API MPMS 13.3-2017 Manual of Petroleum Measurement Standards Chapter 13.3 Measurement Uncertainty (SECOND EDITION) .pdf

1、Manual of Petroleum Measurement Standards Chapter 13.3 Measurement Uncertainty SECOND EDITION, DECEMBER 2017Special Notes API publications necessarily address pr oblems of a general nature. With respect to particular circumstances, local, state, and federal laws and regulations should be reviewed. N

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16、 Washington, DC 20005, standardsapi.org. iiiContents Page 1 Scope . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 2 Normative References . . . . . . . . . . . . . . . . . . . . . . . . .

17、 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 3 Terms, Definitions, Acronyms, Abbreviations, and Symbols . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 3.1 Terms and Definitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

18、. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 3.2 Acronyms, Abbreviations, and Symbols . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 4 Basic Concepts. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

19、 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 4.1 General. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 4.2 Measurement Method. . . . . . . . . . . . .

20、. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 4.3 True Quantity Value . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 4.4 Error . . . . . . . . .

21、. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 4.5 Statistical Basis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

22、. . . . 10 4.6 Uncertainty . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 4.7 Confidence Level . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

23、 . . . . . . . . . . . . . . . . . . 11 4.8 Type A vs Type B Uncertainties. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 4.9 Representative Samples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

24、. . . . . . . . . . . . . . . . . . . . . . . 11 4.10 Mean . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 4.11 Standard Deviation . . . . . . . . . . . . . . . . . . . . . . . . . . .

25、. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 4.12 Standard Uncertainty . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 4.13 Degrees of Freedom . . . . . . . . . . . . . . .

26、. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 4.14 Determining Confidence Interval . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 4.15 Correlation Coefficient . . . . . .

27、. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 4.16 Independent and Dependent Variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 4.17 Combining Uncertainties . .

28、. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 4.18 Probability Distributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 5 Evaluating Un

29、certainty. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 5.1 General. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

30、 . . . . 20 5.2 Determine the Measurement Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 5.3 Record Elemental Error Sources . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

31、. . . 21 5.4 Create a Primary Uncertainty Table . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 5.5 Classify and Evaluate Uncertainty Components . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 5.6

32、 Determine Sensitivity Coefficients . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 5.7 Determine Correlation Coefficients . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 5

33、.8 Determine Combined Standard Uncertainty . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 5.9 Determine Expanded Uncertainty. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 5.10 Report

34、ing Results. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 Annex A (informative) Monte Carlo Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

35、 33 Annex B (informative) Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 Annex C (normative) Formal Proof of Equation (7a) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

36、. . . . 54 Annex D (informative) Report Significant Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57 Annex E (normative) Using a Simplified Estimate of Standard Deviation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60 Annex F

37、 (informative) Dixons Q-Test for Outliers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63 Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

38、. . . . . . . . 65 vContents Page Figures 1 Accuracy/Precision Comparisons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 2 Normal Distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

39、. . . . . . . . . . . . . . . . . . . . . . 18 3 Triangular Distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 4 Rectangular Distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

40、 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 5 Relationship between Measurement Model and Inputs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 6 Relationship between the Uncertainty of the Measurement Model and the Uncertainty of the Inputs. . . . .

41、. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 7 Hierarchal Relationship of all Uncertainty Components of a Measurement Model . . . . . . . . . . . . . . . 22 B.1 Vector c, Matrix Diag(c) and Vector u using

42、 Data from Example B1 . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 B.2 Matrix R using Data from Example B1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44 B.3 Result of Multiplying Diag(c) and u from Figure B.1 Diag(c) u. . . . .

43、 . . . . . . . . . . . . . . . . . . . . . . . . . . 44 B.4 Result of Transposing Figure B.3 Diag(c) uT. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44 B.5 Result of Multiplying Figure B.4 by Matrix R Found in Figure B.1 Diag(c) uT R . . . . . . . . . . . .

44、. 44 B.6 Result of Multiplying the Matrix in Figure B.5 by the Matrix in Figure B.3 . . . . . . . . . . . . . . . . . . . . . . 44 B.7 The Matrices Associated with Diag(c) uT RT and Diag(Diag(c) uT RT) . . . . . . . . . . . . . . 45 B.8 The Relative Contribution of Each Component . . . . . . . . . .

45、 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45 D.1 Uncertainty of the Transmitter Verification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58 D.2 Uncertainty of the Transmitter after Adjustment. . . . . . . . . . . . . . .

46、. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58 Tables 1 Data with Same Mean but Different SDs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 2 Student t Factors for Individual Measurements at Various Confidence Levels . . . . . .

47、. . . . . . . . . . . . 14 3 Example of a Primary Table. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 4 Matrix 1Universe of Components . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

48、 . . . . . . . . . . 30 5 Matrix 2Correlation Matrix (Informative). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 B.1 Example Conditions and Correction Factors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

49、 . . 35 B.2 Primary Uncertainty Table for Meter Factor Example. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 B.3 Classification and Evaluation of Uncertainty Components. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 B.4 Sensitivity of Uncertainty Components . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 B.5 Correlation Matrix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .