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1、MeasurementUncertainty:Methods and ApplicationsFourth EditionMeasurementUncertainty:Methods and ApplicationsFourth EditionbyRonald H. DieckNoticeThe information presented in this publication is for the general education of the reader. Because nei-ther the author nor the publisher have any control ov

2、er the use of the information by the reader, both the author and the publisher disclaim any and all liability of any kind arising out of such use. The reader is expected to exercise sound professional judgment in using any of the information presented in a particu-lar application.Additionally, neith

3、er the author nor the publisher have investigated or considered the effect of any patents on the ability of the reader to use any of the information in a particular application. The reader is responsible for reviewing any possible patents that may affect any particular use of the information pre-sen

4、ted.Any references to commercial products in the work are cited as examples only. Neither the author nor the publisher endorse any referenced commercial product. Any trademarks or tradenames referenced belong to the respective owner of the mark or name. Neither the author nor the publisher make any

5、repre-sentation regarding the availability of any referenced commercial product at any time. The manufac-turers instructions on use of any commercial product must be followed at all times, even if in conflict with the information in this publication.Copyright 2007 ISAThe Instrumentation, Systems, an

6、d Automation SocietyAll rights reserved. Printed in the United States of America. 109876543 ISBN-13: 978-1-55617- 915-0ISBN-10: 1-55617-915-4No part of this work may be reproduced, stored in a retrieval system, or transmitted in any form orby any means, electronic, mechanical, photocopying, recordin

7、g or otherwise, without the prior writ-ten permission of the publisher.ISA67 Alexander Drive, P.O. Box 12277Research Triangle Park, NC 27709www.isa.orgLibrary of Congress Cataloging-in-Publication Data in process.Dieck, Ronald H. Measurement uncertainty : methods and applications / by Ronald H. Diec

8、k. - 4th ed. p. cm. ISBN 1-55617-915-4 1. Mensuration. 2. Uncertainty. I. Title. T50.D53 2006 530.8-dc22 2006036563vTABLE OF CONTENTSPREFACE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ixUNIT 1 Introduction and Overv

9、iew . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31-1. Course Coverage. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31-2. Purpose. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31-3. Audience

10、 and Prerequisites . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41-4. Study Material. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41-5. Organization and Sequence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41-6. Course

11、Objectives/Learning Objectives . . . . . . . . . . . . . . . . . . . . . . 51-7. Course Length . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5UNIT 2 Fundamentals of Measurement Uncertainty Analysis. . . . . . . . . 92-1. The Purpose of Engineering, Experimen

12、tal, or Test Measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92-2. Measurement Error Definition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102-3. Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

13、. . . . . . . . 32Exercises. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34UNIT 3 The Measurement Uncertainty Model . . . . . . . . . . . . . . . . . . . . . 393-1. The Statement of Measurement Uncertainty . . . . . . . . . . . . . . . . . 393-2. Gro

14、uping and Categorizing Error Sources . . . . . . . . . . . . . . . . . . . 403-3. The Calculation of Measurement Uncertainty (Symmetrical Systematic Uncertainties) . . . . . . . . . . . . . . . . . . . . . 433-4. The Uncertainty Statement (Symmetrical Systematic Standard Uncertainties) . . . . . . .

15、 . . . . . 483-5. Computing the Uncertainty Interval (Symmetrical Systematic Uncertainties) . . . . . . . . . . . . . . . . . . . . . 513-6. The Calculation of Measurement Uncertainty (Nonsymmetrical Standard Systematic Uncertainties). . . . . . . . . 543-7. Common Uncertainty Model Summary . . . .

16、. . . . . . . . . . . . . . . . . 593-8. Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60Exercises. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62UNIT 4 How To Do It Summary . . . . . . . . . .

17、. . . . . . . . . . . . . . . . . . . . . . . . 674-1. Review of Nomenclature. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 674-2. How To Do It Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 694-3. Calculation of Random Standard Uncertainties . . . .

18、 . . . . . . . . . . 694-4. Obtaining and Combining Systematic Standard Uncertainties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 734-5. Nonsymmetrical Systematic Standard Uncertainties . . . . . . . . . . 794-6. Step-by-Step Instructions. . . . . . . . .

19、. . . . . . . . . . . . . . . . . . . . . . . . . 804-7. Treatment of Calibration Errors (Uncertainties) . . . . . . . . . . . . . . 834-8. Simplified Uncertainty Analysis for Calibrations . . . . . . . . . . . . . 854-9. Business Decisions and the Impact of Measurement Uncertainty . . . . . . . . .

20、 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 964-10. The Timing of an Uncertainty Analysis . . . . . . . . . . . . . . . . . . . . . 994-11. Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103References . . . . . . . .

21、. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103Exercises. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103vi Table of ContentsUNIT 5 Uncertainty (Error) Propagation . . . . . . . . . . . . . . . . . . . . . . . . . . 1115-1

22、. General Considerations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1115-2. The Need for Uncertainty Propagation. . . . . . . . . . . . . . . . . . . . . 1115-3. Theoretical Considerations: Methods for Uncertainty Propagation . . . . . . . . . . . . . . . . . . . . . . . . .

23、 . . . . . . . . . . . . . . . . . . . 1135-4. Uncertainty Propagation Examples . . . . . . . . . . . . . . . . . . . . . . . . 1265-5. Detailed Equation for Uncertainty Propagation . . . . . . . . . . . . . 1415-6. Uncertainty of Results Derived from X-Y Plots . . . . . . . . . . . . . . 1425-7. Su

24、mmary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 146References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 146Exercises. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

25、. . . . 147UNIT 6 Weighting Method for Multiple Results . . . . . . . . . . . . . . . . . . 1536-1. The Purpose of Multiple Measurements of the Same Test Result . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1536-2. Fundamentals of Weighting by Uncertainty

26、. . . . . . . . . . . . . . . . 153References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161Exercises. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161UNIT 7 Applied Considerations . . . . . . . . . . . . .

27、 . . . . . . . . . . . . . . . . . . . . 1657-1. General Considerations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1657-2. Choice of Error (and Uncertainty) Units . . . . . . . . . . . . . . . . . . . . 1657-3. Treatment of Outliers. . . . . . . . . . . . . . . . . . . . . .

28、 . . . . . . . . . . . . . . 1687-4. Curve Fitting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1717-5. Correlation Coefficients: Their Use and Misuse . . . . . . . . . . . . . 1817-6. Tests for Normality, Probability Plots . . . . . . . . . . . . . . . . . .

29、 . . . . 1837-7. Sampling Error . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1877-8. Selecting Instrumentation Based on Vendor Uncertainty Statements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 192References . . . . . . . . . . . . . . . .

30、 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 194Exercises. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 195UNIT 8 Presentation of Results. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2018-1. General Considerations . .

31、 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2018-2. Presentation Content . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2028-3. Illustration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2028-4. Summary . . . .

32、 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 206APPENDIX A Suggested Reading and Study Materials . . . . . . . . . . . . . . . . . . 209APPENDIX B Glossary. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 212APPENDIX

33、 C Nomenclature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 221APPENDIX D Students t for 95% Confidence. . . . . . . . . . . . . . . . . . . . . . . . . . . 229APPENDIX E 5% Significant Thompsons . . . . . . . . . . . . . . . . . . . . . . . . . . . 233APPENDI

34、X F Areas Under the Normal Curve . . . . . . . . . . . . . . . . . . . . . . . . . . 237APPENDIX G Pressure Instrumentation Selection Example . . . . . . . . . . . . . . 241APPENDIX H Alternate Measurement Uncertainty Analysis Approach . . . . 253APPENDIX I Solutions to All Exercises. . . . . . . .

35、. . . . . . . . . . . . . . . . . . . . . . . . 257Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 273Prime Equations for Uncertainty Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

36、 . 275(H9270)DedicationThe author dedicates this edition to his wife, Donna; to his three children, Mark, Duane, and Heidi, and to their growing families of grandchildren.ixPREFACEThis fourth edition of Measurement Uncertainty: Methods and Applications is designed to provide an understanding of the

37、importance of the role played by measurement uncertainty analysis in any test or experimental measurement process. No test data should be considered without knowing their uncertainty.Examples and problems have been included to illustrate the principles and applications of measurement uncertainty ana

38、lysis. Sections on the business impact of measurement uncertainty and the treatment of calibration uncertainty have been included. The very latest in measurement uncertainty technology is included in this revised edition. In addition, all the material herein is in full harmony with the ISO Guide to

39、the Expression of Uncertainty in Measurement. Specifically, the terminology and symbols are in agreement with the US National Standard on Test Uncertainty and in harmony with the ISO Guide. The term “standard uncertainty” is now employed throughout to indicate that each uncertainty mentioned is one

40、standard deviation of the average for a group of measurements. Thus, instead of reporting “random uncertainty” and “systematic uncertainty,” this text now uses the terms “random standard uncertainty” and “systematic standard uncertainty.”This material will be useful to test engineers, process engine

41、ers, control engineers, researchers, plant supervisors, managers, executives, and all others who need a basic understanding of the assessment and impact of uncertainty in test and experimental measurements. In addition, technical school, college, and university students will find this course useful

42、in gaining insight into the impact of errors in their measurements as well as estimating the effects of such errors with measurement uncertainty analysis.AcknowledgmentsSpecial appreciation is noted for the original and pioneering work of Dr. Robert Abernethy, whose early studies permitted the devel

43、opment of the universal uncertainty model fundamental to the methods of this text. My personal and most sincere gratitude remains that which goes to my Lord and Savior Jesus Christ, who saw fit to grant me the talents and abilities without which this writing would not have been possible at all. In H

44、im there is no uncertainty, only the certainty of life everlasting.Ron Dieck, 2006Unit 1:Introduction andOverview3UNIT 1Introduction and OverviewWelcome to Measurement Uncertainty: Methods and Applications. The first unit of this self-study program provides the information needed to proceed through

45、the course.Learning ObjectivesWhen you have completed this unit you should:A. Know the nature of material to be presented.B. Understand the general organization of the course.C. Know the course objectives.1-1. Course CoverageThis course includes the basics of the measurement uncertainty model, the u

46、se of correlation, curve-fitting problems, probability plotting, combining results from different test methods, calibration errors, and uncertainty (error) propagation for both independent and dependent error sources. Extra attention is directed toward the problem of developing confidence in uncerta

47、inty analysis results and using measurement uncertainty to select instrumentation systems. Special emphasis on understanding is achieved through the working of numerous exercises. After completing this course, the student will be able to apply uncertainty analysis techniques to most experimental tes

48、t problems in order to help achieve the test objectives more productively and at lower cost.1-2. PurposeThe purpose of this book is to convey to the student a comprehensive knowledge of measurement uncertainty methods through documentation that is logically categorized and readily utilized in practi

49、cal situations that confront an experimenter. Course structure is purposely divided into units that represent specific segments of measurement uncertainty methodology. Using this approach, the student will be able to proceed through the text, learning the methodology in an orderly fashion, and then return to specific topics as the need arises during experimental analysis.The book contains numerous exercises intended to provide practical experience in working measurement uncertainty problems; several example calculations are presented to provide learning clarity for specific principles