estimate of A\
Bias of the measurement method
Estimate of d
Detectable difference between two Iaboratmybiases or the biases
of two measurementmethods
True value or accepted reference value of a testproperty
Number of degrees of freedom
Detectable ratio between the repeatability stan-dard deviations
of method B and method A
True value of a standard deviation
Component in a test result representing thevariation due to time
since last calibration
Detectable ratio between the square roots ofthe
between-laborato~ mean squares ofmethod B and method A
p-quantile of the ~2-distribution with v degreesof freedom
Symbols used as subscripts
c
E
i
1()
j
k
L
m
M
o
P
r
R
T
w
1, 2, 3...
(1), (2), (3)..
Calibration-different
Equipment-different
Identifier for a particular laboratory
Identifier for intermediate measures ofprecision; in brackets,
identification ofthe type of intermediate situation
identifier for a particular level
(ISO 5725-2).Identifier for a group of tests or for afactor (ISO
5725-3)
Identifier for a particular test result in alaborato~ i at level
j
Between-laborato~ (interlaboratory)
Identifier for detectable bias
Between-test-sample
Operator-different
Probability
Repeatability
Reproducibility
Time-different
Within-laboratory (intralaboratory)
For test results, numbering in the orderof obtaining them
For test results, numbering in the orderof increasing
magnitude
14
-
IS 15393 (Patil) :2003ISO 5725-1 :1994
90 -
80 -
70 -
60 -
50 -
40 -
30 -
20 -
Annex B(normative)
Charts of uncertainties for precision measures
“.2---- “.3
.------- n.~
\\\
,1t, \
~, \\\ \
\\ \\\%%,: \ \\
%\.. --~
-.. ---. --- -..--- ---------- —----------- --------------
----------- —10 I 1 t 1 I 1 I I I I t I I I I I I I I t 1
0 4 8 12 16 20 24 28 32 36 40Numberof laboratories
Figure B.1 — The amount by which S,can be expected to differ
from the true value within a probabilitylevel of 95 YO
-
IS 15393 (Part 1) :20031S0 5725-1 :1994
~100 -
:c.-
= 90 -ez8
80 -5
70 -
60-
so -
-40-
30-
20-
\\
\’\\; J\\\‘\ ,\
\\\\\
---- if=5, n=2.—. — J=2, n=2
—.. — X=2, n=3— J=l, n=2— _ J.l, n.3
-------- F = 1, n = 4
—.------L>_ .
---- ----- _~ _ —
----.-_\... .
-------- — _?0 I -----------~ —I I I I I I I I I I I I I I I I I
---- --0 4 8 12 16 20 24 28 32 36 40
Numberof Laboratories
Figure B.2 — The amount by whichs~ can be expected to differ
from the true value within a
level of 95 %probability
16
-
IS 15393 (Par-t l) :20031S0 5725-1 :1994
[1]
[2]
[3]
Annex C(informative)
Bibliography
1.S0 3!534-2: 1993, Statistics — Vocabulary and [4]symbols —
Part 2: Statistical quality .contro/.
ISO 3534-3:1985, Statistics — Vocabulary andsyrnbo/s — Part 3:
Design of experiments. [5]
ISO 5725-5:—11, Accuracy (trueness and pre-cision) of
measurement methods and results — [6]Part 5: Alternative methods
for the determi-nation of the precision of a standard measure-
ment method.
ISO 5725-6:1994, Accuracy (trueness and pre-cision) of
measurement methods and results —Part 6: Use in practice of
accuracy values.
ISO Guide 33:1989, Use of certified referencematerials.
ISO Guide 35:1989, Certification of referencemateria/s — General
and statistical principles.
1) To be published.
17
-
( Contirwecffrorn second cover)
This standard ( Part 1 ) covers the general principles and
definitions of accuracy ( trueness andprecision ) of measurement
methods and results. The other parts of this standard are:
IS No.
IS 15393 ( Part 2 )ISO 5725-2:1994
IS 15393( Part 3 )ISO 5725-3:994
IS 15393( Part 4 )ISO 5725-4:1994
IS 15393 ( Part 5 )ISO 5725-5:1994
IS 15393( Part 6 )ISO 5725-6:1994
: 2003/
: 2003/
: 2003/
: 2003/
: 2003/
Title
Accuracy ( trueness and precision ) of measurement methods
andresults : Part 2 Basic method for the determination of
repeatability andreproducibility of a standard measurement
method
Accuracy ( trueness and precision ) of measurement methods
andresults : Part 3 Intermediate measures of the precision of a
standardmeasurement method
Accuracy ( trueness and precision ) of measurement methods
andresults : Part 4 Basic methods for the determination of the
trueness ofa standard measurement method
Accuracy ( trueness and precision ) of measurement methods
andresults: Part 5 Alternative methods for the determination of the
precisionof a standard measurement method
Accuracy ( trueness and precision ) of measurement methods
andresults :-Part 6 Use in practice of accuracy values
The concerned Technical Committee has reviewed the provisions of
ISO 3534-1 :1993 ‘Statistics —Vocabulary and symbols : Part 1
Probability and general statistical terms’ referred in this
adoptedstandard and decided that it is acceptable for use with this
standard.
This standard also gives Bibliography in Annex C, which is
informative.
-
Bureau of Indian Standards
BIS is a statutory institution established under the Bureau
o~lndian Standards Act, 1986 to promoteharmonious development of
the activities of standardization, marking and quality
certification of goods andattending to connected matters in the
country.
Copyright
B IS has the copyright of all its publications. No part of these
publications may be reproduced in any form withoutthe prior
permission in writing of BIS. This does not preclude the free use,
in the course of implementing thestandard, of necessary details,
such as symbols and sizes, type or grade designations. Enquiries
relating tocopyright be addressed to the Director (Publications),
BIS.
Review of Indian Standards
Amendments are issued to standards as the need arises on the
basis of comments. Standards are also reviewedperiodical ly; a
standard along with amendments is reaffirmed when such review
indicates that no changes areneeded; if the review indicates that
changes are needed, it is taken up for revision. Users of Indian
Standardsshou Id ascertain that they are in possession of the
latest amendments or edition by referring to the latest issueof
‘B1S Catalogue’ and ‘Standards : Monthly Additions’.
This Indian Standard has been developed from Doc : No. BP 25 (
0188 ).
Amendments Issued Since Publication
Amend No. Date of Issue Text Affected
BUREAU OF INDIAN STANDARDS
Headquarters:
Manak Bhavan, 9 Bahadur Shah Zafar Marg, New Delhi 110002
Telegrams: ManaksansthaTelephones: 23230131,2323.3375,2323 9402 (
Common to all offices)
Regional Offices: Telephone
Central : Manak Bhawm, 9 Bahadur Shah Zafar Marg{
23237617NEW DELHI 110002 23233841
Eastern : 1/14 C. 1.T. Scheme VII M, V. I. P. Road,
Kankurgachi{
23378499,23378561KOLKATA700 054 23378626,23379120
Northern: SCO 335-336, Sector 34-A, CHANDIGARH 160022
{
603843609285
Southern :C. I. T. Campus, IV Cross Road, CHENNAI 600113
{22541216,2254144222542519,22542315
Western : Manakalaya, E9 MlDC, Marol, Andheri (East)
{28329295,28327858
MUMBA1400093 28327391,28327892
Branches : AHMEDABAD. BANGALORE. BHOPAL. BHUBANESHWAR.
COIMBATORE.FARIDABAD. GHAZIABAD. GUWAHATI. HYDERABAD. JAIPUR.
KANPUR.LUCKNOW. ‘NAGPUR.NALAGARH.PATNA. PUNE. RAJKOT.
THIRUVANANTHAPURAM.VISA’KHAPATNAM.
Printed at New India Printing Press, Khurja, India