SANS 100098-3-2009 Uncertainty of measurement Part 3 Guide to the expression of uncertainty in measurement (GUM 1995)《不确定性测量 第3部分 测量中的不确定性表述法指南(GUM 1995)》.pdf

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3、damage whatsoever than may result from the use of this material or the information contain therein, irrespective of the cause and quantum thereof. ISBN 978-0-626-21955-0 SANS 100098-3:2009Edition 1 ISO/IEC Guide 98-3:2008Edition 1SOUTH AFRICAN NATIONAL STANDARD Uncertainty of measurement Part 3: Gui

4、de to the expression of uncertainty in measurement (GUM:1995) This national standard is the identical implementation of ISO/IEC Guide 98-3:2008 and is adopted with the permission of the International Organization for Standardization. Published by SABS Standards Division 1 Dr Lategan Road Groenkloof

5、Private Bag X191 Pretoria 0001Tel: +27 12 428 7911 Fax: +27 12 344 1568 www.sabs.co.za SABS SANS 100098-3:2009 Edition 1 ISO/IEC Guide 98-3:2008 Edition 1 Table of changes Change No. Date Scope National foreword This South African standard was approved by National Committee SABS TC 1046, SA REMCO in

6、 accordance with procedures of the SABS Standards Division, in compliance with annex 3 of the WTO/TBT agreement. This SANS document was published in May 2009. First edition 2008 ISO/IEC 2008 GUIDE 98-3 Uncertainty of measurement Part 3: Guide to the expression of uncertainty in measurement (GUM:1995

7、) Incertitude de mesure Partie 3: Guide pour lexpression de lincertitude de mesure (GUM:1995) SANS 100098-3:2009This s tandard may only be used and printed by approved subscription and freemailing clients of the SABS .ISO/IEC GUIDE 98-3:2008(E) PDF disclaimer This PDF file may contain embedded typef

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12、 ISO copyright office Case postale 56 CH-1211 Geneva 20 Tel. + 41 22 749 01 11 Fax + 41 22 749 09 47 E-mail copyrightiso.org Web www.iso.org Published in Switzerland ii ISO/IEC 2008 All rights reservedSANS 100098-3:2009This s tandard may only be used and printed by approved subscription and freemail

13、ing clients of the SABS .ISO/IEC GUIDE 98-3:2008(E) ISO/IEC 2008 All rights reserved iiiContents Page Preliminary v Foreword vi 0 Introductionvii 1 Scope1 2 Definitions 2 2.1 General metrological terms2 2.2 The term “uncertainty” .2 2.3 Terms specific to this Guide 3 3 Basic concepts 4 3.1 Measureme

14、nt .4 3.2 Errors, effects, and corrections .5 3.3 Uncertainty.5 3.4 Practical considerations.7 4 Evaluating standard uncertainty8 4.1 Modelling the measurement.8 4.2 Type A evaluation of standard uncertainty.10 4.3 Type B evaluation of standard uncertainty.11 4.4 Graphical illustration of evaluating

15、 standard uncertainty 15 5 Determining combined standard uncertainty.18 5.1 Uncorrelated input quantities 18 5.2 Correlated input quantities.21 6 Determining expanded uncertainty .23 6.1 Introduction23 6.2 Expanded uncertainty.23 6.3 Choosing a coverage factor .24 7 Reporting uncertainty .24 7.1 Gen

16、eral guidance 24 7.2 Specific guidance 25 8 Summary of procedure for evaluating and expressing uncertainty 27 Annex A Recommendations of Working Group and CIPM 28 A.1 Recommendation INC-1 (1980) 28 A.2 Recommendation 1 (CI-1981) .29 A.3 Recommendation 1 (CI-1986) .29 Annex B General metrological ter

17、ms .31 B.1 Source of definitions.31 B.2 Definitions 31 Annex C Basic statistical terms and concepts39 C.1 Source of definitions.39 C.2 Definitions 39 C.3 Elaboration of terms and concepts .45 Annex D “True” value, error, and uncertainty.49 D.1 The measurand 49 D.2 The realized quantity.49 D.3 The “t

18、rue” value and the corrected value.49 D.4 Error50 SANS 100098-3:2009This s tandard may only be used and printed by approved subscription and freemailing clients of the SABS .ISO/IEC GUIDE 98-3:2008(E) iv ISO/IEC 2008 All rights reservedD.5 Uncertainty .51 D.6 Graphical representation 51 Annex E Moti

19、vation and basis for Recommendation INC-1 (1980)54 E.1 “Safe”, “random”, and “systematic” .54 E.2 Justification for realistic uncertainty evaluations54 E.3 Justification for treating all uncertainty components identically.55 E.4 Standard deviations as measures of uncertainty.58 E.5 A comparison of t

20、wo views of uncertainty .59 Annex F Practical guidance on evaluating uncertainty components .61 F.1 Components evaluated from repeated observations: Type A evaluation of standard uncertainty61 F.2 Components evaluated by other means: Type B evaluation of standard uncertainty.64 Annex G Degrees of fr

21、eedom and levels of confidence .70 G.1 Introduction70 G.2 Central Limit Theorem.71 G.3 The t-distribution and degrees of freedom .72 G.4 Effective degrees of freedom .73 G.5 Other considerations.75 G.6 Summary and conclusions .76 Annex H Examples79 H.1 End-gauge calibration .79 H.2 Simultaneous resi

22、stance and reactance measurement.85 H.3 Calibration of a thermometer89 H.4 Measurement of activity93 H.5 Analysis of variance 98 H.6 Measurements on a reference scale: hardness104 Annex J Glossary of principal symbols.109 Bibliography 114 Alphabetical index 116 SANS 100098-3:2009This s tandard may o

23、nly be used and printed by approved subscription and freemailing clients of the SABS .ISO/IEC GUIDE 98-3:2008(E) ISO/IEC 2008 All rights reserved vThis Guide establishes general rules for evaluating and expressing uncertainty in measurement that are intended to be applicable to a broad spectrum of m

24、easurements. The basis of the Guide is Recommendation 1 (CI-1981) of the Comit International des Poids et Mesures (CIPM) and Recommendation INC-1 (1980) of the Working Group on the Statement of Uncertainties. The Working Group was convened by the Bureau International des Poids et Mesures (BIPM) in r

25、esponse to a request of the CIPM. The ClPM Recommendation is the only recommendation concerning the expression of uncertainty in measurement adopted by an intergovernmental organization. This Guide was prepared by a joint working group consisting of experts nominated by the BIPM, the International E

26、lectrotechnical Commission (IEC), the International Organization for Standardization (ISO), and the International Organization of Legal Metrology (OIML). The following seven organizations* supported the development of this Guide, which is published in their name: BIPM: Bureau International des Poids

27、 et Mesures IEC: International Electrotechnical Commission IFCC: International Federation of Clinical Chemistry* ISO: International Organization for Standardization IUPAC: International Union of Pure and Applied Chemistry* IUPAP: International Union of Pure and Applied Physics* OlML: International O

28、rganization of Legal Metrology Users of this Guide are invited to send their comments and requests for clarification to any of the seven supporting organizations, the mailing addresses of which are given on the inside front cover*. _ * Footnote to the 2008 version: In 2005, the International Laborat

29、ory Accreditation Cooperation (ILAC) officially joined the seven founding international organizations. * Footnote to the 2008 version: The names of these three organizations have changed since 1995. They are now: IFCC: International Federation for Clinical Chemistry and Laboratory Medicine IUPAC: In

30、ternational Organization for Pure and Applied Chemistry IUPAP: International Organization for Pure and Applied Physics. * Footnote to the 2008 version: Links to the addresses of the eight organizations presently involved in the JCGM (Joint Committee for Guides in Metrology) are given on http:/www.bi

31、pm.org/en/committees/jc/jcgm. SANS 100098-3:2009This s tandard may only be used and printed by approved subscription and freemailing clients of the SABS .ISO/IEC GUIDE 98-3:2008(E) vi ISO/IEC 2008 All rights reservedForeword In 1977, recognizing the lack of international consensus on the expression

32、of uncertainty in measurement, the worlds highest authority in metrology, the Comit International des Poids et Mesures (CIPM), requested the Bureau International des Poids et Mesures (BIPM) to address the problem in conjunction with the national standards laboratories and to make a recommendation. T

33、he BIPM prepared a detailed questionnaire covering the issues involved and distributed it to 32 national metrology laboratories known to have an interest in the subject (and, for information, to five international organizations). By early 1979 responses were received from 21 laboratories 1.1)Almost

34、all believed that it was important to arrive at an internationally accepted procedure for expressing measurement uncertainty and for combining individual uncertainty components into a single total uncertainty. However, a consensus was not apparent on the method to be used. The BIPM then convened a m

35、eeting for the purpose of arriving at a uniform and generally acceptable procedure for the specification of uncertainty; it was attended by experts from 11 national standards laboratories. This Working Group on the Statement of Uncertainties developed Recommendation INC-1 (1980), Expression of Exper

36、imental Uncertainties 2. The CIPM approved the Recommendation in 1981 3 and reaffirmed it in 1986 4. The task of developing a detailed guide based on the Working Group Recommendation (which is a brief outline rather than a detailed prescription) was referred by the CIPM to the International Organiza

37、tion for Standardization (ISO), since ISO could better reflect the needs arising from the broad interests of industry and commerce. Responsibility was assigned to the ISO Technical Advisory Group on Metrology (TAG 4) because one of its tasks is to coordinate the development of guidelines on measurem

38、ent topics that are of common interest to ISO and the six organizations that participate with ISO in the work of TAG 4: the International Electrotechnical Commission (IEC), the partner of ISO in worldwide standardization; the CIPM and the International Organization of Legal Metrology (OIML), the two

39、 worldwide metrology organizations; the International Union of Pure and Applied Chemistry (IUPAC) and the International Union of Pure and Applied Physics (IUPAP), the two international unions that represent chemistry and physics; and the International Federation of Clinical Chemistry (IFCC). TAG 4 i

40、n turn established Working Group 3 (ISO/TAG 4/WG 3) composed of experts nominated by the BIPM, IEC, ISO, and OIML and appointed by the Chairman of TAG 4. It was assigned the following terms of reference: To develop a guidance document based upon the recommendation of the BIPM Working Group on the St

41、atement of Uncertainties which provides rules on the expression of measurement uncertainty for use within standardization, calibration, laboratory accreditation, and metrology services; The purpose of such guidance is to promote full information on how uncertainty statements are arrived at; to provi

42、de a basis for the international comparison of measurement results. This first edition of ISO/IEC Guide 98-3 cancels and replaces the Guide to the Expression of Uncertainty in Measurement (GUM), BIPM, IEC, IFCC, ISO, IUPAC, IUPAP, OIML, 1993, corrected and reprinted in 1995. 1) See the Bibliography.

43、 * Footnote to the 2008 version: In producing this 2008 version of the GUM, necessary corrections only to the printed 1995 version have been introduced by JCGM/WG 1. These corrections occur in Subclauses 4.2.2, 4.2.4, 5.1.2, B.2.17, C.3.2, C.3.4, E.4.3, H.4.3, H.5.2.5 and H.6.2. SANS 100098-3:2009Th

44、is s tandard may only be used and printed by approved subscription and freemailing clients of the SABS .ISO/IEC GUIDE 98-3:2008(E) ISO/IEC 2008 All rights reserved vii0 Introduction 0.1 When reporting the result of a measurement of a physical quantity, it is obligatory that some quantitative indicat

45、ion of the quality of the result be given so that those who use it can assess its reliability. Without such an indication, measurement results cannot be compared, either among themselves or with reference values given in a specification or standard. It is therefore necessary that there be a readily

46、implemented, easily understood, and generally accepted procedure for characterizing the quality of a result of a measurement, that is, for evaluating and expressing its uncertainty. 0.2 The concept of uncertainty as a quantifiable attribute is relatively new in the history of measurement, although e

47、rror and error analysis have long been a part of the practice of measurement science or metrology. It is now widely recognized that, when all of the known or suspected components of error have been evaluated and the appropriate corrections have been applied, there still remains an uncertainty about

48、the correctness of the stated result, that is, a doubt about how well the result of the measurement represents the value of the quantity being measured. 0.3 Just as the nearly universal use of the International System of Units (SI) has brought coherence to all scientific and technological measuremen

49、ts, a worldwide consensus on the evaluation and expression of uncertainty in measurement would permit the significance of a vast spectrum of measurement results in science, engineering, commerce, industry, and regulation to be readily understood and properly interpreted. In this era of the global marketplace, it is imperative that the method for evaluating and expressing uncertainty be uniform throughout the world so that measurements performed in different countries can be easily compared. 0.4 The id