# BS EN ISO 20988-2007 (2010)

BRITISH STANDARD BS EN ISO 209882007 Air quality Guidelines for estimating measurement uncertainty The European Standard EN ISO 209882007 has the status of a British Standard ICS 13.040.01Confirmed October 2010BS EN ISO 209882007 This British Standard was published under the authority of the Standards Policy and Strategy Committee on 31 July 2007 BSI 2007 ISBN 978 05 80 54876 5 National foreword This British Standard was published byB SI. It is the UK implementation of EN ISO 209882007 . The UK participation in its preparation was entrusted by Technical Committee EH/2, Air quality,t o Subcommittee EH/2/4, General aspects. A list of organizations represented on this committee can be obtained on request to its secretary. This publication does not purport to include all the necessary provisionso f a contract. Users are responsible for its correct application. Compliance with a British Standard cannot confer immunity from legal obligations. Amendments issued since publication Amd. No. Date CommentsEUROPEAN STANDARD NORME EUROPENNE EUROPISCHE NORM EN ISO 20988 June 2007 ICS 13.040.01 English Version Air quality Guidelines for estimating measurement uncertainty ISO 209882007 Qualit de lair Lignes directrices pour estimer lincertitude de mesure ISO 209882007 Luftbeschaffenheit Leitlinien zur Schtzung der Messunsicherheit ISO 209882007 This European Standard was approved by CEN on 9 June 2007. CEN members are bound to comply with the CEN/CENELEC Internal Regulations which stipulate the conditions for giving this European Standard the status of a national standard without any alteration. Up-to-date lists and bibliographical references concerning such national standards may be obtained on application to the CEN Management Centre or to any CEN member. This European Standard exists in three official versions English, French, German. A version in any other language made by translation under the responsibility of a CEN member into its own language and notified to the CEN Management Centre has the same status as the official versions. CEN members are the national standards bodies of Austria, Belgium, Bulgaria, Cyprus, Czech Republic, Denmark, Estonia, Finland , France, Germany, Greece, Hungary, Iceland, Ireland, Italy, Latvia, Lithuania, Luxembourg, Malta, Netherlands, Norway, Poland, Portugal, Romania, Slovakia, Slovenia, Spain, Sweden, Switzerland and United Kingdom. EUROPEAN COMMITTEE FOR STANDARDIZATION COMIT E UROP E N DE NORMALISATION EUROPI SCHES KOMITEE F R NORMUNG Management Centre rue de Stassart, 36 B-1050 Brussels 2007 CEN All rights of exploitation in any and by any means reserved worldwide for CEN national Members . Ref. No. EN ISO 209882007 EForeword This document EN ISO 209882007 has been prepared by Technical Committee ISO/TC 146 “Air quality“i n collaboration with Technical Committee CEN/TC 264 “Airq uality“, the secretariat of which ish eld by DIN . This European Standard shall be given the status of a national standard, either by publication of an identical texto r by endorsement, at the latestb yD ecember 2007, and conflicting national standards shall bew ithdrawn at the latest by December 2007. According to the CEN/CENELEC Internal R egulations, the national standards organizations o f the following countries are bound to implement this European Standard Austria, Belgium , Bulgaria, Cyprus, Czech Republic, Denmark, Estonia, Finland, France, Germany, Greece, Hungary, Iceland, Ireland, Italy, Latvia, Lithuania, Luxembourg, Malta, Netherlands, Norway, Poland, Portugal, Romania, Slovakia, Slovenia, Spain, Sweden, Switzerland and United Kingdom. Endorsement notice The text of ISO 209882007 has been approved by CEN as EN ISO 209882007 without any modifications. EN ISO 209882007Reference number ISO 209882007E INTERNATIONAL STANDARD ISO 20988 First edition 2007-06-15 Air quality Guidelines for estimating measurement uncertainty Qualit de lair Lignes directrices pour estimer lincertitude de mesure EN ISO 209882007ii iii Contents Page Foreword iv Introduction v 1S cope . 1 2N ormative references . 1 3T erms and definitions. 1 4S ymbols and abbreviated terms . 5 5B asic concepts 6 5.1 Outline 6 5.2 Measurement uncertainty. . 9 5.3 Correction for systematic effects 10 5.4P rovision of data. 11 6P roblem specification. 13 6.1O bjectives 13 6.2M easurement.1 3 6.3 Uncertainty parameters 15 6.4I nput data. 15 6.4.1G eneral. 15 6.4.2A ssessment of representativeness 16 6.5E ffects not described bys eries of observations. 17 7S tatistical analysis1 8 7.1 Objectives1 8 7.2 Indirect approach 19 7.3 Direct approach.2 1 7.4 Statistical validity 22 8E stimation of variances and covariances. . 23 8.1G eneral. 23 8.2V ariance estimates of Type A2 3 8.3 Variance estimates of Type B2 3 8.4 Estimation of covariances. 2 4 9E valuation of uncertainty parameters 25 9.1O bjective 25 9.2C ombined standard uncertainty 25 9.3 Expanded uncertainty. .2 6 9.3.1 General. 26 9.3.2E xpanded uncertainty of results exhibiting a Gaussian distribution 27 10 Reporting . 28 Annex A inative Testing a coverage probability. 30 Annex B inative TypeA uation s for experimental designs A1 to A8. 34 Annex C inative Examples 49 Bibliography. 81 EN ISO 209882007iv Foreword ISO the International Organization for Standardization is a worldwide federation of national standards bodies ISO m ember b odies. T he work o f preparing I nternational Standards is n ormally carried o ut t hrough I SO technical committees. Each member bodyi nterested in a subject for which a technical committee has been established has the right to be represented on that committee. International organizations, governmental and non-governmental, in liaison with I SO, also t ake part in the work. ISO c ollaborates c loselyw ith the International Electrotechnical Commission IEC on all matters of electrotechnical standardization. International Standards are drafted in accordance with the rules given in the ISO/IEC Directives, Part 2 . The main task of t echnical committees i s to prepare International S tandards. Draft International Standards adopted by t he technical c ommittees a re c irculated t o the member b odies f or v oting. P ublication as an International Standard requires approval by at least 75 of the member bodies casting a vote. Attention is drawn to the possibility that some of the elements of this document may be the subject of patent rights. ISO shall not be held responsible for identifying any or all such patent rights. ISO 20988 was p repared by T echnical Committee ISO/TC 146, Air quality, Subcommittee SC 4, General aspects. EN ISO 209882007v Introduction The general concept of uncertainty estimation is described in the Guide to the Expression of Uncertainty in Measurement GUM. Practical considerations o f the GUM are focussed on uation of series of unbiased observations. In air quality measurements, series of observations may rarelyb ec onsidered unbiased due to the presence of random effects not varying throughout a series of observations . This I nternational Standard supports e valuation of r andom e ffects causing variation or b ias in series o f observations f or t he purpose of u ncertaintye stimation. Appropriate d ata may be c ollected i n experimental designs p roviding comparison with reference materi al, or with reference instruments, or w ith independent measurements of the same type. In provision of experimental data for uncertaintye stimation, it is important to ensure representativeness for variations and bias occurring in intended use of the of measurement. Generic g uidance ands tatistical p rocedures presented by t hisI nternational Standard are addressedt o technical e xperts of air quality measurement, acting, e.g. in standardization, validation or documentation of s ofm easurement in ambient air, indoor air, stationary source emissions, workplace atmospheres o r meteorology. This International Standard does n ot provide comprehensive ination on p lanning and cution of experimental designs to be uated for the purpose of uncertainty estimation. Uncertainties of results of measurement caused by incomplete time-coverage of measurement data are no t considered i n this d ocument, but in I SO 11222 2 . Uncertainties o f results o f measurement induced by incomplete spatial coverage by measurement data are not considered in this document. EN ISO 209882007blank1 Air quality Guidelines for estimating measurement uncertainty 1 Scope This I nternational Standard provides c omprehensive guidance and specific statistical procedures f or uncertainty estimation in air quality measurements including measurements of a mbient air, stationary source emissions, indoor air,w orkplace atmospheres and meteorology. It applies the general recommendations o f the Guide to the Expression of Uncertainty in Measuremen t GUM to boundaryc onditions met in air quality measurement. The boundary conditions considered include measurands varying rapidly in time, as well as the presence of b ias i n a series o f observations o btained u nder c onditions o f intended use of m ethods o f air quality measurement. The s of measurement considered comprise s corrected for systematic effects by repeated observation of reference materials , s calibrated by paired measurement with a reference , s not corrected for systematic effects because theya re unbiased by design, and s not corrected for systematic effects in intended use deliberately taking into account a bias. Experimental data for uncertainty estimation can be provided either by a single experimental design in a direct approach or by a combination of different experimental designs in an indirect approach. 2 Normativer eferences The following referenced d ocuments a re i ndispensable for the application of t his d ocument. For dated references, only the edition cited applies. For undated references, the latest edition of t he referenced document including any amendments applies . ISO/IEC Guide 981995, Guide to the expression of uncertainty in measurement GUM 3 Terms and definitions 3.1 uncertainty of measurement measurement uncertainty parameter, associated with the result of a measurement, that characterizes the dispersion of the values tha t could reasonably be attributed to the measurand ISO/IEC Guide 981995, B.2.18; VIM1993, 3.9 3.2 standard uncertainty uncertainty of the result of measurement expressed as a standard deviation ISO/IEC Guide 981995, 2.3.1 EN ISO 2098820072 NOTE The standard uncertainty of a result of measurement is an estimate of the standard deviation of the population of all possible results of measurement which can be obtained by m eans of the same of measurement for the measurand exhibiting a unique value. 3.3 combined standard uncertainty standard uncertainty of the result of measurement when that result is obtained from the values of a number of other quantities, equal to the positive square root of a sum of terms, the terms being the variances or covariance of these other quantitiesw eighted according to how the measurement result variesw ith changes in these quantities ISO/IEC Guide 981995, 2.3.4 NOTE The adjective “combined” can be omitted often without loss of generality. 3.4 expanded uncertainty quantityd efining an interval y U p y ; y U p y about the result of a measurement y that may be expected to encompass a large fraction p of the distribution of values that could reasonably be attributed to the measurand NOTE 1 Adapted from ISO/IEC Guide 981995, 2.3.5. NOTE2I f the uncertainty h as b een obtained mainly b y Type A uation, t he interval y U p y ; y U p y c an b e understood as confidence interval for the true value of the measurand on a level of confidence p . NOTE3T he interval y U p y ; y U p y characterizes t he r ange o f values w ithin w hich the true value o f the measurand is confidently expected to lie see ISO/IEC Guide 981995, 2.2.4. 3.5 coverage factor numerical factor u sed as m ultiplier o f the combined s tandard uncertainty in o rder t o obtain an expanded uncertainty ISO/IEC Guide 981995, 2.3.6 3.6 coverage probability fraction of results of measurement expected to be encompassed by a specified interval 3.7 Type A uation of uncertainty of uation of uncertainty by the statistical analysis of series of observations ISO/IEC Guide 981995, 2.3.2 3.8 Type B uation of uncertainty of uation of uncertainty by means other than the statistical analysis of series of observations ISO/IEC Guide 981995, 2.3.3 3.9 standard deviation positive square root of the variance ISO/IEC Guide 981995, C.2.12 NOTE In general, the standard deviation of the population of a random variable X is estimated by the positive square root of an estimate of the variance of the population of X . EN ISO 2098820073 3.10 experimental standard deviation for a series o f N measurements of the same measurand, the quantity s x characterizing the dispersion of the results is given by the ula 2 1 1 N j xj x sx N x j being the result of the j th measurement and x being the arithmetic mean of the N results considered NOTE 1 Adapted from ISO/IEC Guide 981995, B.2.17. NOTE 2 s 2 x is an unbiased estimate o f the variance 2 X of the i nvestigated random variable X , if t he series o f observations x j with j 1 to N is unbiased. 3.11 variance the expectation of the square of the centred random variable 2 2 X X ISO/IEC Guide 981995, C.2.11 NOTE The population variance 2 X of a random variable X can be estimated by the square of the experimental standard deviation s 2 x of a simple random sample of unbiased observations x j with j 1 to N of the random variable X . Otherwise, s 2 x underestimates the population variance. 3.12 covariance mean of the product of two centred random variables in their joint probability distribution NOTE 1 Adapted from ISO 3534-1 2006, 2.43. NOTE 2 The covariance cov x , y is a sample statistic used to estimate the covariance of the populations of x and y . 3.13 expectation expected value 1 For a discrete random variable X taking the values x i with probabilities p i , the expectation, if it exists, is E X p i x i , the sum being extended over all values x iwhich may be taken by X . 2 For a continuous random variable X having the probabilityd ensity function f x , the expectation, ifi t exists , is x x f x X E d , the integral being extended over the intervals of variation of X . ISO/IEC Guide 981995, C.2.9 3.14 degrees of freedom in general, the number of terms in a summ inus the number ofc onstraints on the terms of the sum ISO/IEC Guide 981995, C.2.31 NOTE For a variance e