IEC-MISC-UNCERT-1995.pdf

I- GUIDE TO THE EXPRESSION OF UNCERTAINTY IN MEASUREMENT CORRECTED AND REPRINTED, 1995 BIPM International Bureau of Weights and Measures IEC International Eleai-otechnical Commission IFCC Intemational Federation of Clinical Chemistry IS0 International Organization for Standardization IUPAC International Union o f Pure and Applied Chemistry IUPAP International Union of Pure and OML internotionaYOrganization of Metrology Applied Ph sics BIPM IEC IFCC IS0 Bureau international des poids et mesures Pavillon de Breteuil F-92312 Sèvres Cedex France International Electrotechnical Commission 3, rue de Varembé Case ostale 131 CH-lfll Genève 20 Switzerland International Federation of Clinical Chemistry Technical Secretariat Centre du Médicament Université de Nancy 1 30, rue lionnois F-54000 Nancy France International Or anization for Standardization 1, rue de Varemte G g , . s t 56 Switzerland enève 20 IUPAC International Union of Pure and Applied Chemistry Bank Court Chambers 2-3 Pound Wav Templars Squak, Cowley Oxford OX4 3YF United Kingdom IUPAP International Union of Pure and Applied Physics Secretariat Vittens gata 11 S-421 65 V. Frölunda Sweden International Organization of legal Metrology 11, rue Turgot F-75009 Paris France OIML O ISO, 1995 This Guide establishes general rules for evaluating and expressing uncertainty in measurement that are intended to be applicable to a broad spectrum of measurements. The bash of the Guide is Recommendation 1 (CI-1981) of the Comité International des Poids et Mesures (CIPM) and Recommendation INC-l(l980) of the Working Group on the Statement of Uncertainties. The Working Group was convened by the Bureau International des Poids et Mesures (BIPM) in response to a request of the CIPM. me CIPM 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 Electrotechnicai Commission (IEC). the International Organization for Standardization (SO), 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 et Mesures IEC International Electrotechnical Commission IFCC International Federation of Clinical Chemistry IS0 International Organization for Standardization IUPAC International Union of Pure and Applied Chemistry IUPAP International Union of Fure and Applied Physics OIML International Organization 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. Guide to the Expression of Uncertainty in Measurement First edition 1995 ISBN 92-67-10188-9 O International Organization for Standardization 1995 Printed in Switzerland Expression of Uncertainty: 1993 (E) Contents Contents Page Foreword v O Introduction . vii 1 Scope 1 2 Definitions . 2 2.1 General metrological terms . . . . . . . . . 2 2.2 The term “uncertainty” . . . . . . . . . . . 2 2.3 Terms specific to this Guide . . . . . . . . 3 3 Basic concepts . 4 3.1 Measurement . . . . . . . . . . . . . . . . . 4 3.2 Errors. effects. and corrections . . . . . . 5 3.3 Uncertainty . . . . . . . . . . . . . . . . . . . 5 3.4 Practical considerations . . . . . . . . . . . 7 4 Evaluating standard uncertainty . . . . . . . . . . . 9 4.1 Modelling the measurement . . . . . . . . 9 uncertainty . . . . . . . . . . . . . . . . . . . 10 uncertainty . . . . . . . . . . . . . . . . . . . 11 standard uncertainty . . . . . . . . . . . . . 14 4.2 4.3 4.4 Graphical illustration of evaluating Type A evaluation of standard Type B evaluation of standard 5 Determining combined standard uncertainty . . . 19 5.1 Uncorrelated input quantities . . . . . . . . 19 5.2 Correlated input quantities . . . . . . . . . 20 6 Determining expanded uncertainty . . . . . . . . . 23 6.1 Introduction . . . . . . . . . . . . . . . . . . 23 6.2 Expanded uncertainty . . . . . . . . . . . . 23 6.3 Choosing a coverage factor . . . . . . . . . 24 7 Reporting uncertainty . . . . . . . . . . . . . . . . . 25 7.1 General guidance . . . . . . . . . . . . . . . 25 7.2 Specific guidance . . . . . . . . . . . . . . . 25 8 Summary of procedure for evaluating and expressing uncertainty . . . . . . . . . . . . . . . . 28 Page Annexes A Recommendations of Working Group and CIPM . . . . . . . . . . . . . . . . . . . . . . . . . . 29 A.l Recommendation INC-1 (1980) . . . . . . 29 A.2 Recommendation 1 (CI-1981) . . . . . . . 30 A.3 Recommendation 1 (CI-1986) . . . . . . . 30 B General metrological terms . . . . . . . . . . . . . 31 B.l Source of definitions . . . . . . . . . . . . . 31 B.2 Definitions . . . . . . . . . . . . . . . . . . . 31 C Basic statistical terms and concepts . . . . . . . . 35 C.l Source of definitions . . . . . . . . . . . . . 35 C.2 Definitions . . . . . . . . . . . . . . . . . . . 35 C.3 Elaboration of terms and concepts . . . . . 38 D “True” value. error. and uncertainty . . . . . . . 40 D.l Themeasurand . . . . . . . . . . . . . . . . 40 D.2 The realized quantity . . . . . . . . . . . . . 40 D.3 The “true” value and the corrected value . . . . . . . . . . . . . . . . . . . . . . 40 D.4 Error 41 D.5 Uncertainty . . . . . . . . . . . . . . . . . . . 41 D.6 Graphical representation . . . . . . . . . . . 42 E Motivation and basis for Recommendation INC-1 E.l “Safe. “random. and “systematic” . . . 45 E.2 Justification for realistic uncertainty E.3 E.4 E S (1980) . . . . . . . . . . . . . . . . . . . . . . . . . . 45 evaluations . . . . . . . . . . . . . . . . . . . 45 components identically . . . . . . . . . . . . 46 uncertainty . . . . . . . . . . . . . . . . . . . 48 Justification for treating all uncertainty Standard deviations as measures of A comparison of two views of uncertainty . . . . . . . . . . . . . . . . . . . 49 . 111 Contents Expression of Uncertainty: 1993 (E) F Practical guidance on evaluating uncertainty F . 1 Components evaluated from repeated observations: Type A evaluation of Components evaluated by other means: Type B evaluation of standard components . . . . . . . . . . . . . . . . . . . . . . . 5 1 standard uncertainty . . . . . . . . . . . . . 5 1 uncertainty . . . . . . . . . . . . . . . . . . . 5 3 F.2 G Degrees of freedom and levels of confidence . . 59 G.l Introduction . . . . . . . . . . . . . . . . . . 59 G.2 Central Limit Theorem . . . . . . . . . . . 60 G.3 The t-distribution and degrees of freedom . . . . . . . . . . . . . . . . . . . . . 60 G.4 Effective degrees of freedom . . . . . . . . 61 G.5 Other considerations . . . . . . . . . . . . . 63 6.6 Summary and conclusions . . . . . . . . . . 64 H Examples 67 H.l End-gauge calibration . . . . . . . . . . . . 67 H.2 Simultaneous resistance and reactance measurement . . . . . . . . . . . . . . . . . . 72 H.3 Calibration of a thermometer . . . . . . . . 76 H.4 Measurement of activity . . . . . . . . . . . 79 H.5 Analysis of variance . . . . . . . . . . . . . 83 H.6 Measurements on a reference scale: hardness . . . . . . . . . . . . . . . . . . . . 88 J Glossary of principal symbols . . . . . . . . . . . 91 K Bibliography . . . . . . . . . . . . . . . . . . . . . . 94 Alphabetical index . . . . . . . . . . . . . . . . . . . . 96 iv Expression of Uncertainty: 1993 (E) Foreword Foreword In 1977, recognizing the lack of international consensus on the expression of uncertainty in measurement, the world's highest authority in metrology, the Comité 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. The 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 intemational organizations). By early 1979 responses were received from 21 laboratories i .' Almost 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 meeting 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 Experimental 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 Intemational Organization for Standardization (ISO), since IS0 could better reflect the needs arising from the broad interests of industry and commerce. Responsibility wa assigned to th IS0 Technical Advisory Group on Metrology (TAG 4) because one of its tasks is to coordinate the development of guidelines on measurement topics that are of common interest to IS0 and the six organizations that participate with IS0 in the work of TAG 4: the Intemational Electrotechnical Commission (IEC), the partner of IS0 in worldwide standardization; the CIPM and the International Organization of Legal Metrology (OIML), the two 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 in 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 Statement 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 provide a basis for the international comparison of measurement results. 1) See the bibliography on page 94 et seq. V Expression of Uncertainty: 1993 (E) O Introduction O Introduction 0.1 When reporting the result of a measurement of a physical quantity, it is obligatory that some quantitative indication of the quality of the result be given SQ 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 implemented, easily understood, and generally accepted procedure for characterizing the quality of a result of a measurement, that is, for evaluating and expressing its uncertainíy. 0.2 The concept of uncertains, as a quantifiable attribute is relatively new in the history of measurement, although error 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 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 ail scientific and technological measurements, 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 uncertainty of the result of a measurement should be: The ideal method for evaluating and expressing the - universal: the method should be applicable to all kinds of measurements and to all types of input data used in measurements. The actual quantity used to express uncertainty should be: - internally consistent: it should be directly derivable from the components that contribute to it, as well as independent of how these components are grouped and of the decomposition of the components into subcomponents; - transferable: it should be possible to use directly the uncertainty evaluated for one result as a component in evaluating the uncertainty of another measurement in which the first result is used. Further, in many industrial and commercial applications, as well as in the areas of health and safety, it is often necessary to provide an interval about the measurement result that may be expected to encompass. a large fraction of the distribution of values that could reasonably be attributed to the quantity subject to measurement. Thus the ideal method for evaluating and expressing uncertainty in measurement should be capable of readily providing such an interval, in particular, one with a coverage probability or level of confidence that corresponds in a realistic way with that required. vii O Introduction Expression of Uncertainty: 1993 (E) 0.5 The approach upon which this guidance document is based is that outlined in Recommendation INC-1 (1980) 2 of the Working Group on the Statement of Uncertainties, which was convened by the BIPM in response to a request of the CIPM (see Foreword). This approach, the justification of which is discussed in annex E, meets all of the requirements outlined above. This is not the case for most other methods in current use. Recommendation INC-1 (1980) was approved and reaffirmed by the CIPM in its own Recommendations 1 (CI-1981) 3 and 1 (CI-1986) 4; the English translations of these CIPM Recommendations are reproduced in annex A (see A.2 and A.3, respectively). Because Recommendation INC- 1 (1 980) is the foundation upon which this document rests, the English translation is reproduced in 0.7 and the French text, which is authoritative, is reproduced in A. 1. 0.6 A succinct summary of the procedure specified in this guidance document for evaluating and expressing uncertainty in measurement