“Evaluating Measurement Accuracy, 2nd Edition” is intended for those who are 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: scientists who advance the field of metrology, engineers and experimental scientists who use measurements as tool in their professions, students and graduate students in natural sciences and engineering, and, in parts describing practical recommendations, technicians performing mass measurements in industry, quality control, and trade. This book presents material from the practical perspective and offers solutions and recommendations for problems that arise in conducting real-life measurements.
This new edition adds a method for estimating accuracy of indirect measurements with independent arguments, whose development Dr. Rabinovich was able to complete very recently. This method, which is called the Method of Enumeration, produces estimates that are no longer approximate, similar to the way the method of reduction described in the first edition removed approximation in estimating uncertainty of indirect measurements with dependent arguments. The method of enumeration completes addressing the range of problems whose solutions signify the emergence of the new theory of accuracy of measurements. A new method is added for building a composition of histograms, and this method forms a theoretical basis for the method of enumeration.Additionally, as a companion to this book, a concise practical guide that assembles simple step-by-step procedures for typical tasks the practitioners are likely to encounter in measurement accuracy estimation is available at SpringerLink.
Table of Contents:
Preface
Chapter 1 General Concepts in the Theory of Measurement
1.1 Basic Concepts and Terms
1.2 The Basic Metrological Problems
1.3 New Forms of International Cooperation in Metrology
1.4 Postulates of the Theory of Measurements
1.5 Classification of Measurements
1.6 Classification of Measurement Errors
1.7 General Approach to Evaluation of Measurement Inaccuracy
1.8 Presentation of Measurement Results
Chapter 2 Measuring Instruments and Their Properties
2.1 Types of Measuring Instruments
2.2 Metrological Characteristics of Measuring Instruments
2.3 Rating of the Errors of Measuring Instruments
2.4 Dynamic Characteristics of Measuring Instruments
2.5 Calibration and Verification of Measuring Instruments
2.6 Designing a Calibration Scheme
2.7 Statistical Analysis of Measuring Instrument Errors
Chapter 3 Statistical Methods for Experimental Data Processing
3.1 Methods for Describing Random Quantities
3.2 Requirements for Statistical Estimates
3.3 Evaluation of the Parameters of Normal Distribution
3.4 Elimination of Outlying Data
3.5 Construction of Confidence Intervals
3.6 Reliability of Estimation of the Variance of a Sample from a Normal Distribution
3.7 Reliability of Estimation of the Standard Deviation of the Mean of a Sample from a Normal Distribution
3.8 Testing Hypotheses About the Form
of the Distribution Function3.9 Testing for Homogeneity of Samples
3.10 Robust Estimates
3.11 Application of the Bayes’ Theorem
Chapter 4 Direct Measurements
4.1 Relation Between Single and Direct Measurements
4.2 Classification of Elementary Errors
4.3 Modeling of Elementary Errors
4.3.1 Absolutely Constant Errors
4.3.2 Conditionally Constant Errors
4.3.3 Purely Random Errors
4.3.4 Quasirandom Errors
4.4 Composition of Uniform Distributions
4.5 Methods for Precise Measurements
4.6 Accuracy of Single Measurements Using a Measuring Instrument Under Reference Conditions
4.7 Accuracy of Single Measurements Using a Measuring Instrument Under Rated Conditions
4.8 Accuracy of Multiple Measurements Having Only Random Errors
4.9 Accuracy of Multiple Measurements Having Both Random and Systematic Errors
4.10 Analysis of the Accuracy of the Weighted Summation of Systematic and Random Errors
4.11 Comparison of Different Methods for Combining Systematic and Random Errors
Chapter 5 Indirect Measurements
5.1 Terminology and Classification
5.2 Correlation Coefficient and Its Calculation
5.3 Method for Constructing the Composition of Histograms
5.4 The Traditional Method
5.5 Merits and Shortcomings of the Traditional Method
5.6 The Method of Reduction
5.7 The Method of Transformation
5.8 The Method of Enumera
tion5.9 Total Uncertainty of Indirect Measurements
5.10 Accuracy of Single Indirect Measurements
5.11 Accuracy of a Single Measurement with a Chain of Instruments
5.12 The Monte Carlo Method
Chapter 6 Combined and Simultaneous Measurements
6.1 General Remarks About the Method of Least Squares
6.2 Measurements with Linear Equally Accurate Conditional Equations
6.3 Measurements with Linear Unequally Accurate Conditional Equations
6.4 Linearization of Nonlinear Conditional Equations
6.5 Examples of the Application of the Method of Least Squares
6.6 General Remarks on Determination of the Parameters in Formulas from Empirical Data
6.7 Construction of Transfer Functions of Meaning Transducers
Chapter 7 Combining The Results of Measurements
7.1 Introductory Remarks
7.2 Theoretical Principles
7.3 Effect of the Error of the Weights on the Error of the Weighted Mean
7.4 Combining the Results of Measurements with Predominately Random Errors
7.5 Combining the Results of Measurements with Both Systematic and Random Errors
7.6 Combining the Results of Single Measurements
Chapter 8 Examples of Measurements and Measurement Data Processing
8.1 Voltage Measurement with a Pointer-Type Voltmeter
8.1.1 A Priori Estimation of Measurement Inaccuracy
8.1.2 Universal Estimation of Measurement Inaccuracy
8.1.3 Individual Estimation of Measurement Inaccuracy8.2 Voltage Measurement with a Potentiometer and a Voltage Divider
8.3 Comparison of Mass Measures
8.4 Measurement of Electric Power at High Frequency
8.5 An Indirect Measurement of the Electrical Resistance of a Resistor
8.5.1 Application of the Traditional Method
8.5.2 Application of the Method of Reduction
8.6 Measurement of the Density of a Solid Body
8.6.1 Application of the Traditional Method
8.6.2 Application of the Method of Transformation
8.6.3 Application of the Method of Enumeration
8.7 Measurement of Ionization Current
8.8 Measurement of the Activity of a Radioactive Source
Chapter 9 The International Vocabulary of Metrology and the Guide to the Expression of Uncertainty in Measurement: Analysis, Criticism, and Recommendations
9.1 Introduction
9.2 Comparison of Standard Deviation and Confidence Interval as Measurement Accuracy Indicators
9.3 Critique of the International Vocabulary of Metrology
9.4 Critique of the Guide to the Expression of Uncertainty in Measurement
9.4.1 Scope of GUM
9.4.2 Philosophy of GUM
9.4.3 Terminology of the GUM
9.4.4 Evaluation of the Uncertainty in the GUM
9.5 Roots of the Drawbacks of GUM and VIM
9.6 Perspectives on Fixing GUM and VIM
Conclusion Measuremen
t Data Processing: Past, Present and Next Steps
Glossary
Index
