Rabinovich Evaluating Measurement Accuracy

A Practical Approach
2010
ISBN: 978-1-4419-1456-9
Verlag: Springer US
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 272 Seiten

'Evaluating Measurement Accuracy' is intended for anyone who is concerned with measurements in any field of science or technology. It reflects the latest developments in metrology and offers new results, but is designed to be accessible to readers at different levels: meteorologists, engineers and experimental scientists who use measurements as tools in their professions, graduate and undergraduate students in the natural sciences and engineering, and technicians performing complex measurements in industry, quality control, and trade. The material of the book is presented from the practical perspective and offers solutions and recommendations for problems that arise in conducting real-life measurements. This inclusion is a notable and unique aspect of this title as complex measurements done in industry and trade are often neglected in metrological literature, leaving the practitioners of these measurements to devise their own ad-hoc techniques.

Autoren/Hrsg.

Rabinovich, Semyon G.

Inhaltsverzeichnis

1;Evaluating
Measurement Accuracy
;1
1.1;Preface
;5
1.2;Contents
;9
1.3;About the Author
;13
1.4;Abbreviations
;15
1.5;1 General Concepts in the Theory of Measurements;17
1.5.1;1.1 Basic Concepts and Terms;17
1.5.2;1.2 The Basic Metrological Problems;20
1.5.3;1.3 New Forms of International Cooperation in Metrology;26
1.5.4;1.4 Postulates of the Theory of Measurements;28
1.5.5;1.5 Classification of Measurements;34
1.5.6;1.6 Classification of Measurements Errors;38
1.5.7;1.7 General Approach to Evaluation of Measurement Inaccuracy;41
1.5.8;1.8 Presentation of Measurement Results;42
1.6;2 Measuring Instruments and Their Properties;46
1.6.1;2.1 Types of Measuring Instruments;46
1.6.2;2.2 Metrological Characteristics of Measuring Instruments;48
1.6.3;2.3 Rating of the Errors of Measuring Instruments;51
1.6.4;2.4 Dynamic Characteristics of Measuring Instruments;64
1.6.5;2.5 Calibration and Verification of Measuring Instruments;68
1.6.6;2.6 Designing a Calibration Scheme;73
1.6.7;2.7 Statistical Analysis of Measuring Instrument Errors;80
1.7;3 Statistical Methods for Experimental Data Processing;85
1.7.1;3.1 Methods for Describing Random Quantities;85
1.7.2;3.2 Requirements for Statistical Estimates;89
1.7.3;3.3 Evaluation of the Parameters of the Normal Distribution;90
1.7.4;3.4 Elimination of Outlying Data;94
1.7.5;3.5 Construction of Confidence Intervals;96
1.7.6;3.6 Testing Hypotheses about the Form of the Distribution Function;101
1.7.7;3.7 Testing for Homogeneity of Samples;103
1.7.8;3.8 Robust Estimates;109
1.7.9;3.9 Application of the Bayes' Theorem;113
1.8;4 Direct Measurements;115
1.8.1;4.1 Relation Between Single and Multiple Measurements;115
1.8.2;4.2 Classification of Elementary Errors;118
1.8.3;4.3 Modeling of Elementary Errors;122
1.8.3.1;4.3.1 Absolutely Constant Errors;123
1.8.3.2;4.3.2 Conditionally Constant Errors;123
1.8.3.3;4.3.3 Purely Random Errors;124
1.8.3.4;4.3.4 Quasirandom Errors;124
1.8.4;4.4 Composition of Uniform Distributions;125
1.8.5;4.5 Methods for Precise Measurements;131
1.8.6;4.6 Accuracy of Single Measurements Using Measuring Instruments Under Reference Conditions;133
1.8.7;4.7 Accuracy of Single Measurements Using Measuring Instruments Under Rated Conditions;136
1.8.8;4.8 Accuracy of Multiple Measurements;142
1.8.9;4.9 Comparison of Different Methods for Combining Systematic and Random Errors;150
1.9;5 Indirect Measurements;154
1.9.1;5.1 Terminology and Classification;154
1.9.2;5.2 Correlation Coefficient and Its Calculation;155
1.9.3;5.3 The Traditional Method of Experimental Data Processing;158
1.9.4;5.4 Merits and Shortcomings of the Traditional Method;162
1.9.5;5.5 The Method of Reduction;165
1.9.6;5.6 The Method of Transformation;167
1.9.7;5.7 Total Uncertainty of Indirect Measurements;174
1.9.8;5.8 Accuracy of Single Indirect Measurements;179
1.9.9;5.9 Accuracy of a Single Measurement with a Chain of Instruments;180
1.9.10;5.10 Application of the Monte Carlo Method;182
1.10;6 Combined and Simultaneous Measurements;185
1.10.1;6.1 General Remarks About the Method of Least Squares;185
1.10.2;6.2 Measurements with Linear Equally AccurateConditional Equations;187
1.10.3;6.3 Measurements with Linear Unequally Accurate Conditional Equations;190
1.10.4;6.4 Linearization of Nonlinear Conditional Equations;192
1.10.5;6.5 Examples of the Application of the Method of Least Squares;193
1.10.6;6.6 General Remarks on Determination of the Parameters in Formulas from Empirical Data;198
1.10.7;6.7 Construction of Transfer Functions of Measuring Transducers;200
1.11;7 Combining the Results of Measurements;205
1.11.1;7.1 Introductory Remarks;205
1.11.2;7.2 Theoretical Principles;205
1.11.3;7.3 Effect of the Error of the Weights on the Errorof the Weighted Mean;209
1.11.4;7.4 Combining the Results of Measurements with Predominately Random Errors;211
1.11.5;7.5 Combining the Results of Measurements Containing Both Systematic and Random Errors;213
1.11.6;7.6 Combining the Results of Single Measurements;216
1.12;8 Examples of Measurements and Measurement Data Processing;221
1.12.1;8.1 Voltage Measurement with a Pointer-Type Voltmeter;221
1.12.1.1;8.1.1 A Priori Estimation of Measurement Inaccuracy;221
1.12.1.2;8.1.2 Universal Estimation of Measurement Inaccuracy;224
1.12.1.3;8.1.3 Individual Estimation of Measurement Inaccuracy;226
1.12.2;8.2 Voltage Measurement with a Potentiometer and a Voltage Divider;227
1.12.3;8.3 Comparison of Mass Measures;232
1.12.4;8.4 Measurement of Electric Power at High Frequency;233
1.12.5;8.5 An Indirect Measurement of the Electrical Resistance of a Resistor;234
1.12.5.1;8.5.1 Application of the Traditional Method;234
1.12.5.2;8.5.2 Application of the Method of Reduction;237
1.12.6;8.6 Measurement of the Density of a Solid Body;238
1.12.6.1;8.6.1 Application of the Traditional Method;238
1.12.6.2;8.6.2 Application of the Method of Transformation;241
1.12.7;8.7 Measurement of Ionization Current;245
1.12.8;8.8 Measurement of the Activity of a Radioactive Source;247
1.13;9 Conclusion;251
1.13.1;9.1 Measurement Data Processing: Past, Present,and Next Steps;251
1.13.2;9.2 Remarks on the International Vocabulary of Metrology;253
1.13.3;9.3 Drawbacks of the ``Guide to the Expression of Uncertainty in Measurement'';256
1.14;Appendix;261
1.15;Glossary;267
1.16;References;272
1.17;Erratum
;275
1.18;Index;277