1、BRITISH STANDARD Assessment of uncertainty in calibration and use of flow measurement devices Part 1. Linear calibration relationships ICs 17.120.01 BS IS0 TR 7066-1 : 1997 STD-BSI BS IS0 TR 70bb-1-ENGL 1997 = lb29bb7 ObZbl32 15b BS IS0 TR 7066-1 : 1997 This British Standard, having been prepared un
2、der the direction of the Sector Board for Materials and Chemicals, was published under the authority of the Standards Board and comes into effect on 15 July 1997 National foreword This British standard reproduces verbatim ISO/TR 7066-1 : 1997 and implements it as the UK national standard It supersed
3、es BS 7118 : Part 1 : 1990 which is withdrawn. The UK participation in its preparation was entrusted by Technical Committee CPY30, Measurement of fluid flow in closed conduits, to Subcommittee CPIBOB, General topics, which has the responsibility to: - aid enquirers to understand the text; - present
4、to the responsible internationailEuropean committee any enquiries on the interpretation, or proposals for change, and keep the UK inkrests - monitor reiated international and European developments and promulgate them in the UK. informed, A list of organizations represented on this subcommittee can b
5、e obtained on request to its secretary. 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 entied International Standards Correspondence Index, or using the Find faci
6、lity of the BSI Standards Electronic Catalogue. Compliance with a British Standard does not of itself confer immunity from legal obligations. Summary of pages This document comprises a front cover, an inside front cover, the ISOITR title page, pages ii to v, a blank page, pages 1 to 28, an inside ba
7、ck cover and a back cover. Amendments issued since publication AmdNo. (Date I Text affected O BSI 1997 I I ISBN O 680 27684 X BS IS0 JX 7066-1 : 1997 TECHNICAL REPORT ISO/TR 7066-1 First edition 1997-02-01 Assessment of uncertainty in calibration and use of flow measurement devices - Part I: Linear
8、calibration relationships Evaluation de lincertitude dans ltalonnage et lutilisation des appareils de mesure du dbit - Partie 7 : Relations dtalonnage linaires Reference number ISO/TR 7066-1 :1997(E) STD*BSI BS IS0 TR 7bb-1-ENGL 1797 LbZYbb7 ObZb13Y T27 W BS IS0 IR 7066-1 : 1997 Contents Page 6 7 8
9、9 10 11 Scope . Normative references Definitions and symbols Genera I Random uncertainties and systematic error limits in individual measurements Linearity of calibration graph Linearization of data . Fitting the best straight line . Fitting the best weighted straight line . Procedure when y is inde
10、pendent of x Calculation of uncertainty 5 6 8 8 11 11 12 12 Systematic error limits and reporting procedure . 12 13 Extrapolated values . 13 14 Uncertainty in the use of the calibration graph for a single flowrate measurement 13 Annexes A Calculation of the variance of a general function . 16 B Exam
11、ple of an open channel calibration 17 C Example of determination of uncertainty in calibration of a closed conduit . 22 Descriptors: fluid flow. liquid flow. flow measurement. measuring instruments. calibration. error analysis. rules of calculation . * cn * - STD*BSI BS IS0 TR 70bb-L-ENGL 1777 M Lb2
12、Libb7 ObZb135 7b5 M BS IS0 TR 7066-1 : 1997 Foreword IS0 (the International Organization for Standardization) is a worldwide federation of national standards bodies (IS0 member bodies). The work of preparing International Standards is normally carried out through IS0 technical committees. Each membe
13、r 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-governmental, in liaison with ISO, also take part in the work. IS0 collaborates closely with the International Elec
14、trotechnical Commission (IEC) on all matters of electrotechnical standardization. The main task of technical committees is to prepare International Standards. In exceptional circumstances a technical committee may propose the publication of a Technical Report of one of the following types: - type 1,
15、 when the required support cannot be obtained for the publi- cation of an International Standard, despite repeated efforts; type 2, when the subject is still under technical development or where for any other reason there is the future but not immediate possibility of an agreement on an Internationa
16、l Standard; type 3, when a technical committee has collected data of a different kind from that which is normally published as an International Standard (“state of the art”, for example). - - Technical Reports of types 1 and 2 are subject to review within three years of publication, to decide whethe
17、r they can be transformed into International Standards. Technical Reports of type 3 do not necessarily have to be reviewed until the data they provide are considered to be no longer valid or useful. ISO/TR 7066-1, which is a Technical Report of type 1, was prepared by Technical Committee ISO/TC 30,
18、Measurement of fluid flow in closed conduits, Subcommittee SC 9, Uncertainties in flow measurement. This document is being issued as a type 1 Technical Report because no consensus could be reached between IS0 TC 30/SC 9 and IS0 TAG 4, Metrology, concerning the harmonization of this document with the
19、 Guide to the expression of uncertainty in measurement, which is a basic docu- ment in the ISO/IEC Directives. A future revision of this Technical Report will align it with the Guide. This first edition as a Technical Report cancels and replaces the first edition as an International Standard (IS0 70
20、66-1 :198), which has been technically revised. ISO/TR 7066 consists of the following parts, under the general title Assessment of uncertainty in calibration and use of flow measurement devices: . 111 - STD-BSI BS IS0 TR 70bb-1-ENGL 1977 = Lb2ibbS ObZbL3b AT1 W BS IS0 TR 7066-1 : 1997 - - Part 7: Li
21、near calibration relationships Part 2: Non-lnear calibration relationships Annex A forms an integral part of this part of ISO/TR 7066. Annexes B and C are for information only. iv STD-BSI BS IS0 TR 7Ubb-L-ENGL 1797 Lb2Libb7 ObZbL37 738 BS IS0 TR 7066-1 : 1997 Introduction One of the first Internatio
22、nal Standards to specifically address the subject of uncertainty in measurement was IS0 5168, Measurement of fluid flow - Estimation of uncertainty of a flow-rate measurement, published in 1978. The extensive use of IS0 5168 in practical applications identified many improvements to its methods; thes
23、e were incorporated into a draft revision of this International Standard, which in 1990 received an over- whelming vote in favour of its publication. IS0 7066-1, Assessment of uncertainty in the calibration and use of flow measurement devices - Parr 7: Linear calibration relationships, published in
24、1989, was drawn up according to the principles outlined in IS0 5168:1978. The draft revision of IS0 7066-1 is consistent with both the draft revision of IS0 5168 and with IS0 7066-2:1988. However, the draft revisions of both ISO/TR 51 68 and ISOflR 7066-1 were withheld from publication for a number
25、of years since, despite lengthy discussions, no consensus could be reached with the draft version of a document under development by a Working Group of IS0 Technical Advisory Group 4, Metrology IS0 TAG 4/WG 3). The TAG 4 document, Guide to the expression of uncertainty in measurement (GUM), was publ
26、ished in late 1993 as a basic document in the ISO/IEC Directives. At a meeting of the IS0 Technical Management Board in May 1995 it was decided to publish the revisions of IS0 5168 and IS0 7066-1 as Technical Reports. This document is published as a type 1 Technical Report instead of an Internationa
27、l Standard because it is not consistent with the GUM. A future revision of this part of ISOflR 7066 will align the two documents. V * * rn STD*BSI BS IS0 TR 70bb-L-ENGL 1997 Lb2qbbS ObZb238 b7i BS IS0 “R 7066-1 : 1997 Assessment of uncertainty in calibration and use of flow measurement devices - Par
28、t 1: Linear calibration relationships 1 Scope 1.1 This part of ISOflR 7066 describes the procedures to be used in deriving the calibration curve for any method of measuring flowrate in closed conduits or open channels, and of assessing the uncertainty associated with such calibrations. Procedures ar
29、e also given for estimation of the uncertainty arising in measurements obtained with the use of the resultant graph, and for calculation of the uncertainty in the mean of a number of measurements of the same flowrate. 1.2 Only linear relationships are considered in this part of ISO/TR 7066; the unce
30、rtainty in non-linear relationships forms the subject of iSO/TR 7066-2. This part of ISOflR 7066 is applicable, therefore, only if a) the relationship between the two variables is itself linear, or one or both variables can be transformed in such a manner as to create a linear relationship between t
31、hem, as, for instance by the use of logarithms, or the total range can be subdivided in such a way that within each subdivision the relationship between the two variables can be regarded as being linear; and if b) systematic deviations from the fitted line are negligible compared with the uncertaint
32、y associated with the individual observations forming the graph. . NOTE - Examples of the application of the principles contained in this part of ISO/TR.7066 are given in annexes B and C. 2 Normative references The following standards contain provisions which, through reference in this text, constit
33、ute provisions of this part of ISO/TR 7066. At the time of publication, the editions indicated were valid. All standards are subject to revision, and parties to agreements based on this part of ISO/TR 7066 are encouraged to investigate the possibility of applying the most recent editions of the stan
34、dards indicated below. Members of IEC and IS0 maintain registers of currently valid International Standards. 1 BS IS0 TR 7066-1 : 1997 IS0 772: 1996, Hydrometric determinations - Vocabulary and symbols. IS0 1100-2:-1), Liquid flow measurement in open channels - Part 2: Determination of the stagedisc
35、harge rela tionship. IS0 4006: 1991, Measurement of fluid flow in closed conduits - Vocabulary and symbols. ISO/TR 51 68:-2) Measurement of fluid flow - Evaluation of uncertainties. IS0 7066-2:1988, Assessment of uncertainty in the calibration and use of flow measurement devices - Part 2: Non- linea
36、r calibration relationships. 3 Definitions and symbols For the purposes of this part of ISOflR 7066, the definitions and symbols given in IS0 772 and IS0 4006 and the following definitions and symbols apply. 3.1 Definitions 3.1.1 calibration graph: Curve drawn through the points obtained by plotting
37、 some index of the response of a flow meter against some function of the flowrate. 3.1.2 confidence limh Upper and lower limits about an observed or calculated value within which the true value is expected to lie with a specified probability, assuming a negligible uncorrected systematic error. 3.1.3
38、 correlation coefficient: Indicator of the degree of relationship between two variables. NOTE - Such a relationship may be causal or may operate through the agency of a third variable, but a decision on this point cannot be made on statistical grounds alone. 3.1.4 covariance: First product moment me
39、asured about the variate means, .e. 3.1.5 error of measurement: Collective term meaning the difference between the measured value and the true value. It includes both systematic and random components. 3.1.6 error, random: That component of the error of measurement which varies unpredictably from mea
40、surement to measurement. NOTE - No correction is possible for this type of error, the cause of which may be known or unknown. 3.1.7 error, systematic: That component of the error of measurement which remains constant or varies predictably from measurement to measurement. NOTE - The cause of this typ
41、e of error may be known or unknown. 1 ) To be published. (Revision of IS0 1 1 00-2:1982) 2) To be published. 2 3.1.8 error, spurious: Error which invalidates a measurement. Such errors generally have a single cause, such as instrument malfunction or the misrecording of one or more digits of the meas
42、urement value. 3.1.9 function: Mathematical formula expressing the relationship between two or more variables. 3.1.10 line of best fd: Line drawn through a series of points in such a way as to minimize the variance of the points about the line. 3.1.11 residual: Difference between an observed value a
43、nd the corresponding value calculated from the regression equation. 3.1.12 sample experimental standard deviation: Measure of the dispersion about the mean of a series of n values of a measurand, defined by the formula: NOTE - If the n measurements are regarded as a sample of the underlying populati
44、on, then the formula below provides a sample estimate of the population standard deviation. 3.1.13 systematic error limit: That component of the total uncertainty associated with the systematic error. Its value cannot be reduced by taking many measurements. 3.1.14 uncertainty, random: Estimate chara
45、cterizing the range of values within which it is asserted with a given degree of confidence that the true value of the measurand may be expected to lie. - - - E _. - - - - - - - - * * Its magnitude in terms of mean values may be reduced by taking many measurements. 3.1.15 variance: Measure of disper
46、sion based on the mean squared deviation from the arithmetic mean, defined as cn 3.2 Symbols NOTE - Symbols used in the open channel and closed conduit examples of annexes B and C where these differ from, or are in addition to, those listed below are included at the beginning of the respective annex
47、es. a Intercept of the calibration curve on the ordinate b Gradient or slope of the calibration curve C Coefficient in a weighted least-squares equation Cov( ) Covariance of variables in brackets eR( ) Random uncertainty of variable in brackets es( ) Systematic error limits of variable in brackets I
48、n Natural logarithm n Q Flow ra te r Correlation coefficient Number of measurements used in deriving the calibration curve 3 BS IS0 TR 7066-1 : 1997 s( 1 SR t Wi X Y U UADD URSS Y A P 0 e Experimental standard deviation of variable in brackets Standard deviation (standard error) of points about best
49、-fitting straight line “Students” t (as obtained from IS0 5168 or from any set of statistical tables) ith weighting factor, in weighted leastsquares Independent variable; variable subject to the smallest error Dependent variable; variable subject to the greatest error Total or overall uncertainty Uncertainty using the additive model; provides between approximately 95 YO and 99 YO coverage UADD =es + FI Uncertainty using the root-sum-square model; provides approximately 95 % coverage URSS = (es2 + eA2lv2 Ratio of the sta
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