Manual of Petroleum Measurement Standards

Chapter 13—Statistical Aspects of

Measuring and Sampling

Section 2—Methods of Evaluating

Meter Proving Data

SECOND EDITION, APRIL 2018

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Copyright © 2018 American Petroleum Institute

Foreword

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iii

Contents

Page

1. Scope 1

2. Normative References 1

3. Terms, Definitions, and Acronyms 1

4. Significance and Use 3

5. Elements that Influence Meter Factors 3

6. General Suggestions to Improve the Monitoring Process 4

7. Data Signals 4

8. Ways to Monitor Meter Factors 5

   1. General 5

   2. Logging 5

   3. Run Charting 8

   4. Univariate Control Charting 10

   5. Multivariate Control Charts for Meter Factors 14

Annex A (informative) Tests for Normality 17

Annex B (informative) Other Charts 21

Annex C (informative) Data Tables for Charts in Main Body 24

Annex D (informative) Runs Rules 30

Bibliography 31

Figures

1. Three Patterns that Suggest Further Investigation 8

2. Basic Run Charts 9

3. Run Chart of Deviations from the Curve with Fixed Limits of ±0.15 % Deviation from the Curve on the Primary y-axis and Relative Density on the Secondary y-axis 10

4. Control Chart of Meter Factors using sd of Trial Factors 11

5. Control Chart of Meter Factors using Range % of the Trial Factors 12

6. Control Chart of Meter Factors using Moving Range (mR) of the Meter Factors 12

7. Control Chart of Meter Factors Using Limits Calculated from Moving Averages 13

8. Generalized Multivariate Chart 15

9. Multivariate Chart for Table 3 Data and the Associated Four Univariate Charts 16

1. Normal Probability Plot for Table 3 Data 17

2. Normal Probability Plots for Non-normal Data 19

1. Run Chart using Policy Run-to-Run Limit of 0.05 % 21

2. Control Chart with Limits Calculated from Percentiles of the Meter Factors 22

Tables

1. Responses to Consider when Limits are Exceeded 4

2. Meaning of Column Titles in Table 3 6

3. Meter Factor Log 7

4. Relative Contribution of Each Component to the T-squared Statistic 16

1. Data for the QQ Plot in Figure A.1 18

2. Anderson-Darling Statistics for Table 3 Data 20

3. Shapiro-Wilk Statistics for Table 3 Data 20

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Contents

Tables (Continued)

Page

B.2 Data Set for the Control Chart Based on Percentiles 22

1. Underlying Data for Figure 4 24

2. Underlying Data for Figure 5 26

3. Underlying Data for Figure 6 27

4. Underlying Data for Figure 7 29

vi

Introduction

Minimizing petroleum measurement errors, estimating remaining errors and informing affected parties of errors is important to the petroleum industry. A consistent basis for estimating the size and significance of errors is essential for communication among affected parties. A fundamental source of measurement error is the inaccuracy of the meter factor which is a number that represents the performance of a meter throughout a batch.

Meter factors are monitored to gain confidence in the reported volumes and to detect trends or sudden deviations as indications of when to perform maintenance on or calibration of measurement equipment. The purpose of this standard is to suggest procedures for monitoring variations in meter factors so that uncertainties are understood and consistent with the objectives of parties affected by the measurement operations. The procedures for monitoring meter performance, limits on meter factor variations and actions to take because of these variations are left to the agreement among the parties affected by the measurement operations which can depend on company policy, contract agreements, regulations and laws.

vii

Section 2—Methods of Evaluating Meter Proving Data

1. Scope

   This standard establishes the basic concepts and procedures to estimate and report meter performance uncertainty in consistent and comparable ways.

   
   

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 reference document (including any amendments) applies.

   
   

   API Manual of Petroleum Measurement Standards (MPMS) Chapter 1, Online Terms and Definitions Database

   
   

   API MPMS Chapter 4, Proving Systems

   
   

   API MPMS Chapter 5, Metering

   
   

   API MPMS Chapter 12, Calculation of Petroleum Quantities

   
   

   API MPMS Chapter 13.3, Measurement Uncertainty Quantities

   
   

3. Terms, Definitions, and Acronyms

For the purposes of this document, the following terms and definitions apply. Terms of more general use may be found in the API MPMS Chapter 1, Online Terms and Definitions Database. Acronyms are defined in the text at first use.

3.1

3 standard deviation limit

A control limit equal to 3 standard deviations from the arithmetic mean of the set.

NOTE For a set of normal data this limit is also known as the 3-sigma limit.

3.2

action limits

Horizontal lines found on a run chart or control chart which, if exceeded, suggests that some sort of action is necessary to modify the underlying process or to modify the reports generated from the process. Related terms: tolerance limit, warning limit.

3.3

central line

A line on a control chart or run chart that represents the central value.

3.4

central value

The mean value of the statistic under consideration. Synonym: central tendency.

3.5

control chart

A graphical method for evaluating whether a process is in or out of statistical control.

1