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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

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

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]

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

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

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

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.

,.

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

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

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

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

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