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ASME PTC 19.1 2018

ASME PTC 19.1 2018

$98.04

ASME PTC 19.1-2018 – Test Uncertainty

Published By Publication Date Number of Pages
ASME 2018 81
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The scope of this Standard is to specify procedures for (a) evaluation of uncertainties in test measurements, parameters, and methods (b) 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 or their pedigree (Type A or Type B).

PDF Catalog

PDF Pages PDF Title
4 CONTENTS
7 NOTICE
8 FOREWORD
9 COMMITTEE ROSTER
10 CORRESPONDENCE WITH THE PTC COMMITTEE
12 INTRODUCTION
14 Section 1 Object and Scope
1-1 OBJECT
1-1.1 Objectives
1-2 SCOPE
1-2.1 Uncertainty Propagation Methods
1-2.2 Uncertainty Propagation Classifications
15 1-3 APPLICATIONS
16 Section 2 Nomenclature and Glossary
2-1 NOMENCLATURE
2-1.1 Symbols
2-1.2 Indices
2-2 GLOSSARY
18 Section 3 Fundamental Concepts
3-1 ASSUMPTIONS
3-2 MEASUREMENT ERROR
3-2.1 Random Error
3-2.2 Systematic Error
3-3 MEASUREMENT UNCERTAINTY
3-3.1 Random Standard Uncertainty of a Measurand
19 Figures
Figure 3-2-1 Illustration of Measurement Errors
20 Figure 3-2-2 Measurement Error Components
Figure 3-3.1-1 Population Distribution
21 3-3.2 Systematic Standard Uncertainty of a Measurand
22 3-3.3 Combined Standard Uncertainty and Expanded Uncertainty
23 3-4 PRETEST AND POST-TEST UNCERTAINTY ANALYSES
3-4.1 Pretest Uncertainty Analysis
Figure 3-3.3-1 Uncertainty Interval
24 3-4.2 Post-test Uncertainty Analysis
25 Section 4 Defining the Measurement Process
4-1 OVERVIEW
4-2 SELECTION OF THE APPROPRIATE “TRUE VALUE”
4-3 IDENTIFICATION OF ERROR SOURCES
4-3.1 Calibration Uncertainty
4-3.2 Uncertainty Due to Test Article and/or Instrumentation Installation
26 4-3.3 Data Acquisition Uncertainty
4-3.4 Data Reduction Uncertainty
4-3.5 Uncertainty Due to Methods and Other Effects
Figure 4-3.1-1 Generic Measurement Calibration Hierarchy
27 4-4 CATEGORIZATION OF UNCERTAINTIES
4-4.1 Alternate Categorization Approach
4-4.2 Time Interval Effects
4-4.3 Test Objective
28 4-5 COMPARATIVE TESTING
Figure 4-4.3-1 “Within” and “Between” Sources of Data Scatter
29 Section 5 Uncertainty of a Measurement
5-1 RANDOM STANDARD UNCERTAINTY OF THE MEAN
5-1.1 General Case
5-1.2 Using Previous Values of sX¯
30 5-1.3 Using Elemental Random Error Sources
5-1.4 Using Estimates of Sample Standard Deviation
5-2 SYSTEMATIC STANDARD UNCERTAINTY OF A MEASUREMENT
31 5-3 CLASSIFICATION OF UNCERTAINTY SOURCES
5-4 COMBINED STANDARD AND EXPANDED UNCERTAINTY OF A MEASUREMENT
5-4.1 Example
32 Tables
Table 5-4.1-1 Circulating Water-Bath Temperature Measurements (Example 5-4.1)
33 Table 5-4.1-2 Systematic Standard Uncertainty of Average Circulating Water-Bath Temperature Measurement(Example 5-4.1)
34 Section 6 Uncertainty of a Result Calculated From Multiple Parameters
6-1 RESULTS CALCULATED FROM MULTIPLE PARAMETERS
6-1.1 Single and Repeated Tests
6-1.2 Multiple Results: Test With the Result Calculated Multiple Times at a Given Condition
35 6-1.3 Determining Uncertainties in Results Calculated From Multiple Parameters
6-2 DIRECT METHOD OF DETERMINING RANDOM STANDARD UNCERTAINTY FROM A SAMPLE OF MULTIPLE RESULTS
6-2.1 Direct Calculation of the Random Standard Uncertainty From a Sample of Multiple Results
6-2.2 Some Practical Consideration for Multiple Results at a Given Test Condition
36 6-3 TAYLOR SERIES METHOD (TSM) OF PROPAGATION FOR DETERMINING RANDOM AND SYSTEMATIC UNCERTAINTIES OF A RESULT
6-3.1 Random Standard Uncertainty of a Result (TSM)
Figure 6-3.1-1 Venturi Calibration
37 6-3.2 Systematic Standard Uncertainty of a Result (TSM)
Figure 6-3.1-2 Normalized Venturi Inlet and Throat Pressures for a Test
Table 6-3.1-1 Comparison of TSM and Direct Method Values of Random Standard Uncertainty in Cd
38 6-3.3 Combined Standard Uncertainty and Expanded Uncertainty of a Result (TSM)
6-4 COMBINED STANDARD UNCERTAINTY AND UNCERTAINTY COVERAGE INTERVAL FOR A RESULT [MONTE CARLO METHOD OF PROPAGATION (MCM)]
6-4.1 Single Result at a Given Test Condition
6-4.2 Multiple Results at a Given Test Condition
39 Figure 6-4.1-1 Monte Carlo Method for Uncertainty Propagation for a Single Test Result
40 Figure 6-4.2-1 Monte Carlo Method for Uncertainty Propagation for Multiple Results
41 6-4.3 Coverage Interval at a Given Level of Confidence
Figure 6-4.3-1 Probabilistically Symmetric CoverageInterval
42 Section 7 Additional Uncertainty Considerations
7-1 CORRELATED SYSTEMATIC ERRORS (USING TSM PROPAGATION)
7-1.1 Correlated Systematic Errors
7-1.2 Examples
43 Figure 7-1.2-1 Piping Arrangement With Four Flowmeters
Table 7-1.2-1 Burst Pressures
46 7-2 NONSYMMETRIC SYSTEMATIC UNCERTAINTY (TSM PROPAGATION)
7-2.1 Nonsymmetric Systematic Uncertainty Interval for a True Value
47 Figure 7-2.1-1 Gaussian Distribution for Nonsymmetric Systematic Errors
Figure 7-2.1-2 Rectangular Distribution for Nonsymmetric Systematic Errors
Figure 7-2.1-3 Triangular Distribution for Nonsymmetric Systematic Errors
48 7-2.2 Example 1
Table 7-2.1-1 Expressions for q for the Gaussian, Rectangular, and Triangular Distributions inFigures 7-2.1-1 through 7-2.1-3
Table 7-2.1-2 Systematic Standard Uncertainties, bxns , for the Gaussian, Rectanglar, and Triangular Distributions inFigures 7-2.1-1 through 7-2.1-3
49 7-2.3 Nonsymmetric Systematic Uncertainty Interval for a Derived Result
Figure 7-2.2-1 Triangular Distribution of Temperatures
50 7-2.4 Example 2
7-3 REGRESSION UNCERTAINTY (TSM)
7-3.1 Linear Regression Analysis
51 7-3.2 Least-Squares
7-3.3 Random Standard Uncertainty for Ŷ Determined From Regression Equation
7-3.4 Systematic Standard Uncertainty for Ŷ Determined From Regression Equation
52 Table 7-3.4-1 Systematic Standard Uncertainty Components for Ŷ Determined From Regression Equation
53 7-3.5 Uncertainty for Ŷ From Regression Equation
54 Section 8 A Comprehensive Example
8-1 PART 1: OVERVIEW
Figure 8-1-1 Heat Exchanger Cores Using Hot Air-Cooling Water Configuration
55 8-1.1 Random Standard Uncertainty for the Result, q
8-1.2 Systematic Standard Uncertainties
8-2 PART 2: GENERIC CALIBRATION ANALYSIS
56 8-3 PART 3: DETERMINATION OF THE UNCERTAINTY IN q FOR A SINGLE CORE DESIGN
8-3.1 Case A: No Shared Error Sources in Any Measurements
Figure 8-2-1 Measurement of a Generic Thermocouple Output
57 Figure 8-2-2 Measurement of a Calibrated Thermocouple Output
58 8-3.2 Case B: Possible Shared Error Sources in Temperature Measurements
Figure 8-3-1 Monte Carlo Uncertainty Analysis
59 Figure 8-3.2-1 Uniform Distributions for Elemental Systematic Error Sources
60 8-4 PART 4: DETERMINATION OF THE UNCERTAINTY IN Δq FOR TWO CORE DESIGNS TESTED SEQUENTIALLY USING THE SAME FACILITY AND INSTRUMENTATION
8-4.1 Random Uncertainty for the Result Δq
8-4.2 TSM Analysis: Systematic Standard Uncertainty for the Result Δq
63 8-4.3 MCM Analysis.
65 Section 9 References
66 NONMANDATORY APPENDIX A STATISTICAL CONSIDERATION
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
67 Table A-1-1 Factors for Calculating the Two-Sided 95% Probability Intervals for a Normal Distribution
A-1.3 Prediction Interval to Contain All of a Specified Number of Future Observations
68 Figure A-1.3-1 How the Lengths of the Statistical Intervals for the Example Compare
A-1.4 How to Select the Right Interval
69 A-1.5 Where to Get More Information
A-1.6 The Example Problem
A-1.7 References
A-2 OUTLIER TREATMENT
A-2.1 General
70 Figure A-2.1-1 Outlier Outside the Range of Acceptable Data
A-2.2 Thompson τ Technique (Modified)
A-2.3 Example
71 Table A-2.2-1 Modified Thompson τ (at the 5% Significance Level)
Table A-2.3-1 Example of Use of Modified Thompson τ Method
A-3 REFERENCES
72 NONMANDATORY APPENDIX B GUIDELINES FOR DEGREES OF FREEDOM AND CONFIDENCE INTERVALS
B-1 INTRODUCTION
B-2 GENERAL UNCERTAINTY ANALYSIS MODEL (TSM)
73 B-3 LARGE SAMPLE UNCERTAINTY ANALYSIS APPROXIMATION
B-4 REFERENCES
74 Table B-2-1 Values for Two-Sided Confidence Interval Student’s t Distribution
75 NONMANDATORY APPENDIX C THE CENTRAL LIMIT THEOREM
C-1 THE CENTRAL LIMIT THEOREM (FROM [C1])
C-2 REFERENCE
76 NONMANDATORY APPENDIX D GENERAL REGRESSION UNCERTAINTY (TSM)
D-1 INTRODUCTION
D-2 LEAST-SQUARES
D-3 SYSTEMATIC UNCERTAINTY
77 D-4 GENERAL APPROACH TO LINEAR REGRESSION UNCERTAINTY
D-5 HIGHER ORDER REGRESSION EQUATIONS
D-6 REFERENCE

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