Evaluating Measurement Accuracy

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.

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 Function

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

tion

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



8.1.3 Individual 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 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