Foreword
Scope
Definitions
Symbols and units
General symbols
Statistical symbols
Central proving
On-line proving
Principles of statistical measurement
Introduction
Distribution of measurements
Estimate of true quantity
Estimate of standard deviation
Estimate of the uncertainty
Estimate of repeatability
Estimate of maximum range
Combination of errors
The estimate s(y) of the standard deviation of y (see 2.1.4) is given by:
The estimate u(y) of the uncertainty of y (see 2.1.5) is similar in form to equation (2.13), that is:
Measurement procedure
Introduction
Statistical control
Measurement reliability
Performance charts
Control charts
Chart preparation
Parallel control charts
Moving-average control charts
Non-linear control charts
Reconciliation charts
Collection of data
Proving conditions
General
Pressure
Temperature
Flowrate
Viscosity
Meter data
Number of provings
Number of flowrates required
Number of viscosities
Test report
Reliability of data collected and resulting values
Central proving operational conditions
Reliability of data collected
Outlier test
Tests for short-term variability or scatter
Test for repeatability
Test of the range
Resulting values
Variation in meter factor with (Q,v)
Performance charts
General
Preparation of data
Flowrate Q
Viscosity
Meter characteristics
K-factor
Meter correction factor
Relative error
Meter calibration and performance charts
Calibration curve for turbine and displacement meters
PD meters
Turbine meters
Universal calibration curve for turbine meters
Polynomial method
Direct matrix
Table
Control charts and tests
Quality of meters
Frequency of proving
Re-proving as a function of time
Re-proving as a function of volume
Control charts and tests corresponding to any meter
Control charts and tests via polynomials
Control charts via direct matrix
Worked examples
Scope of examples
Example 1: Test for outliers
Given
Find
Solution
Example 2: Test for repeatability
Given
Find
Solution
Example 3: Test of the range
Given
Find
Solutions
Example 4: Resulting values
Given
Find
Solution
Example 5: Preparation of data
Given
Find
Solution
Example 6: Universal calibration curve (UCC)
Given
Find
Solutions
Analysis of 1978 Test Report
Analysis of 1979 Test Report
Analysis of 1980 Test Report
Collection of data
Proving conditions
4.1.1.1 General
4.1.1.2 Sensitivity of meter
Meter data
Prover volume corrections
Number of provings
Effect of flowrate
Controlling conditions
Number of flowrates
Re-proving
Reliability of data collected
Operating conditions
Data analysis
Effects of random errors
K-factor - flowrate curves
Monitoring proving conditions
Performance charts
General
Initial proving data
Prior data
Control charts
General
Statistical tables (informative)
t-distribution values for 95 % and 99 % probability (two-sided) (informative)
Normal (Gaussian) distribution (informative)
Outlier tests (informative)
Procedure for Dixon's Test for outliers
Random uncertainty of polynomial approximation (informative)
Bibliography (informative)