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ASME PTC 19.1 2013

ASME PTC 19.1 2013

$98.04

ASME PTC 19.1 Test Uncertainty

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ASME 2013 116
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This Standard specifies procedures for evaluation of uncertainties in test measurements, parameters and methods, and for propagation of those uncertainties into the uncertainty of a test result. Depending on the application, uncertainty sources may be classified either by the presumed effect (systematic or random) on the measurement or test result, or by the process in which they may be quantified (Type A or Type B). The end result of an uncertainty analysis is a numerical estimate of the test uncertainty with an appropriate confidence level

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PDF Pages PDF Title
5 CONTENTS
8 NOTICE
9 FOREWORD
10 COMMITTEE ROSTER
11 CORRESPONDENCE WITH THE PTC COMMITTEE
13 Section 1 Introduction
1-1 GENERAL
1-2 UNCERTAINTY CLASSIFICATIONS
1-3 ADVANTAGES OF USING THIS CODE
1-4 APPLICATIONS
14 1-5 DISCLAIMER
15 Section 2 Object and Scope
2-1 OBJECT
2-2 SCOPE
16 Section 3 Nomenclature and Glossary
3-1 NOMENCLATURE
3-2 GLOSSARY
18 Section 4 Fundamental Concepts
4-1 ASSUMPTIONS
4-2 MEASUREMENT ERROR
4-2.1 Random Error
4-2.2 Systematic Error
4-3 MEASUREMENT UNCERTAINTY
4-3.1 Random Standard Uncertainty
19 Figures

Fig. 4-2-1 Illustration of Measurement Errors
Fig. 4-2-2 Measurement Error Components
20 4-3.2 Systematic Standard Uncertainty
Fig. 4-3.1-1 Population Distribution
21 4-3.2.1 Identifying Elemental Sources of Systematic Error.
4-3.2.2 Evaluating Elemental Systematic Standard Uncertainties.
4-3.2.2.1 Published Information.
4-3.2.2.2 Special Data
22 4-3.2.2.3 Engineering Judgment.
4-3.2.3 Combining Elemental Systematic Standard Uncertainties.
23 4-3.3 Combined Standard Uncertainty and Expanded Uncertainty
4-4 PRETEST AND POST-TEST UNCERTAINTY ANALYSES
4-4.1 Pretest Uncertainty Analysis
4-4.2 Post-Test Uncertainty Analysis
24 Fig. 4-3.3-1 Uncertainty Interval
25 Section 5 Defining the Measurement Process
5-1 OVERVIEW
5-2 SELECTION OF THE APPROPRIATE “TRUE VALUE”
5-3 IDENTIFICATION OF ERROR SOURCES
5-3.1 Calibration Uncertainty
5-3.2 Uncertainty Due to Test Article and/or Instrumentation Installation
26 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
Fig. 5-3.1-1 Generic Measurement Calibration Hierarchy
27 5-4.1 Alternate Categorization Approach
5-4.2 Time Interval Effects
5-4.3 Test Objective
5-5 COMPARATIVE TESTING
28 Fig. 5-4.3-1 “Within” and “Between” Sources of Data Scatter
29 Section 6 Uncertainty of a Measurement
6-1 RANDOM STANDARD UNCERTAINTY OF THE MEAN
6-1.1 General Case
6-1.2 Using Previous Values of sX
30 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
31 6-4 COMBINED STANDARD AND EXPANDED UNCERTAINTY OF A MEASUREMENT
32 Tables
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)
33 Section 7 Uncertainty of a Result
7-1 PROPAGATION OF MEASUREMENT UNCERTAINTIES INTO A RESULT
7-1.1 Single and Repeated Tests
7-2 SENSITIVITY
7-2.1 Analytically
34 7-2.2 Numerically
7-3 RANDOM STANDARD UNCERTAINTY OF A RESULT
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
35 7-5 COMBINED STANDARD UNCERTAINTY AND EXPANDED UNCERTAINTY OF A RESULT
36 Section 8 Additional Uncertainty Considerations
8-1 CORRELATED ERRORS
8-1.1 Correlated Systematic Errors
37 Table 8-1 Burst Pressures
39 8-1.2 Correlated Random Errors
40 8-2 NONSYMMETRIC SYSTEMATIC UNCERTAINTY
8-2.1 Nonsymmetric Systematic Uncertainty Interval for a True Value
41 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
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
42 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
43 8-2.2 Nonsymmetric Systematic Uncertainty Interval for a Derived Result
Fig. 8-2.1-4 Triangular Distribution of Temperatures
44 8-3 FOSSILIZATION OF CALIBRATIONS
45 8-4 SPATIAL VARIATIONS 14
46 8-5 ANALYSIS OF REDUNDANT MEANS
Fig. 8-5-1 Three Cases of Redundant Means
47 8-6 REGRESSION UNCERTAINTY
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
48 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.
49 8-6.5 Uncertainty for Y From Regression Equation
8-7 SIMPLIFIED UNCERTAINTY ANALYSIS FOR CALIBRATIONS
8-7.1 Assumptions Applicable to Both Example Cases
8-7.2 In-Spec Calibration Uncertainty
8-7.2.1 Additional Assumptions
8-7.2.2 In-Spec Uncertainty Calculation.
Table 8-6.4.5-1 Systematic Standard Uncertainty Components for Yˆ Determined From Regression Equation
50 8-7.3 Calibration Constant or Curve Uncertainty Calculation
8-7.3.1 Additional Assumptions.
8-7.3.2
8-7.3.3
8-7.3.3.1
8-7.3.3.2
8-7.3.3.3
8-7.3.4
8-7.3.4.1
8-7.3.4.2
8-7.3.5
51 8-7.4 Reporting Calibration Measurement Uncertainty
52 Section 9 Step-by-Step Calculation Procedure
9-1 GENERAL CONSIDERATIONS
9-2 CALCULATION PROCEDURE
53 Table 9-2-1 Table of Data, Independent Parameters
Table 9-2-2 Summary of Data, Calculated Result
54 Section 10 Examples
EXAMPLES AS ILLUSTRATIONS OF TERMS AND METHODS
10-1 COMBINED CYCLE PERFORMANCE UNCERTAINTY
10-1.1 Purpose
10-1.2 Defined Measurement Process
10-1.2.1 Description of Test Instrumentation.
55 Fig. 10-1.1-1 Train Thermal Performance Test
56 10-1.3 Analysis
10-1.3.1 Calculation of Net Electrical Output and Net Heat Rate for Reference Conditions.
10-1.4 Sensitivities
57 10-1.5 Uncertainty of the Measurements
10-1.5.1 Electrical Output.
10-1.5.2 Ambient Inlet Temperature.
58 10-1.5.3 Ambient Pressure.
10-1.5.4 Relative Humidity.
10-1.5.5 Fuel Flow.
59 10-1.5.6 Lower Heating Value.
10-1.5.7 Fuel Analysis.
10-1.6 Uncertainty of Result
60 Table 10-1.6-1 Combined Cycle Net Facility Electrical Output Uncertainty Including the Correlated Uncertainties
61 Table 10-1.6-2 Combined Cycle Net Facility Heat Rate Uncertainty Including the Correlated Uncertainties
62 Table 10-1.6-3 Combined Cycle Net Facility Electrical Output Uncertainty Excluding the Correlated Uncertainties
63 Table 10-1.6-4 Combined Cycle Net Facility Heat Rate Uncertainty Excluding the Correlated Uncertainties
64 10-2 TAYLOR SERIES PROPAGATION FOR RANDOM ERRORS THAT ARE NOT INDEPENDENT
10-2.1 Purpose
10-2.2 The Test Data
Table 10-2.2-1 Test Pressure Data for an Orifice Measuring Flow in a Pipe
65 10-2.3 Approach A: Assuming No Correlation
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
66 10-3 FLOW MEASUREMENT USING PITOT TUBES
10-3.1 Define the Measurement Process
Table 10-2.5-1 Individual Delta Pressure Measurements
67 10-3.2 Data Summary
10-3.3 Velocity Results
Fig. 10-3.1-1 Four Circumferential and Ten Radial Traverse Locations
68 10-3.4 List Elemental Uncertainty Sources
10-3.5 Calculate Random Standard Uncertainty
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
69 10-3.6 Propagate Random Standard Uncertainty
10-3.7 Calculate Systematic Standard Uncertainties
10-3.7.1 Calibration.
Table 10-3.6-1 Random Standard Uncertainty for Both Average Circumferential Velocities and Grand Average Velocity
70 10-3.7.2 Spatial Variation.
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
71 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
10-4.1 Purpose
72 10-4.2 Definition of Measurement Process
10-4.3 Analysis
10-4.3.1 Data Reduction Equation.
10-4.3.2 Identification of Parameters.
10-4.3.3 Sensitivities.
Table 10-3.9-1 Components of Uncertainty in the Grand Average Pipe Velocity
73 Table 10-4.3.2-1 Identification of Parameters
74 10-4.4 Random Standard Uncertainty
10-4.5 Systematic Standard Uncertainty
10-5 HUMIDITY MEASUREMENT
10-5.1 Introduction
75 Table 10-4.3.3-1 Calculated Sensitivities of Each Parameter
76 Table 10-4.4-1 Random Standard Uncertainty Estimated for Each Parameter
77 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
78 Table 10-4.5-3 Combined Standard Uncertainty and Expanded Uncertainty of the Result
79 10-5.2 Definition of the Measurement Process
Fig. 10-5.1-1 Schematic of Moisture Absorption and Removal System
80 10-5.3 Analysis
10-5.3.1 Data Analysis Equation.
10-5.3.2 Parameters.
10-5.3.3 Sensitivities.
Table 10-5.2-1 Measured Values and Statistical Properties
81 10-5.4 Estimation of the Systematic and Random Standard Uncertainties
82 Fig. 10-5.3.3-1 Example for Estimating Sensitivity From a Chart
Table 10-5.4-1 Estimated Values, Standard Uncertainties, and Calculated Sensitivities
83 10-5.5 Estimation of the Combined Standard Uncertainty and the Expanded Uncertainty
10-6 PERIODIC COMPARATIVE TESTING
10-6.1 Problem Definition
84 Fig. 10-6.1-1 Installed Arrangement
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
85 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
86 10-6.2 Comparison With Independent Control
10-6.3 Comparative Uncertainties
88 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
89 Fig. 10-6.2-1 Comparison of Test Results Using the Initial Field Test as the Control
Table 10-6.3-1 Uncertainty Propagation for Comparative Uncertainty Analysis
90 Table 10-6.3-2 Correlated Terms for Comparative Uncertainty Analysis
91 Section 11 References
93 Section 12 Additional References
95 Nonmandatory Appendix A Statistical Considerations
A-1 UNDERSTANDING STATISTICAL INTERVALS
A-1.1 Confidence Interval for the Population Mean
A-1.2 Tolerance Interval to Contain a Specific Proportion of the Population
96 A-1.3 Prediction Interval to Contain All of a Specified Number of Future Observations
A-1.4 How to Select the Right Interval
97 A-1.5 Where to Get More Information
98 A-1.6 References
A-2 WEIGHTING METHOD
99 A-3 OUTLIER TREATMENT
A-3.1 General
A-3.2 Thompson tau Technique Modified1
A-3.3 Example
102 A-4 PARETO DIAGRAMS
A-4.1 General
A-4.2 Example
105 Nonmandatory Appendix B Guidelines for Degree of Freedom and Confidence Intervals
B-1 GENERAL UNCERTAINTY ANALYSIS MODEL
106 B-2 LARGE SAMPLE UNCERTAINTY ANALYSIS APPROXIMATION
107 Nonmandatory Appendix C Propagation of Uncertainty Through Taylor Series
C-1 INTRODUCTION
C-2 DEFINITIONS
C-3 PRELIMINARY CONSIDERATIONS
108 C-4 PROPAGATION OF UNCERTAINTY/ERROR THROUGH TAYLOR SERIES
C-4.1 The First Order Approximation
C-4.2 Assessing the Validity of the First Order Approximation
110 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
111 Nonmandatory Appendix D The Central Limit Theorem
112 Nonmandatory Appendix E General Regression Uncertainty
E-1 INTRODUCTION
E-2 LEAST-SQUARES
E-3 SYSTEMATIC UNCERTAINTY
113 E-4 GENERAL APPROACH TO LINEAR REGRESSION UNCERTAINTY
E-5 HIGHER ORDER REGRESSION EQUATIONS
E-6 REFERENCE

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ASME PTC 19.1 2013
$98.04