1、Manual of Petroleum Measurement Standards Chapter 13.3 Measurement Uncertainty FIRST EDITION, MAY 2016Special Notes API publications necessarily address problems of a general nature. With respect to particular circumstances, local, state, and federal laws and regulations should be reviewed. Neither
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9、system, or transmitted by any means, electronic, mechanical, photocopying, recording, or otherwise, without prior written permission from the publisher. Contact the Publisher, API Publishing Services, 1220 L Street, NW, Washington, DC 20005. Copyright 2016 American Petroleum InstituteForeword This s
10、tandard is in response to the call by industry and regulators for a standardized method to determine the uncertainty associated with various aspects of petroleum measurement. This method is based on the 2008 edition of the International Organization of Standards (ISO) Guide to the Expression of Unce
11、rtainty in Measurement (GUM)- JCGM 100:2008-which was developed to be a guide for the writers of technical standards. Although this document could be used for analysis of an entire system or facility, that use is outside the scope of the document. The uncertainty estimate is only as good as the unde
12、rlying data and engineering judgment. All of the numerical values used and assumptions made must be documented. The statement in Section 3.4 of the ISO GUM reproduced below applies to this standard: “Although this Guide provides a framework for assessing uncertainty, it cannot substitute for critica
13、l thinking, intellectual honesty and professional skill. The evaluation of uncertainty is neither a routine task nor a purely mathematical one; it depends on detailed knowledge of the nature of the measurand and of the measurement. The quality and utility of the uncertainty quoted for the result of
14、a measurement therefore ultimately depend on the understanding, critical analysis and integrity of those who contribute to the assignment of its value.” Nothing contained in any API publication is to be construed as granting any right, by implication or otherwise, for the manufacture, sale, or use o
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20、visions are invited and should be submitted to the Standards Department, API, 1220 L Street, NW, Washington, DC 20005, standardsapi.org. iiiContents Page 1 Scope . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
21、. . . . . . . . . . . . . 1 2 Normative References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 3 Terms, Definitions, Acronyms, Abbreviations, and Symbols. . . . . . . . . . . . . . . . . . . . . . . . . . .
22、 . . . . . . . . . . 2 3.1 Terms and Definitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 3.2 Acronyms, Abbreviations, and Symbols . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
23、. . . . . . . . . . . . . . . . . . 6 4 Basic Concepts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 4.1 General . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
24、 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 4.2 Measurement Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 4.3 True Quantity Value. . . . . . . . . . . . . . . . .
25、 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 4.4 Error . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 4.5 Statist
26、ical Basis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 4.6 Uncertainty . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
27、 . . . . . . . . . . . . . . . . 8 4.7 Confidence Level (Confidence Interval) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 4.8 Type A vs Type B Uncertainties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
28、 . . . . . . . . . . . . . . . . . . . . . . 9 4.9 Representative Samples. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 4.10 Mean . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
29、 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 4.11 Standard Deviation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 4.12 Standard Uncertainty . . . . . . . . . .
30、 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 4.13 Degrees of Freedom . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 4.14 Determinin
31、g Confidence Interval. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 4.15 Correlation Coefficient . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
32、 . . 13 4.16 Independent and Dependent Variables. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 4.17 Combining Uncertainties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
33、. . . . . . . . . 13 4.18 Probability Distributions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 5 Evaluating Uncertainty . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
34、 . . . . . . . . . . . . . . . . . . . . . . 17 5.1 General . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 5.2 Determine the Measurement Model . . . . . . . . . . . . . . . . . . . . .
35、 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 5.3 Record Elemental Error Sources. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 5.4 Create a Primary Uncertainty Table. . . . . . . . . . . . . . . . .
36、 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 5.5 Classify and Evaluate Uncertainty Components . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 5.6 Determine Sensitivity Coefficients . . . . . . . . . . . . . . . . .
37、 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 5.7 Determine Correlation Coefficients. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 5.8 Determine Combined Standard Uncertainty . . . . . . . . .
38、 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 5.9 Determine Expanded Uncertainty . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 5.10 Reporting Results . . . . . . . . . . . . . . . . . . . .
39、 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 Annex A (informative) Monte Carlo Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 Annex B (informative) Examples . . . . .
40、 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 Annex C (normative) Formal Proof of Equation 7(a) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48 Annex D (informative) Report
41、Significant Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50 Annex E (normative) Using a Simplified Estimate of Standard Deviation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54 Bibliography . . . . . . . . . . . . . . . .
42、 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57 vPage Figures 1 Normal Distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
43、. . . . 16 2 Triangular Distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 3 Rectangular Distribution. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
44、. . . . . . . . . . . . . . . . 17 4 Relationship between Measurement Model and Inputs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 5 Relationship between the Uncertainty of the Measurement Model and the Uncertainty of the Inputs. . 19 6 Hierarchal Relationship
45、of all Uncertainty Components of a Measurement Model. . . . . . . . . . . . . . . . . . 19 D.1 Uncertainty of the Transmitter Verification. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52 D.2 Uncertainty of the Transmitter After Adjustment. . .
46、. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52 Tables 1 t-Distribution Values . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 D.1 U 95 , Probable Error and Effective
47、 Increment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53 E.1 Range to Standard Deviation Conversion Factors, D(n). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55 E.2 Student t Factors for Individual Measurements
48、 at Various Confidence Levels. . . . . . . . . . . . . . . . . . . . . 56 Matrices 1 Universe of Components . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 2 Correlation Matrix (Informative). . . . . . . . . . . . .
49、 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 viMeasurement Uncertainty 1 Scope This standard establishes a methodology to develop uncertainty analyses for use in writing API Manual of Petroleum Measurement Standards (MPMS) documents that are consistent with the ISO GUM and NIST Technical Note 1297. 2 Normative References The following referenced documents 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 (inc
