《BS-ISO-13752-1998.pdf》由会员分享，可在线阅读，更多相关《BS-ISO-13752-1998.pdf（22页珍藏版）》请在三一文库上搜索。
1、BRITISH STANDARD BS ISO 13752:1998 Air quality Assessment of uncertainty of a measurement method under field conditions using a second method as reference ICS 13.040.01 Licensed Copy: sheffieldun sheffieldun, na, Sun Nov 26 03:16:24 GMT+00:00 2006, Uncontrolled Copy, (c) BSI BS ISO 13752:1998 This B
2、ritish Standard, having been prepared under the direction of the Health and Environment Sector Board, was published under the authority of the Standards Board and comes into effect on 15 June 1998 BSI 05-1999 ISBN 0 580 29704 7 National foreword This British Standard reproduces verbatim ISO 13752:19
3、98 and implements it as the UK national standard. The UK participation in its preparation was entrusted by Technical Committee EH/2, Air quality, to Subcommittee EH/2/4, General aspects, which has the responsibility to: aid enquirers to understand the text; present to the responsible international/E
4、uropean committee any enquiries on the interpretation, or proposals for change, and keep the UK interests informed; monitor related international and European developments and promulgate them in the UK. A list of organizations represented on this subcommittee can be obtained on request to its secret
5、ary. Cross-references The British Standards which implement international or European publications referred to in this document may be found in the BSI Standards Catalogue under the section entitled “International Standards Correspondence Index”, or by using the “Find” facility of the BSI Standards
6、Electronic Catalogue. A British Standard does not purport to include all the necessary provisions of a contract. Users of British Standards are responsible for their correct application. Compliance with a British Standard does not of itself confer immunity from legal obligations. Summary of pages Th
7、is document comprises a front cover, an inside front cover, pages i and ii, the ISO title page, pages ii to iv, pages 1 to 12 and a back cover. This standard has been updated (see copyright date) and may have had amendments incorporated. This will be indicated in the amendment table on the inside fr
8、ont cover. Amendments issued since publication Amd. No.DateComments Licensed Copy: sheffieldun sheffieldun, na, Sun Nov 26 03:16:24 GMT+00:00 2006, Uncontrolled Copy, (c) BSI BS ISO 13752:1998 BSI 05-1999i Contents Page National forewordInside front cover Forewordiii Text of ISO 137521 Licensed Copy
9、: sheffieldun sheffieldun, na, Sun Nov 26 03:16:24 GMT+00:00 2006, Uncontrolled Copy, (c) BSI ii blank Licensed Copy: sheffieldun sheffieldun, na, Sun Nov 26 03:16:24 GMT+00:00 2006, Uncontrolled Copy, (c) BSI Licensed Copy: sheffieldun sheffieldun, na, Sun Nov 26 03:16:24 GMT+00:00 2006, Uncontroll
10、ed Copy, (c) BSI BS ISO 13752:1998 ii BSI 05-1999 Contents Page Forewordiii Introduction1 1Scope1 2Normative references1 3Symbols and abbreviated terms1 4Principle2 5Requirements3 6Parallel measurements4 7Graphical analysis of dispersion4 8Estimation of coefficients of regression model4 9Estimation
11、of measurement uncertainty7 Annex A (informative) Template of spreadsheet to calculate regression and variance function8 Annex B (informative) Example of spreadsheet to calculate regression and variance function10 Annex C (informative) Bibliography12 Figure 1 Flow scheme of maximum likelihood regres
12、sion3 Figure B.1 Example of window Solver Parameters10 Table A.1 Formulae of the blank spreadsheet form8 Table A.2 Text blank spreadsheet from9 Table B.1 Spreadsheet example 11 Descriptors: Air, quality, air pollution, tests, field tests, measuring techniques, estimation, measurement uncertainty, ru
13、les of calculation. Licensed Copy: sheffieldun sheffieldun, na, Sun Nov 26 03:16:24 GMT+00:00 2006, Uncontrolled Copy, (c) BSI BS ISO 13752:1998 BSI 05-1999iii Foreword ISO (the International Organization for Standardization) is a worldwide federation of national standards bodies (ISO member bodies)
14、. The work of preparing International Standards is normally carried out through ISO technical committees. Each member body interested 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
15、-governmental, in liaison with ISO, also take part in the work. ISO collaborates closely with the International Electrotechnical Commission (IEC) on all matters of electrotechnical standardization. Draft International Standards adopted by the technical committees are circulated to the member bodies
16、for voting. Publication as an International Standard requires approval by at least 75 % of the member bodies casting a vote. International Standard ISO 13752 was prepared by Technical Committee ISO/TC 146, Air quality, Subcommittee SC 4, General aspects. Annex A, Annex B and Annex C of this Internat
17、ional Standard are for information only. Licensed Copy: sheffieldun sheffieldun, na, Sun Nov 26 03:16:24 GMT+00:00 2006, Uncontrolled Copy, (c) BSI iv blank Licensed Copy: sheffieldun sheffieldun, na, Sun Nov 26 03:16:24 GMT+00:00 2006, Uncontrolled Copy, (c) BSI BS ISO 13752:1998 BSI 05-19991 Intro
18、duction Performance characteristics for air quality measuring methods are defined in ISO 6879. Corresponding test procedures are given in ISO 9169 except for accuracy, which is dealt with in this International Standard as measurement uncertainty following the concepts of the Guide to the expression
19、of uncertainty in measurement 5. The measurement uncertainty under field conditions is also covered in ISO 7935 and ISO 10849. However, the procedure given in these International Standards is limited to either the determination of a concentration-independent systematic deviation, assuming a concentr
20、ation-independent dispersion, or a concentration-proportional systematic deviation, assuming a concentration-proportional dispersion. 1 Scope This International Standard specifies a method for assessing the measurement uncertainty of a calibrated measurement method (test method) applied under field
21、conditions using a second method as a reference (reference method). The reference method may not necessarily be a legally prescribed measurement method. The measurement uncertainty is derived from measurements made in parallel on real samples by comparing the measured values of the test method with
22、those of the reference method. The result is only valid within the range of the measurements obtained. The test is designed especially for method validation. 2 Normative references The following standards contain provisions which, through reference in this text, constitute provisions of this Interna
23、tional Standard. For dated references, subsequent amendments to, or revisions of, any of these publications do not apply. However, parties to agreements based on this International Standard are encouraged to investigate the possibility of applying the most recent editions of the normative documents
24、indicated below. For undated references, the latest edition of the normative document referred to applies. Members of ISO and IEC maintain registers of currently valid International Standards. ISO 6879:1995, Air quality Performance characteristics and related concepts for air quality measuring metho
25、ds. ISO 9169:1994, Air quality Determination of performance characteristics of measurement methods. 3 Symbols and abbreviated terms For the purposes of this International Standard, the following symbols and abbreviated terms apply. a0, a1, a2coefficients of the variance function AQCAir Quality Chara
26、cteristic (usually concentration) b0, b1coefficients of the linear regression function or calibration function FF statistic kcoverage factor Llikelihood llogarithmic likelihood N, N1, N2number of pairs (xi, yi) and number of pairs of subpopulation 1 and 2 respectively P(yi)probability of yi riresidu
27、al at xi s, sistandard deviation as a function of AQC and at value xi of AQC respectively s9transformed standard deviation as a function of AQC sa0, sa1, sa2standard deviation of a0, a1 and a2 respectively sb0, sb1standard deviation of b0 and b1 respectively sx, systandard deviation of all values xi
28、 and yi respectively sycorstandard deviation of the measured y-value after correction for the systematic error (bias) s%Ystandard deviation (uncertainty) of the systematic error (bias) Uexpanded uncertainty (coverage factor k = 2) as a measure of measurement uncertainty Xvariable of x-method x, xiva
29、lue of AQC and i-th value of AQC respectively x9itransformed value xi , mean and weighted mean of all values xi and mean of all values yi respectively Yvariable of y-method yimeasured value of y-method at xi or output value of y-method at xi x, x, y Licensed Copy: sheffieldun sheffieldun, na, Sun No
30、v 26 03:16:24 GMT+00:00 2006, Uncontrolled Copy, (c) BSI BS ISO 13752:1998 2 BSI 05-1999 4 Principle A number N of pairs of measured values (x1, y2), ., (xN, xN) are obtained from parallel field measurements. The measured values from the reference method (x-method) are considered as true values. The
31、 difference between the values of a measurement pair is attributed to measurement deviation of the test method (y- method). It is assumed that there is a linear relationship between the X and Y variable estimated by: The regression coefficients b0 and b1 can be calculated arithmetically if one of th
32、e following assumptions on dispersion of the y-values holds: standard deviation of the test method is independent of x (i.e. standard deviation is constant) and estimated by: standard deviation of the test method is proportional to x (i.e. coefficient of variation is constant) and estimated by: NOTE
33、 1The first assumption can be considered as fluctuations of the background or intercept value b0 without fluctuations of the slope b1 and the second as fluctuations of the slope without fluctuations of the background or intercept value. NOTE 2The value of the coefficients of the regression function
34、(estimation of bias) is not seriously affected by deviations from the assumption on the standard deviation. However, the estimated random part of measurement uncertainty heavily depends on the assumption. The general variance function used in this International Standard accounts not only for the var
35、iability of intercept and slope but also for statistical noise, the standard deviation of which is proportional to the square root of the value itself (approximately proportional to the square root of x): NOTE 3Coefficients have been taken as squares because the coefficient rather than its square re
36、flects the physical meaning. NOTE 4The calculation procedure of the general variance function according to ISO 9169 cannot be used because repetitive measurements are not available. The coefficients of this model b0 and b1 of equation (1) and a0, a1 and a2 of equation (4) cannot be calculated arithm
37、etically. They are estimated iteratively on the criterion of maximum likelihood as an indicator of best fit (see Figure 1). After selecting a set of start values for the coefficients and using the assumption on normality, the probability, P(yi), of every data point, (xi, yi), belonging to the line c
38、an be calculated: The likelihood L is the mathematical product of the individual probabilities of y-values: The likelihood L is the indicator of fit. The coefficients are changed and the likelihood computed until a maximum value for L is obtained. The corresponding coefficients are the most likely c
39、oefficients for the regression model. For the determination by maximum likelihood a computerized optimization procedure is necessary. The uncertainty of a measured value for any AQC value is derived from the regression function and the variance function respectively. y9itransformed value yi estimate
40、d value of Y at value x of AQC estimated value of Y at value xi of AQC ycormeasured value of the y-method after correction for the systematic error (bias) %ysystematic error (bias) at value x of AQC random number from normal distribution with central value 0 and standard deviation 1 6iweighting fact
41、or at xi .(1) .(2) .(3) y yi .(4) .(5) .(6) Licensed Copy: sheffieldun sheffieldun, na, Sun Nov 26 03:16:24 GMT+00:00 2006, Uncontrolled Copy, (c) BSI BS ISO 13752:1998 BSI 05-19993 5 Requirements 5.1 General The method described in this International Standard requires that: a linear relationship ex
42、ists between the variables compared; if the relationship is different but mathematically known the procedure may be adapted. the measurement errors of the test method are normally distributed. the measurement uncertainty of the reference method is insignificant compared to that of the test method; i
43、f not, it is falsely attributed to the test method and this will result in overestimating its measurement uncertainty. the impact of differences in composition between the air sampled by the two methods is negligible compared to the expected uncertainty of the test method; if not, this error compone
44、nt is falsely attributed to the test method and will result in overestimating measurement uncertainty. The uncertainty of the coefficients calculated by this International Standard will be reduced by increasing the number of measurement pairs. Therefore, it is recommended that at least 30 measuremen
45、t pairs be obtained if the general variance model described in this International Standard is applied. Figure 1 Flow scheme of maximum likelihood regression Licensed Copy: sheffieldun sheffieldun, na, Sun Nov 26 03:16:24 GMT+00:00 2006, Uncontrolled Copy, (c) BSI BS ISO 13752:1998 4 BSI 05-1999 5.2
46、Test method (y-method) Specify all steps of the measurement method which will be subject to the assessment and execute the measurements as specified. 5.3 Reference method (x-method) In view of the provisions and environmental conditions, e.g. interfering, substances, temperature etc., to be expected
47、 at the test site, investigate whether the assumption is justified that the x-method yields insignificant uncertainty compared to the y-method. This investigation may be based on the properties of the measurement principle, literature data or results of laboratory tests or field tests. Describe the
48、x-method in detail and execute the measurements accordingly. 5.4 Test conditions Make sure that the test conditions resemble the conditions under which the test method is going to be used (test period, range of the air quality characteristic, range of physical and chemical influence variables, and o
49、perational conditions). Describe the provisions and the environmental conditions at the test site. The measurement equipment of both methods should be installed so that: the difference in composition between parallel samples is insignificant and, the equipment for one method does not influence that for the other. 5.5 Data processing In the case of the general variance model, data processing requires computer facilities for finding the maximum fit (likelihood) by adjusting the values of a0, a1, a2, b0 and b1. 6 Parallel measuremen