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PTC 19.1 Test Uncertainty, 2013
- CONTENTS
- NOTICE
- FOREWORD
- COMMITTEE ROSTER
- CORRESPONDENCE WITH THE PTC COMMITTEE
- Section 1 Introduction [Go to Page]
- 1-1 GENERAL
- 1-2 UNCERTAINTY CLASSIFICATIONS
- 1-3 ADVANTAGES OF USING THIS CODE
- 1-4 APPLICATIONS
- 1-5 DISCLAIMER
- Section 2 Object and Scope [Go to Page]
- 2-1 OBJECT
- 2-2 SCOPE
- Section 3 Nomenclature and Glossary [Go to Page]
- 3-1 NOMENCLATURE
- 3-2 GLOSSARY
- Section 4 Fundamental Concepts [Go to Page]
- 4-1 ASSUMPTIONS
- 4-2 MEASUREMENT ERROR [Go to Page]
- 4-2.1 Random Error
- 4-2.2 Systematic Error
- 4-3 MEASUREMENT UNCERTAINTY [Go to Page]
- 4-3.1 Random Standard Uncertainty
- 4-3.2 Systematic Standard Uncertainty [Go to Page]
- 4-3.2.1 Identifying Elemental Sources of Systematic Error.
- 4-3.2.2 Evaluating Elemental Systematic Standard Uncertainties. [Go to Page]
- 4-3.2.2.1 Published Information.
- 4-3.2.2.2 Special Data
- 4-3.2.2.3 Engineering Judgment.
- 4-3.2.3 Combining Elemental Systematic Standard Uncertainties.
- 4-3.3 Combined Standard Uncertainty and Expanded Uncertainty
- 4-4 PRETEST AND POST-TEST UNCERTAINTY ANALYSES [Go to Page]
- 4-4.1 Pretest Uncertainty Analysis
- 4-4.2 Post-Test Uncertainty Analysis
- Section 5 Defining the Measurement Process [Go to Page]
- 5-1 OVERVIEW
- 5-2 SELECTION OF THE APPROPRIATE "TRUE VALUE"
- 5-3 IDENTIFICATION OF ERROR SOURCES [Go to Page]
- 5-3.1 Calibration Uncertainty
- 5-3.2 Uncertainty Due to Test Article and/or Instrumentation Installation
- 5-3.3 Data Acquisition Uncertainty
- 5-3.4 Data Reduction Uncertainty
- 5-3.5 Uncertainty Due to Methods and Other Effects
- 5-4 CATEGORIZATION OF UNCERTAINTIES [Go to Page]
- 5-4.1 Alternate Categorization Approach
- 5-4.2 Time Interval Effects
- 5-4.3 Test Objective
- 5-5 COMPARATIVE TESTING
- Section 6 Uncertainty of a Measurement [Go to Page]
- 6-1 RANDOM STANDARD UNCERTAINTY OF THE MEAN [Go to Page]
- 6-1.1 General Case
- 6-1.2 Using Previous Values of sX
- 6-1.3 Using Elemental Random Error Sources
- 6-1.4 Using Estimates of Sample Standard Deviation
- 6-2 SYSTEMATIC STANDARD UNCERTAINTY OF A MEASUREMENT
- 6-3 CLASSIFICATION OF UNCERTAINTY SOURCES
- 6-4 COMBINED STANDARD AND EXPANDED UNCERTAINTY OF A MEASUREMENT
- Section 7 Uncertainty of a Result [Go to Page]
- 7-1 PROPAGATION OF MEASUREMENT UNCERTAINTIES INTO A RESULT [Go to Page]
- 7-1.1 Single and Repeated Tests
- 7-2 SENSITIVITY [Go to Page]
- 7-2.1 Analytically
- 7-2.2 Numerically
- 7-3 RANDOM STANDARD UNCERTAINTY OF A RESULT [Go to Page]
- 7-3.1 Single Test
- 7-3.2 Repeated Tests
- 7-3.3 Multiple Tests: Combined Tests
- 7-4 SYSTEMATIC STANDARD UNCERTAINTY OF A RESULT
- 7-5 COMBINED STANDARD UNCERTAINTY AND EXPANDED UNCERTAINTY OF A RESULT
- Section 8 Additional Uncertainty Considerations [Go to Page]
- 8-1 CORRELATED ERRORS [Go to Page]
- 8-1.1 Correlated Systematic Errors
- 8-1.2 Correlated Random Errors
- 8-2 NONSYMMETRIC SYSTEMATIC UNCERTAINTY [Go to Page]
- 8-2.1 Nonsymmetric Systematic Uncertainty Interval for a True Value
- 8-2.2 Nonsymmetric Systematic Uncertainty Interval for a Derived Result
- 8-3 FOSSILIZATION OF CALIBRATIONS
- 8-4 SPATIAL VARIATIONS 14
- 8-5 ANALYSIS OF REDUNDANT MEANS
- 8-6 REGRESSION UNCERTAINTY [Go to Page]
- 8-6.1 Linear Regression Analysis
- 8-6.2 Least-Squares
- 8-6.3 Random Standard Uncertainty for Y Determined From Regression Equation
- 8-6.4 Systematic Standard Uncertainty for Y Determined From Regression Equation [Go to Page]
- 8-6.4.1 Systematic Standard Uncertainty in Yj Data.
- 8-6.4.2 Systematic Standard Uncertainty in Xj Data With No Systematic Standard Uncertainty in Xnew.
- 8-6.4.3 Systematic Standard Uncertainty in Xj Data With Correlated Systematic Standard Uncertainty in Xnew.
- 8-6.4.4 Systematic Standard Uncertainty in Xj Data With Uncorrelated Systematic Standard Uncertainty in Xnew.
- 8-6.4.5 Systematic Standard Uncertainty for Y.
- 8-6.5 Uncertainty for Y From Regression Equation
- 8-7 SIMPLIFIED UNCERTAINTY ANALYSIS FOR CALIBRATIONS [Go to Page]
- 8-7.1 Assumptions Applicable to Both Example Cases
- 8-7.2 In-Spec Calibration Uncertainty [Go to Page]
- 8-7.2.1 Additional Assumptions
- 8-7.2.2 In-Spec Uncertainty Calculation.
- 8-7.3 Calibration Constant or Curve Uncertainty Calculation [Go to Page]
- 8-7.3.1 Additional Assumptions.
- 8-7.3.2
- 8-7.3.3 [Go to Page]
- 8-7.3.3.1
- 8-7.3.3.2
- 8-7.3.3.3
- 8-7.3.4 [Go to Page]
- 8-7.3.4.1
- 8-7.3.4.2
- 8-7.3.5
- 8-7.4 Reporting Calibration Measurement Uncertainty
- Section 9 Step-by-Step Calculation Procedure [Go to Page]
- 9-1 GENERAL CONSIDERATIONS
- 9-2 CALCULATION PROCEDURE
- Section 10 Examples [Go to Page]
- EXAMPLES AS ILLUSTRATIONS OF TERMS AND METHODS
- 10-1 COMBINED CYCLE PERFORMANCE UNCERTAINTY [Go to Page]
- 10-1.1 Purpose
- 10-1.2 Defined Measurement Process [Go to Page]
- 10-1.2.1 Description of Test Instrumentation.
- 10-1.3 Analysis [Go to Page]
- 10-1.3.1 Calculation of Net Electrical Output and Net Heat Rate for Reference Conditions.
- 10-1.4 Sensitivities
- 10-1.5 Uncertainty of the Measurements [Go to Page]
- 10-1.5.1 Electrical Output.
- 10-1.5.2 Ambient Inlet Temperature.
- 10-1.5.3 Ambient Pressure.
- 10-1.5.4 Relative Humidity.
- 10-1.5.5 Fuel Flow.
- 10-1.5.6 Lower Heating Value.
- 10-1.5.7 Fuel Analysis.
- 10-1.6 Uncertainty of Result
- 10-2 TAYLOR SERIES PROPAGATION FOR RANDOM ERRORS THAT ARE NOT INDEPENDENT [Go to Page]
- 10-2.1 Purpose
- 10-2.2 The Test Data
- 10-2.3 Approach A: Assuming No Correlation [Go to Page]
- 10-2.3.1 Approach A Computation.
- 10-2.4 Approach B: Assuming Correlation Exists
- 10-2.5 Approach C: Computation of Deltas and Their Standard Deviation
- 10-3 FLOW MEASUREMENT USING PITOT TUBES [Go to Page]
- 10-3.1 Define the Measurement Process
- 10-3.2 Data Summary
- 10-3.3 Velocity Results
- 10-3.4 List Elemental Uncertainty Sources
- 10-3.5 Calculate Random Standard Uncertainty
- 10-3.6 Propagate Random Standard Uncertainty
- 10-3.7 Calculate Systematic Standard Uncertainties [Go to Page]
- 10-3.7.1 Calibration.
- 10-3.7.2 Spatial Variation.
- 10-3.8 Propagate Systematic Standard Uncertainties
- 10-3.9 Uncertainty of Result
- 10-4 POST-TEST UNCERTAINTY ANALYSIS EXAMPLE: HRSG HIGH PRESSURE STEAM FLOW [Go to Page]
- 10-4.1 Purpose
- 10-4.2 Definition of Measurement Process
- 10-4.3 Analysis [Go to Page]
- 10-4.3.1 Data Reduction Equation.
- 10-4.3.2 Identification of Parameters.
- 10-4.3.3 Sensitivities.
- 10-4.4 Random Standard Uncertainty
- 10-4.5 Systematic Standard Uncertainty
- 10-5 HUMIDITY MEASUREMENT [Go to Page]
- 10-5.1 Introduction
- 10-5.2 Definition of the Measurement Process
- 10-5.3 Analysis [Go to Page]
- 10-5.3.1 Data Analysis Equation.
- 10-5.3.2 Parameters.
- 10-5.3.3 Sensitivities.
- 10-5.4 Estimation of the Systematic and Random Standard Uncertainties
- 10-5.5 Estimation of the Combined Standard Uncertainty and the Expanded Uncertainty
- 10-6 PERIODIC COMPARATIVE TESTING [Go to Page]
- 10-6.1 Problem Definition
- 10-6.2 Comparison With Independent Control
- 10-6.3 Comparative Uncertainties
- Section 11 References
- Section 12 Additional References
- Figures
[Go to Page]
- Fig. 4-2-1 Illustration of Measurement Errors
- Fig. 4-2-2 Measurement Error Components
- Fig. 4-3.1-1 Population Distribution
- Fig. 4-3.3-1 Uncertainty Interval
- Fig. 5-3.1-1 Generic Measurement Calibration Hierarchy
- Fig. 5-4.3-1 “Within” and “Between” Sources of Data Scatter
- Fig. 8-2.1-1 Gaussian Distribution for Nonsymmetric Systematic Errors
- Fig. 8-2.1-2 Rectangular Distribution for Nonsymmetric Systematic Errors
- Fig. 8-2.1-3 Triangular Distribution for Nonsymmetric Systematic Errors
- Fig. 8-2.1-4 Triangular Distribution of Temperatures
- Fig. 8-5-1 Three Cases of Redundant Means
- Fig. 10-1.1-1 Train Thermal Performance Test
- Fig. 10-3.1-1 Four Circumferential and Ten Radial Traverse Locations
- Fig. 10-5.1-1 Schematic of Moisture Absorption and Removal System
- Fig. 10-5.3.3-1 Example for Estimating Sensitivity From a Chart
- Fig. 10-6.1-1 Installed Arrangement
- Fig. 10-6.1-2 Pump Design Curve With Factory and Field Test Data Shown
- Fig. 10-6.1-3 Comparison of Test Results With Independent Control Conditions
- Fig. 10-6.2-1 Comparison of Test Results Using the Initial Field Test as the Control
- Tables [Go to Page]
- Table 6-4.1-1 Circulating Water-Bath Temperature Measurements (Example 6-4.1)
- Table 6-4.1-2 Systematic Standard Uncertainty of Average Circulating Water-Bath Temperature Measurement (Example 6-4.1)
- Table 8-1 Burst Pressures
- Table 8-2.1-1 Expressions for q for the Gaussian, Rectangular, and Triangular Distributions in Figs. 8-2.1-1 Through 8-2.1-3
- Table 8-2.1-2 Systematic Standard Uncertainties, bXns, for the Gaussian, Rectangular, and Triangular Distributions in Figs. 8-2.1-1 Through 8-2.1-3
- Table 8-6.4.5-1 Systematic Standard Uncertainty Components for Yˆ Determined From Regression Equation
- Table 9-2-1 Table of Data, Independent Parameters
- Table 9-2-2 Summary of Data, Calculated Result
- Table 10-1.6-1 Combined Cycle Net Facility Electrical Output Uncertainty Including the Correlated Uncertainties
- Table 10-1.6-2 Combined Cycle Net Facility Heat Rate Uncertainty Including the Correlated Uncertainties
- Table 10-1.6-3 Combined Cycle Net Facility Electrical Output Uncertainty Excluding the Correlated Uncertainties
- Table 10-1.6-4 Combined Cycle Net Facility Heat Rate Uncertainty Excluding the Correlated Uncertainties
- Table 10-2.2-1 Test Pressure Data for an Orifice Measuring Flow in a Pipe
- Table 10-2.5-1 Individual Delta Pressure Measurements
- Table 10-3.2-1 Average Values at Each Traverse Circumferential and Radial Location
- Table 10-3.3-1 Standard Deviations at Each Traverse Circumferential and Radial Location
- Table 10-3.3-2 Summarized Average Circumferential Velocities and Grand Average Velocity
- Table 10-3.6-1 Random Standard Uncertainty for Both Average Circumferential Velocities and Grand Average Velocity
- Table 10-3.7.1-1 Systematic Standard Uncertainty for Average Circumferential Velocities
- Table 10-3.7.1-2 Systematic Standard Uncertainty Due to Instrumentation Sources for Grand Average Circumferential Velocities
- Table 10-3.9-1 Components of Uncertainty in the Grand Average Pipe Velocity
- Table 10-4.3.2-1 Identification of Parameters
- Table 10-4.3.3-1 Calculated Sensitivities of Each Parameter
- Table 10-4.4-1 Random Standard Uncertainty Estimated for Each Parameter
- Table 10-4.5-1 Systematic Standard Uncertainty Estimated for Each Parameter
- Table 10-4.5-2 Identified Elemental Uncertainty Components and Values That Are Assumed to Be the Same for Each Parameter
- Table 10-4.5-3 Combined Standard Uncertainty and Expanded Uncertainty of the Result
- Table 10-5.2-1 Measured Values and Statistical Properties
- Table 10-5.4-1 Estimated Values, Standard Uncertainties, and Calculated Sensitivities
- Table 10-5.5-1 Standard Uncertainties, Combined Standard Uncertainty, and Expanded Uncertainty of the Result
- Table 10-6.1-1 Pump Design Data (Tc = 20°C)
- Table 10-6.1-2 Summary of Test Results
- Table 10-6.2-1 Uncertainty Propagation for Comparison With Independent Control
- Table 10-6.2-2 Summary Uncertainties
- Table 10-6.2-3 Summary of Results for Each Test
- Table 10-6.3-1 Uncertainty Propagation for Comparative Uncertainty Analysis
- Table 10-6.3-2 Correlated Terms for Comparative Uncertainty Analysis
- Nonmandatory Appendix A Statistical Considerations [Go to Page]
- A-1 UNDERSTANDING STATISTICAL INTERVALS [Go to Page]
- A-1.1 Confidence Interval for the Population Mean
- A-1.2 Tolerance Interval to Contain a Specific Proportion of the Population
- A-1.3 Prediction Interval to Contain All of a Specified Number of Future Observations
- A-1.4 How to Select the Right Interval
- A-1.5 Where to Get More Information
- A-1.6 References
- A-2 WEIGHTING METHOD
- A-3 OUTLIER TREATMENT [Go to Page]
- A-3.1 General
- A-3.2 Thompson tau Technique Modified1
- A-3.3 Example
- A-4 PARETO DIAGRAMS [Go to Page]
- A-4.1 General
- A-4.2 Example
- Nonmandatory Appendix B Guidelines for Degree of Freedom and Confidence Intervals [Go to Page]
- B-1 GENERAL UNCERTAINTY ANALYSIS MODEL
- B-2 LARGE SAMPLE UNCERTAINTY ANALYSIS APPROXIMATION
- Nonmandatory Appendix C Propagation of Uncertainty Through Taylor Series [Go to Page]
- C-1 INTRODUCTION
- C-2 DEFINITIONS
- C-3 PRELIMINARY CONSIDERATIONS
- C-4 PROPAGATION OF UNCERTAINTY/ERROR THROUGH TAYLOR SERIES [Go to Page]
- C-4.1 The First Order Approximation
- C-4.2 Assessing the Validity of the First Order Approximation
- C-4.3 The Limitation of the Present Approach
- C-5 PROPAGATION OF SYSTEMATIC AND RANDOM COMPONENTS OF UNCERTAINTY
- C-6 THE PROBABILITY DENSITY FUNCTION OF A RESULT
- Nonmandatory Appendix D The Central Limit Theorem
- Nonmandatory Appendix E General Regression Uncertainty [Go to Page]
- E-1 INTRODUCTION
- E-2 LEAST-SQUARES
- E-3 SYSTEMATIC UNCERTAINTY
- E-4 GENERAL APPROACH TO LINEAR REGRESSION UNCERTAINTY
- E-5 HIGHER ORDER REGRESSION EQUATIONS
- E-6 REFERENCE [Go to Page]