1、 g49g50g3g38g50g51g60g44g49g42g3g58g44g55g43g50g56g55g3g37g54g44g3g51g40g53g48g44g54g54g44g50g49g3g40g59g38g40g51g55g3g36g54g3g51g40g53g48g44g55g55g40g39g3g37g60g3g38g50g51g60g53g44g42g43g55g3g47g36g58measurement uncertaintyThe European Standard EN ISO 20988:2007 has the status of a British Standard
2、ICS 13.040.01Air quality Guidelines for estimating BRITISH STANDARDBS EN ISO 20988:2007BS EN ISO 20988:2007This British Standard was published under the authority of the Standards Policy and Strategy Committee on 31 July 2007 BSI 2007ISBN 978 0 580 54876 5Amendments issued since publicationAmd. No.
3、Date Commentscontract. Users are responsible for its correct application.Compliance with a British Standard cannot confer immunity from legal obligations.National forewordThis British Standard was published by BSI. It is the UK implementation of EN ISO 20988:2007.The UK participation in its preparat
4、ion was entrusted by Technical Committee EH/2, Air quality, to 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 provisions of a EUROPEAN STANDARDNORME
5、EUROPENNEEUROPISCHE 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 (I
6、SO 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 bibliograph
7、ical 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 CEN
8、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, Italy,
9、 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 Brus
10、sels 2007 CEN All rights of exploitation in any form and by any means reservedworldwide 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“ in collaboration with Technical Committee CEN/TC
11、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 December 2007, and conflicting national standards shall be withdrawn at the latest by De
12、cember 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 Republic, Denmark, Estonia, Finland, France, Germany, Greece, Hungary, Iceland, Ire
13、land, 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 20988:20
14、07Reference numberISO 20988:2007(E)INTERNATIONAL STANDARD ISO20988First edition2007-06-15Air quality Guidelines for estimating measurement uncertainty Qualit de lair Lignes directrices pour estimer lincertitude de mesureEN ISO 20988:2007ii iiiContents Page Foreword iv Introduction v 1 Scope . 1 2 No
15、rmative references . 1 3 Terms and definitions. 1 4 Symbols and abbreviated terms . 5 5 Basic concepts 6 5.1 Outline 6 5.2 Measurement uncertainty 9 5.3 Correction for systematic effects 10 5.4 Provision of input data. 11 6 Problem specification. 13 6.1 Objectives 13 6.2 Measurement. 13 6.3 Uncertai
16、nty parameters 15 6.4 Input data. 15 6.4.1 General. 15 6.4.2 Assessment of representativeness 16 6.5 Effects not described by series of observations. 17 7 Statistical analysis 18 7.1 Objectives 18 7.2 Indirect approach 19 7.3 Direct approach. 21 7.4 Statistical validity 22 8 Estimation of variances
17、and covariances 23 8.1 General. 23 8.2 Variance estimates of Type A 23 8.3 Variance estimates of Type B 23 8.4 Estimation of covariances . 24 9 Evaluation of uncertainty parameters 25 9.1 Objective 25 9.2 Combined standard uncertainty 25 9.3 Expanded uncertainty 26 9.3.1 General. 26 9.3.2 Expanded u
18、ncertainty of results exhibiting a Gaussian distribution 27 10 Reporting . 28 Annex A (informative) Testing a coverage probability . 30 Annex B (informative) Type A evaluation methods for experimental designs A1 to A8. 34 Annex C (informative) Examples 49 Bibliography . 81 EN ISO 20988:2007iv Forewo
19、rd ISO (the International Organization for Standardization) is a worldwide federation of national standards bodies (ISO member bodies). The work of preparing International Standards is normally carried out through ISO technical committees. Each member body interested in a subject for which a technic
20、al committee has been established has the right to be represented on that committee. International organizations, governmental and non-governmental, in liaison with ISO, also take part in the work. ISO collaborates closely with the International Electrotechnical Commission (IEC) on all matters of el
21、ectrotechnical standardization. International Standards are drafted in accordance with the rules given in the ISO/IEC Directives, Part 2. The main task of technical committees is to prepare International Standards. Draft International Standards adopted by the technical committees are circulated to t
22、he member bodies for voting. Publication 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 id
23、entifying any or all such patent rights. ISO 20988 was prepared by Technical Committee ISO/TC 146, Air quality, Subcommittee SC 4, General aspects. EN ISO 20988:2007vIntroduction The general concept of uncertainty estimation is described in the Guide to the Expression of Uncertainty in Measurement (
24、GUM). Practical considerations of the GUM are focussed on evaluation of series of unbiased observations. 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 Sta
25、ndard supports evaluation of random effects causing variation or bias in series of observations for 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 measur
26、ements of the same type. In provision of experimental data for uncertainty estimation, it is important 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
27、 addressed to technical experts of air quality measurement, acting, e.g. in standardization, validation 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
28、 information on planning 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 not considered in this document, but in ISO 112222. Uncertainties of results of
29、 measurement induced by incomplete spatial coverage by measurement data are not considered in this document. EN ISO 20988:2007blank1Air quality Guidelines for estimating measurement uncertainty 1 Scope This International Standard provides comprehensive guidance and specific statistical procedures fo
30、r uncertainty estimation in air quality measurements including measurements of ambient air, stationary source emissions, indoor air, workplace atmospheres and meteorology. It applies the general recommendations of the Guide to the Expression of Uncertainty in Measurement (GUM) to boundary conditions
31、 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 observations obtained under conditions of intended use of methods of air quality measurement. The methods of measurement considered comprise
32、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 they are unbiased by design, and methods not corrected for systematic effects in intended us
33、e 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 Normative references The following referenced documents
34、 are indispensable for the application of this document. For dated references, only the edition cited applies. For undated references, the latest edition of the referenced document (including any amendments) applies. ISO/IEC Guide 98:1995, Guide to the expression of uncertainty in measurement (GUM)
35、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 that could reasonably be attributed to the measurand ISO/IEC Guide 98:1995, B.2.18; VIM:1993, 3.9 3.2 standard unce
36、rtainty 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 o
37、btained by means 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
38、 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 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 unc
39、ertainty 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 distribution 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 uncert
40、ainty 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 measurand 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 me
41、asurand 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 uncertainty in order to obtain an expanded uncertainty ISO/IEC Guide 98:1995, 2.3.6 3.6 coverage probability fraction of results of measurement
42、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 t
43、han 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 a
44、n estimate of the variance of the population of X. EN ISO 20988:200733.10 experimental standard deviation for a series of N measurements of the same measurand, 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 m
45、easurement 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 estimate 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
46、 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 variable 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
47、= 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 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 us
48、ed 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 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 conti
49、nuous random variable X having the probability density function f(x), the expectation, if it exists, is = xxfxXE 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 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 numbe
