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
About the Author:
The goal of Evaluating Measurement Accuracy: A Practical Approach is to present methods for estimating the accuracy of measurements performed in industry, trade, and scientific research. From developing the theory of indirect measurements to proposing new methods of reduction, transformation, and enumeration, this work encompasses the full range of measurement data processing. It includes many examples that illustrate the application of general theory to typical problems encountered in measurement practice. As a result, the book serves as an inclusive reference work for data processing of all types of measurements: single and multiple, combined and simultaneous, direct (both linear and nonlinear), and indirect (both dependent and independent). It is a working tool for experimental scientists and engineers of all disciplines who work with instrumentation. It is also a good resource for natural science and engineering students and for technicians performing measurements in industry.
A key feature of the book is a new general theory of measurements that is both well-grounded and oriented towards real-life needs of measurement practitioners. Although the traditional theory focuses on multiple measurements, single measurements are the ones most commonly used. This book presents methods for evaluating accuracy of single measurements and answers other fundamental questions not addressed adequately by the traditional theory, such as how to combine various components o
f measurement inaccuracy when evaluating the complete uncertainty of a measurement result. For its second edition, the book adds significant new material to incorporate recent metrological developments and expand coverage, including:
- The new method of enumeration of experimental data processing for independent indirect multiple measurements which is precise and does not rely on questionable assumptions.
- The analysis of reliability of estimates of statistical parameters of samples from a normal distribution.
- A significantly expanded analysis of two fundamental documents in modern metrology, the International Vocabulary of Metrology and the Guide to the Expression of Uncertainty in Measurement.
- Completely rewritten sections devoted to accuracy of a single measurement taken with a chain of instruments and the Monte Carlo method.
