Manual of Petroleum Measurement Standards Chapter 13.3

Measurement Uncertainty

FIRST EDITION, MAY 2016

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Foreword

This standard 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 Uncertainty 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 underlying 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 critical 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 a measurement therefore ultimately depend on the understanding, critical analysis and integrity of those who contribute to the assignment of its value.”

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Contents

Page

1. Scope 1

2. Normative References 1

3. Terms, Definitions, Acronyms, Abbreviations, and Symbols 2

   1. Terms and Definitions 2

   2. Acronyms, Abbreviations, and Symbols 6

4. Basic Concepts 7

   1. General 7

   2. Measurement Method 7

   3. True Quantity Value 8

   4. Error 8

   5. Statistical Basis 8

   6. Uncertainty 8

   7. Confidence Level (Confidence Interval) 8

   8. Type A vs Type B Uncertainties 9

   9. Representative Samples 9

   10. Mean 9

   11. Standard Deviation 9

   12. Standard Uncertainty 10

   13. Degrees of Freedom 11

   14. Determining Confidence Interval 11

   15. Correlation Coefficient 13

   16. Independent and Dependent Variables 13

   17. Combining Uncertainties 13

   18. Probability Distributions 15

5. Evaluating Uncertainty 17

   1. General 17

   2. Determine the Measurement Model 18

   3. Record Elemental Error Sources 18

   4. Create a Primary Uncertainty Table 20

   5. Classify and Evaluate Uncertainty Components 21

   6. Determine Sensitivity Coefficients 24

   7. Determine Correlation Coefficients 26

   8. Determine Combined Standard Uncertainty 27

   9. Determine Expanded Uncertainty 28

   10. Reporting Results 28

Annex A (informative) Monte Carlo Method 30

Annex B (informative) Examples 31

Annex C (normative) Formal Proof of Equation 7(a) 48

Annex D (informative) Report Significant Figures 50

Annex E (normative) Using a Simplified Estimate of Standard Deviation 54

Bibliography 57

Page

Figures

1. Normal Distribution 16

2. Triangular Distribution 16

3. Rectangular Distribution 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 of all Uncertainty Components of a Measurement Model 19

1. Uncertainty of the Transmitter Verification 52

2. Uncertainty of the Transmitter After Adjustment 52

Tables

1 t-Distribution Values 12

D.1 U95, Probable Error and Effective Increment 53

1. Range to Standard Deviation Conversion Factors, D(n) 55

2. Student t Factors for Individual Measurements at Various Confidence Levels 56

Matrices

1. Universe of Components 26

2. Correlation Matrix (Informative) 27

Measurement 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 (including any amendments) applies.

API Manual of Petroleum Measurement Standards (MPMS) Chapter 12, Calculation of Petroleum Quantities, Section 2—Calculation of Liquid Petroleum Quantities Measured by Turbine or Displacement Meters, 1981

API MPMS Chapter 13, Statistical Aspects of Measuring and Sampling, Section 1—Statistical Concepts and Procedures in Measurements, 1985, Reaffirmed 2011

API MPMS Chapter 13, Statistical Aspects of Measuring and Sampling, Section 2—Methods of Evaluating Meter Proving Data, 1994, Reaffirmed 2011

API MPMS Chapter 14.3, (AGA Report No. 3, Part 1), Concentric, Square-Edged Orifice Meters, Part 1—General Equations and Uncertainty Guidelines, 2012

API MPMS Chapter 22.1, Testing Protocols—General Guidelines for Developing Testing Protocols for Devices Used in the Measurement of Hydrocarbon Fluids, 2006, Reaffirmed 2011

Coleman, H.W., and Steele, W.G., Experimentation and Uncertainty Analysis for Engineers, Third Edition, New York: John Wiley & Sons, 2009

Harter, H.L., “Tables of Range and Studentized Range,” Annals of Mathematical Statistics, vol. 31, Beachwood, OH, 1960, pp. 1122–1147

JCGM 100:2008, Evaluation of measurement data—Guide to the expression of uncertainty in measurement, GUM 1995 with minor corrections, 2008

JCGM 101:2008, Evaluation of measurement data—Supplement 1 to the “Guide to the expression of uncertainty in measurement”—Propagation of distributions using a Monte Carlo method, GUM 1995 with minor corrections, 2008

JCGM 200:2012, International vocabulary of metrology—Basic and general concepts and associated terms (VIM), 2012

Olkin, I., “Range Restrictions for Product-Moment Correlation Matrices,” Psychometrika, December 1981, vol. 46, Issue 4, pp. 469–472

Taylor, B.N., and Kuyatt, C.E., Guidelines for Evaluating and Expressing the Uncertainty of NIST Measurement Results, NIST Technical Note 1297, 1994

Wheeler, D.J., EMP III: Evaluating the Measurement Process & Using Imperfect Data, SPC Press, 2006

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