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ASME PTC 19.1-2005
M00052342
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ASME PTC 19.1-2005 Test Uncertainty
standard by ASME International, 10/13/2006
Full Description
This Standard specifies procedures for evaluation of uncertainties in test 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.In stock
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Test Uncertainty
A N A M E R I C A N N A T I O N A L S T A N D A R D
Date of Issuance: October 13, 2006
The 2005 edition of ASME PTC 19.1 will be revised when the Society approves the issuance of the next edition. There will be no Addenda issued to ASME PTC 19.1-2005.
ASME issues written replies to inquiries as code cases and interpretations of technical aspects of this document. Code cases and interpretations are published on the ASME website under the Committee Pages at https://www.asme.org/codes/ as they are issued.
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This code or standard was developed under procedures accredited as meeting the criteria for American National Standards. The Standards Committee that approved the code or standard was balanced to assure that individuals from competent and concerned interests have had an opportunity to participate. The proposed code or standard was made available for public review and comment that provides an opportunity for additional public input from industry, academia, regulatory agencies, and the public-at-large.
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ASME does not take any position with respect to the validity of any patent rights asserted in connection with any items mentioned in this document, and does not undertake to insure anyone utilizing a standard against liability for infringement of any applicable letters patent, nor assumes any such liability. Users of a code or standard are expressly advised that determination of the validity of any such patent rights, and the risk of infringement of such rights, is entirely their own responsibility.
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without the prior written permission of the publisher.
The American Society of Mechanical Engineers Three Park Avenue, New York, NY 10016-5990
Copyright © 2006 by
THE AMERICAN SOCIETY OF MECHANICAL ENGINEERS
All rights reserved Printed in U.S.A.
CONTENTS
Notice . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vii
Foreword viii
Committee Roster . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ix
Section 1 | Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . | 1 |
1-1 | General . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . | 1 |
1-2 | Harmonization With International Standards . . . . . . . . . . . . . . . . . . . | 1 |
1-3 | Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . | 1 |
Section 2 | Object and Scope. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . | 2 |
2-1 | Object. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . | 2 |
2-2 | Scope . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . | 2 |
Section 3 | Nomenclature and Glossary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . | 3 |
3-1 | Nomenclature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . | 3 |
3-2 | Glossary. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . | 3 |
Section 4 | Fundamental Concepts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . | 5 |
4-1 | Assumptions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . | 5 |
4-2 | Measurement Error . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . | 5 |
4-3 | Measurement Uncertainty . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . | 5 |
4-4 | Pretest and Posttest Uncertainty Analyses. . . . . . . . . . . . . . . . . . . . . . | 11 |
Section 5 | Defining the Measurement Process . . . . . . . . . . . . . . . . . . . . . . . . . . . . | 13 |
5-1 | Overview. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . | 13 |
5-2 | Selection of the Appropriate “True Value” . . . . . . . . . . . . . . . . . . . . . | 13 |
5-3 | Identification of Error Sources . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . | 13 |
5-4 | Categorization of Uncertainties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . | 15 |
5-5 | Comparative Versus Absolute Testing. . . . . . . . . . . . . . . . . . . . . . . . . | 16 |
Section 6 | Uncertainty of a Measurement. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . | 17 |
6-1 | Random Standard Uncertainty of the Mean . . . . . . . . . . . . . . . . . . . . | 17 |
6-2 | Systematic Standard Uncertainty of a Measurement . . . . . . . . . . . . . | 18 |
6-3 | Classification of Uncertainty Sources. . . . . . . . . . . . . . . . . . . . . . . . . . | 19 |
6-4 | Combined Standard and Expanded Uncertainty of a Measurement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . | 19 |
Section 7 | Uncertainty of a Result . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . | 22 |
7-1 | Propagation of Measurement Uncertainties Into a Result. . . . . . . . . . | 22 |
7-2 | Sensitivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . | 23 |
7-3 | Random Standard Uncertainty of a Result . . . . . . . . . . . . . . . . . . . . . | 23 |
7-4 | Systematic Standard Uncertainty of a Result. . . . . . . . . . . . . . . . . . . . | 24 |
7-5 | Combined Standard Uncertainty and Expanded Uncertainty of a Result . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . | 24 |
7-6 | Examples of Uncertainty Propagation . . . . . . . . . . . . . . . . . . . . . . . . . | 24 |
Section 8 | Additional Uncertainty Considerations. . . . . . . . . . . . . . . . . . . . . . . . . . | 28 |
8-1 | Correlated Systematic Standard Uncertainties. . . . . . . . . . . . . . . . . . . | 28 |
8-2 | Nonsymmetric Systematic Uncertainty . . . . . . . . . . . . . . . . . . . . . . . . | 31 |
8-3 | Fossilization of Calibrations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . | 35 |
8-4 | Spatial Variation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . | 36 |
8-5 | Analysis of Redundant Means . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . | 36 |
8-6 | Regression Uncertainty. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . | 38 |
Section 9 | Step-by-Step Calculation Procedure. . . . . . . . . . . . . . . . . . . . . . . . . . . . | 41 |
9-1 | General Considerations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . | 41 |
9-2 | Calculation Procedure. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . | 41 |
Section 10 | Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . | 43 |
10-1 | Flow Measurement Using Pitot Tubes. . . . . . . . . . . . . . . . . . . . . . . . . | 43 |
10-2 | Flow Rate Uncertainty . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . | 47 |
10-3 | Flow Rate Uncertainty Including Nonsymmetrical Systematic Standard Uncertainty . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . | 50 |
10-4 | Compressor Performance Uncertainty . . . . . . . . . . . . . . . . . . . . . . . . . | 51 |
10-5 | Periodic Comparative Testing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . | 62 |
Section 11 | References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . | 69 |
Section 12 | Bibliography. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . | 71 |
Figures | ||
4-2-1 | Illustration of Measurement Errors . . . . . . . . . . . . . . . . . . . . . . . . . . . | 6 |
4-2-2 | Measurement Error Components . . . . . . . . . . . . . . . . . . . . . . . . . . . . . | 7 |
4-3.1 | Distribution of Measured Values (Normal Distribution) . . . . . . . . . . | 8 |
4-3.3 | Uncertainty Interval . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . | 11 |
5-3.1 | Generic Measurement Calibration Hierarchy . . . . . . . . . . . . . . . . . . . | 14 |
5-4.3 | Difference Between “Within” and “Between” Sources of Data Scatter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . | 16 |
7-6.2 | Pareto Chart of Systematic and Random Uncertainty Component Contributions to Combined Standard Uncertainty . . . . . . . . . . . . . | 27 |
8-2.1 | Schematic Relation Between Parameters Characterizing Nonsymmetric Uncertainty. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . | 32 |
8-2.2 | Relation Between Parameters Characterizing Nonsymmetric Uncertainty . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . | 34 |
8-5.1 | Three Posttest Cases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . | 37 |
10-1.1 | Traverse Points (Example 10-1) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . | 44 |
10-2.1 | Schematic of a 6 in. 4 in. Venturi. . . . . . . . . . . . . . . . . . . . . . . . . . . | 48 |
10-4.1 | Typical Pressure and Temperature Locations for Compressor Efficiency Determination. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . | 57 |
10-4.7 | The h-s Diagram of the Actual and Isentropic Processes of an Adiabatic Compressor. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . | 61 |
10-5.1-1 | Installed Arrangement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . | 63 |
10-5.1-2 | Pump Design Curve With Factory and Field Test Data Shown . . . . . | 64 |
10-5.1-3 | Comparison of Test Results With Independent Control Conditions . | 64 |
10-5.2 | Comparison of Test Results Using the Initial Field Test as the Control. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . | 67 |
Tables | ||
6-4-1 | Circulating Water Bath Temperature Measurements (Example 6-4.1) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . | 20 |
6-4-2 | Systematic Uncertainty of Average Circulating Water Bath Temperature Measurements (Example 6-4.1). . . . . . . . . . . . . . . . . . | 21 |
7-6.1-1 | Table of Data (Example 7-6.1) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . | 25 |
7-6.1-2 | Summary of Data (Example 7-6.1) . . . . . . . . . . . . . . . . . . . . . . . . . . . . | 26 |
7-6.2-1 | Table of Data (Example 7-6.2) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . | 26 |
7-6.2-2 | Summary of Data (Example 7-6.2) . . . . . . . . . . . . . . . . . . . . . . . . . . . . | 27 |
8-1 | Burst Pressures (Example 8-1-1). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . | 29 |
8-6.4.5 Systematic Standard Uncertainty Components for Yˆ Determined
from Regression Equation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
9-2-1 Table of Data. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
9-2-2 Summary of Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
10-1.2 Average Values (Example 10-1) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
10-1.3-1 Standard Deviations (Example 10-1) . . . . . . . . . . . . . . . . . . . . . . . . . . 45
10-1.3-2 Summary of Average Velocity Calculation (Example 10-1) . . . . . . . . 45
10-1.6 Standard Deviation of Average Velocity (Example 10-1) . . . . . . . . . . 46
10-1.9 Uncertainty of Result (Example 10-1) . . . . . . . . . . . . . . . . . . . . . . . . . 48
10-2.1-1 Uncalibrated Case (Example 10-2) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
10-2.1-2 Absolute Sensitivity Coefficients in Example 10-2 (Calculated
Numerically) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
10-2.1-3 Absolute Sensitivity Coefficients in Example 10-2 (Calculated
Analytically) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
10-2.1-4 Absolute Contributions of Uncertainties of Independent Parameters (Example 10-2: Uncalibrated Case). . . . . . . . . . . . . . . . . . . . . . . . . . 52
10-2.1-5 Summary: Uncertainties in Absolute Terms (Example 10-2:
Uncalibrated Case) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
10-2.1.1-1 Relative Uncertainty of Measurement (Example 10-2: Uncalibrated
Case) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
10-2.1.1-2 Relative Contributions of Uncertainties of Independent Parameters (Example 10-2: Uncalibrated Case). . . . . . . . . . . . . . . . . . . . . . . . . . 53
10-2.1.1-3 Summary: Uncertainties in Relative Terms for the Uncalibrated
Case . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
10-2.1.1-4 Relative Uncertainties of Independent Parameters (Example 10-2: Calibrated Case) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
10-2.1.1-5 Relative Contributions of Uncertainties of Independent Parameters (Example 10-2: Calibrated Case). . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
10-2.1.1-6 Summary: Uncertainties in Relative Terms for the Calibrated
Case . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
10-2.1.1-7 Summary: Comparison Between Calibrated and Uncalibrated
Cases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
Absolute Contributions of Uncertainties of Independent Parameters (Example 10-3: Uncalibrated, Nonsymmetrical Systematic
Uncertainty Case) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
Summary: Uncertainties in Absolute Terms (Example 10-3:
Uncalibrated, Nonsymmetrical Systematic Uncertainty Case) . . . . 56
10-4.1-1 Elemental Random Standard Uncertainties Associated With Error
Sources Identified in Para. 10-4.2 . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
10-4.1-2 Independent Parameters. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
10-4.1-3 Calculated Result . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
10-4.3.2-1 Inlet and Exit Pressure Elemental Systematic Standard
Uncertainties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
10-4.3.2-2 Inlet and Exit Temperature Elemental Systematic Standard
Uncertainties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
10-4.7 Evaluation of Analysis Error . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
10-5.1-1 Pump Design Data (Tc p 20°C) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
10-5.1-2 Summary of Test Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
10-5.2-1 Uncertainty Propagation for Comparison With Independent
Control. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
10-5.2-2 Summary: Uncertainties in Absolute Terms . . . . . . . . . . . . . . . . . . . . 66
10-5.2-3 Summary of Results for Each Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
10-5.3-1 Uncertainty Propagation for Comparative Uncertainty . . . . . . . . . . . 68
10-5.3-2 Sensitivity Coefficient Estimates for Comparative Analysis . . . . . . . . 68
Nonmandatory Appendices
A Statistical Considerations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
B Uncertainty Analysis Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84
C Propagation of Uncertainty Through Taylor Series . . . . . . . . . . . . . . . . . . . . . . . 87
D The Central Limit Theorem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
NOTICE
All Performance Test Codes must adhere to the requirements of ASME PTC 1, General Instructions. The following information is based on that document and is included here for emphasis and for the convenience of the user of the Supplement. It is expected that the Code user is fully cognizant of Sections 1 and 3 of ASME PTC 1 and has read them prior to applying this Supplement.
ASME Performance Test Codes provide test procedures which yield results of the highest level of accuracy consistent with the best engineering knowledge and practice currently available. They were developed by balanced committees representing all concerned interests and specify procedures, instrumentation, equipment-operating requirements, calculation methods, and uncertainty analysis.
When tests are run in accordance with a Code, the test results themselves, without adjustment for uncertainty, yield the best available indication of the actual performance of the tested equipment. ASME Performance Test Codes do not specify means to compare those results to contractual guarantees. Therefore, it is recommended that the parties to a commercial test agree before starting the test and preferably before signing the contract on the method to be used for comparing the test results to the contractual guarantees. It is beyond the scope of any Code to determine or interpret how such comparisons shall be made.
FOREWORD
In March 1979 the Performance Test Codes Supervisory Committee activated the PTC 19.1 Committee to revise a 1969 draft of a document entitled PTC 19.1 “General Considerations.” The PTC 19.1 Committee proceeded to develop a Performance Test Code Instruments and Apparatus Supplement which was published in 1985 as PTC 19.1-1985, “Measurement Uncer- tainty,” and which was intended—along with its subsequent editions—to provide a means of eventual standardization of nomenclature, symbols, and methodology of measurement uncertainty in ASME Performance Test Codes.
Work on the revision of the original 1985 edition began in 1991. The two-fold objective was to improve the usefulness to the reader regarding clarity, conciseness, and technical treatment of the evolving subject matter, as well as harmonization with the ISO “Guide to the Expression of Uncertainty in Measurement.” That revision was published as PTC 19.1- 1998, “Test Uncertainty,” the new title reflecting the appropriate orientation of the document. The effort to update the 1998 revision began immediately upon completion of that docu- ment. This 2005 revision is notable for the following significant departures from the 1998 text:
Nomenclature adopted for this revision is more consistent with the ISO Guide. Uncer- tainties remain conceptualized as “systematic” (estimate of the effects of fixed error not observed in the data), and “random” (estimate of the limits of the error observed from the scatter of the test data). The new aspec