1、September 2007DEUTSCHE NORM English price group 24No part of this standard may be reproduced without prior permission ofDIN Deutsches Institut fr Normung e. V., Berlin. Beuth Verlag GmbH, 10772 Berlin, Germany,has the exclusive right of sale for German Standards (DIN-Normen).ICS 13.040.01!$I0l“13813
2、73www.din.deDDIN EN ISO 20988Air quality Guidelines for estimating measurement uncertainty (ISO 20988:2007)English version of DIN EN ISO 20988:2007-09Luftbeschaffenheit Leitlinien zur Schtzung der Messunsicherheit (ISO 20988:2007)Englische Fassung DIN EN ISO 20988:2007-09www.beuth.deDocument compris
3、es 87 pages11.07This standard has been included in the VDI/DIN Handbook on air quality, Volume 5.DIN EN ISO 20988:2007-09 2 National foreword This standard has been prepared by Technical Committee ISO/TC 146 “Air quality”, Subcommittee SC 4 “General aspects” in collaboration with Technical Committee
4、 CEN/TC 264 “Air quality”. The responsible German body involved in its preparation was the Kommission Reinhaltung der Luft (KRdL) im VDI und DIN (VDI/DIN Air Quality Commission), Section IV Umweltmesstechnik. The DIN Standards and other relevant documents corresponding to the International Standards
5、 and docu-ments referred to in the EN are as follows: ISO 5725-2 DIN ISO 5725-2 ISO 5725-3 DIN ISO 5725-3 ISO 5725-4 DIN ISO 5725-4 ISO 5725-5 DIN ISO 5725-5 ISO 11222 DIN ISO 11222 ISO/IEC Guide 98 DIN V ENV 13005 VIM International Vocabulary of Basic and General Terms in Metrology (VIM) National A
6、nnex NA (informative) Bibliography DIN V ENV 13005, Guide to the expression of uncertainty in measurement DIN ISO 5725-2, Accuracy (trueness and precision) of measurement methods and results Part 2: Basic method for the determination of repeatability and reproducibility of a standard measurement met
7、hod DIN ISO 5725-3, Accuracy (trueness and precision) of measurement methods and results Part 3: Inter-mediate measures of the precision of a standard measurement method DIN ISO 5725-4, Accuracy (trueness and precision) of measurement methods and results Part 4: Basic methods for the determination o
8、f the trueness of a standard measurement method DIN ISO 5725-5, Accuracy (trueness and precision) of measurement methods and results Part 5: Alterna-tive methods for the determination of the precision of a standard measurement method DIN ISO 11222, Air quality Determination of the uncertainty of the
9、 time average of air quality measurements International Vocabulary of Basic and General Terms in Metrology VIM, 2nded., 19941) _ 1) Obtainable from Beuth Verlag GmbH, 10772 Berlin (Postal address: Burggrafenstr. 6, 10787 Berlin), Tel.: +49 30 2601-0, Fax: +49 30 2601-1231. EUROPEAN STANDARDNORME EUR
10、OPENNEEUROPISCHE NORMEN ISO 20988June 2007ICS 13.040.01English VersionAir quality - Guidelines for estimating measurement uncertainty(ISO 20988:2007)Qualit de lair - Lignes directrices pour estimer lincertitudede mesure (ISO 20988:2007)Luftbeschaffenheit - Leitlinien zur Schtzung derMessunsicherheit
11、 (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 EuropeanStandard the status of a national standard without any alteration. Up-to-date lists and bibliogr
12、aphical references concerning such nationalstandards 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 translationunder the responsibility of a C
13、EN member into its own language and notified to the CEN Management Centre has the same status as theofficial versions.CEN members are the national standards bodies of Austria, Belgium, Bulgaria, Cyprus, Czech Republic, Denmark, Estonia, Finland,France, Germany, Greece, Hungary, Iceland, Ireland, Ita
14、ly, Latvia, Lithuania, Luxembourg, Malta, Netherlands, Norway, Poland, Portugal,Romania, Slovakia, Slovenia, Spain, Sweden, Switzerland and United Kingdom.EUROPEAN COMMITTEE FOR STANDARDIZATIONCOMIT EUROPEN DE NORMALISATIONEUROPISCHES KOMITEE FR NORMUNGManagement Centre: rue de Stassart, 36 B-1050 B
15、russels 2007 CEN All rights of exploitation in any form and by any means reservedworldwide for CEN national Members.Ref. No. EN ISO 20988:2007: EContents Page 1 2 3 4 5 5.1 5.2 5.3 5.4 6 6.1 6.2 6.3 6.4 6.4.1 6.4.2 6.5 7 7.1 7.2 7.3 7.4 8 8.1 8.2 8.3 8.4 9 9.1 9.2 9.3 9.3.1 9.3.2 10 EN ISO 20988:200
16、7 (E)2Correction for systematic effects 14 Provision of input data. 15 Measurement uncertainty 13 Basic concepts 10 Outline 10 Symbols and abbreviated terms . 5 Foreword 3 Introduction 4 Scope . 5 Normative references . 5 Terms and definitions. 5 Problem specification. 17 Measurement. 17 Input data.
17、 19 Objectives 17 Uncertainty parameters 19 General. 19 Effects not described by series of observations. 21 Assessment of representativeness 20 Statistical analysis 22 Indirect approach 23 Statistical validity 26 Objectives 22 Direct approach. 25 Estimation of variances and covariances 27 Variance e
18、stimates of Type A 27 Estimation of covariances . 28 General. 27 Variance estimates of Type B 27 Evaluation of uncertainty parameters 29 Combined standard uncertainty 29 Objective 29 Expanded uncertainty 30 Expanded uncertainty of results exhibiting a Gaussian distribution 31 Reporting . 32 General.
19、 30 Annex C (informative) Examples 53 Annex A (informative) Testing a coverage probability . 34 Annex B (informative) Type A evaluation methods for experimental designs A1 to A8. 38 Bibliography . 85 EN ISO 20988:2007 (E) 3 Foreword This document (EN ISO 20988:2007) has been prepared by Technical Co
20、mmittee ISO/TC 146 “Air quality” in collaboration with Technical Committee CEN/TC 264 “Air quality”, the secretariat of which is held by DIN. This European Standard shall be given the status of a national standard, either by publication of an identical text or by endorsement, at the latest by Decemb
21、er 2007, and conflicting national standards shall be withdrawn at the latest by December 2007. According to the CEN/CENELEC Internal Regulations, the national standards organizations of the following countries are bound to implement this European Standard: Austria, Belgium, Bulgaria, Cyprus, Czech R
22、epublic, 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 be
23、en approved by CEN as EN ISO 20988:2007 without any modifications. Introduction The general concept of uncertainty estimation is described in the Guide to the Expression of Uncertainty in Measurement (GUM). Practical considerations of the GUM are focussed on evaluation of series of unbiased observat
24、ions. In air quality measurements, series of observations may rarely be considered unbiased due to the presence of random effects not varying throughout a series of observations. This International Standard supports evaluation of random effects causing variation or bias in series of observations for
25、 the purpose of uncertainty estimation. Appropriate data may be collected in experimental designs providing comparison with reference material, or with reference instruments, or with independent measurements of the same type. In provision of experimental data for uncertainty estimation, it is import
26、ant to ensure representativeness for variations and bias occurring in intended use of the method of measurement. Generic guidance and statistical procedures presented by this International Standard are addressed to technical experts of air quality measurement, acting, e.g. in standardization, valida
27、tion or documentation of methods of measurement in ambient air, indoor air, stationary source emissions, workplace atmospheres or meteorology. This International Standard does not provide comprehensive information on planning and execution of experimental designs to be evaluated for the purpose of u
28、ncertainty estimation. Uncertainties of results of measurement caused by incomplete time-coverage of measurement data are not considered in this document, but in ISO 112222. Uncertainties of results of measurement induced by incomplete spatial coverage by measurement data are not considered in this
29、document. EN ISO 20988:2007 (E)41 Scope This International Standard provides comprehensive guidance and specific statistical procedures for uncertainty estimation in air quality measurements including measurements of ambient air, stationary source emissions, indoor air, workplace atmospheres and met
30、eorology. It applies the general recommendations of the Guide to the Expression of Uncertainty in Measurement (GUM) to boundary conditions met in air quality measurement. The boundary conditions considered include measurands varying rapidly in time, as well as the presence of bias in a series of obs
31、ervations obtained under conditions of intended use of methods of 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
32、 not corrected for systematic effects because they are 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 approac
33、h or by a combination of different experimental designs in an indirect approach. 2 Normative references The following referenced documents are indispensable for the application of this document. For dated references, only the edition cited applies. For undated references, the latest edition of the r
34、eferenced 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 di
35、spersion of the values that 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 20988:2007 (E)5NOTE The standard uncertaint
36、y 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 means of the same method of measurement for the measurand exhibiting a unique value. 3.3 combined standard uncertainty standard uncertainty of the r
37、esult 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 quantities weighted according to how the measurement result varies with changes in
38、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 quantity defining an interval y Up(y); y + Up(y) about the result of a measurement y that may be expected to encompass a large fraction p of the distr
39、ibution of values that could reasonably be attributed to the measurand NOTE 1 Adapted from ISO/IEC Guide 98:1995, 2.3.5. NOTE 2 If the uncertainty has been obtained mainly by Type A evaluation, the interval y Up(y); y + Up(y) can be understood as confidence interval for the true value of the measura
40、nd on a level of confidence p. NOTE 3 The interval y Up(y); y + Up(y) characterizes the range of values within which the true value of the measurand is confidently expected to lie (see ISO/IEC Guide 98:1995, 2.2.4). 3.5 coverage factor numerical factor used as multiplier of the combined standard unc
41、ertainty in order to 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 se
42、ries 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 9
43、8:1995, 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 20988:2007 (E)63.10 experimental standard deviation for a series of N measurements of the same measur
44、and, the quantity s(x) characterizing the dispersion of the results is given by the formula ()()()211Njxj xsxN=x(j) being the result of the jth 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 s2(x) is an unbiased estim
45、ate of the variance 2(X) of the investigated random variable X, if the series of observations x(j) with j = 1 to N is unbiased. 3.11 variance the expectation of the square of the centred random variable: () () 22XEXEX= ISO/IEC Guide 98:1995, C.2.11 NOTE The population variance 2(X) of a random varia
46、ble X can be estimated by the square of the experimental standard deviation s2(x) of a simple random sample of unbiased observations x(j) with j = 1 to N of the random variable X. Otherwise, s2(x) underestimates the population variance. 3.12 covariance mean of the product of two centred random varia
47、bles 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 xi with
48、probabilities pi, the expectation, if it exists, is E(X) = pixi, the sum being extended over all values xiwhich may be taken by X. 2) For a continuous random variable X having the probability density function f(x), the expectation, if it exists, is = xxfxXE d)()( , the integral being extended over t
49、he 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 sum minus the number of constraints on the terms of the sum ISO/IEC Guide 98:1995, C.2.31 NOTE For a variance estimate, the (effective) number of degrees of freedom can be understood as the number of independent pieces of information used to obtain that variance estimate. 3.15 measurement set of operations having the object of determining the value of a
