# BS EN ISO 20988-2007 (2010)

BRITISH STANDARD BS EN ISO 20988:2007 Air quality — Guidelines for estimating measurement uncertainty The European Standard EN ISO 20988:2007 has the status of a British Standard ICS 13.040.01Confirmed October 2010BS EN ISO 20988:2007 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 20988:2007 . 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 EUROPÉENNE EUROPÄISCHE NORM EN ISO 20988 June 2007 ICS 13.040.01 English Version Air quality Guidelines for estimating measurement uncertainty (ISO 20988:2007) Qualité de l air Lignes directrices pour estimer l incertitude de mesure (ISO 20988:2007) Luftbeschaffenheit Leitlinien zur Schätzung der Messunsicherheit (ISO 20988:2007) 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 EUROPƒI SCHES KOMITEE F‹ R NORMUNG Management Centre: rue de Stassart, 36 B-1050 Brussels © 2007 CEN All rights of exploitation in any form and by any means reserved worldwide for CEN national Members . Ref. No. EN ISO 20988:2007: EForeword This document (EN ISO 20988:2007) 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 20988:2007 has been approved by CEN as EN ISO 20988:2007 without any modifications. EN ISO 20988:2007Reference number ISO 20988:2007(E) INTERNATIONAL STANDARD ISO 20988 First edition 2007-06-15 Air quality — Guidelines for estimating measurement uncertainty Qualité de l air — Lignes directrices pour estimer l incertitude de mesure EN ISO 20988:2007ii 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 input 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 (informative) Testing a coverage probability. 30 Annex B (informative) TypeA evaluation methods for experimental designs A1 to A8. 34 Annex C (informative) Examples 49 Bibliography. 81 EN ISO 20988:2007iv 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 20988:2007v 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 evaluation 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 method 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 methods ofm easurement in ambient air, indoor air, stationary source emissions, workplace atmospheres o r meteorology. This International Standard does n ot provide comprehensive information on p lanning and execution of experimental designs to be evaluated 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 20988:2007blank1 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 methods of measurement considered comprise ⎯ methods corrected for systematic effects by repeated observation of reference materials , ⎯ methods calibrated by paired measurement with a reference method, ⎯ methods not corrected for systematic effects because theya re unbiased by design, and ⎯ methods 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 98:1995, 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 98:1995, B.2.18; VIM:1993, 3.9] 3.2 standard uncertainty uncertainty of the result of measurement expressed as a standard deviation [ISO/IEC Guide 98:1995, 2.3.1] EN ISO 20988:20072 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 method 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 input 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 98:1995, 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 98:1995, 2.3.5. NOTE2I f the uncertainty h as b een obtained mainly b y Type A evaluation, 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 98:1995, 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 98:1995, 2.3.6] 3.6 coverage probability fraction of results of measurement expected to be encompassed by a specified interval 3.7 Type A evaluation (of uncertainty) method of evaluation of uncertainty by the statistical analysis of series of observations [ISO/IEC Guide 98:1995, 2.3.2] 3.8 Type B evaluation (of uncertainty) method of evaluation of uncertainty by means other than the statistical analysis of series of observations [ISO/IEC Guide 98:1995, 2.3.3] 3.9 standard deviation positive square root of the variance [ISO/IEC Guide 98:1995, 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 20988:20073 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 formula () () () 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 98:1995, B.2.17. NOTE 2 s 2 ( x ) is an unbiased estimate o f the variance σ 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 XEXE X ⎡⎤ =− ⎢⎥ ⎣⎦ σ [ISO/IEC Guide 98:1995, C.2.11] NOTE The population variance σ 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 ) = Σ 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 interval(s) of variation of X . [ISO/IEC Guide 98:1995, 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 98:1995, C.2.31] NOTE For a variance e