Evaluating Measurement Accuracy

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

3.9 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

5.9 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

8.2 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 andthe 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

Glossary

Index