Evaluating Measurement Accuracy (eBook)

The first 16 years of Dr. Semyon Rabinovich’s career were spent in industry, where he created a number of electrical measuring instruments, including those that were mass-produced, as well as unique direct-voltage measuring instruments reaching the theoretical sensitivity limits. Following this, Dr. Rabinovich organized the Laboratory of Theoretical Metrology at the All-Union State Research Institute of Metrology (VNIIM) in the former USSR and was the head of this lab for the next 16 years. After a period in the aftermath of his decision to emigrate from the USSR when any reference to his name was a taboo, VNIIM now lists Dr. Rabinovich among their “renown scientists” in the theoretical metrology area. After moving to the USA, he took part in the work of two ISA Subcommittees in preparing ISA-RP67.04 “Setpoints for Nuclear Safety-Related Instrumentation” and “Methodologies for the Determination of Setpoints in Nuclear Safety-Related Instrumentation.” He has published six books and more than 100 other publications including 21 patents. Previously this book was published by American Institute of Physics. 

Preface to the Third Edition 6
Contents 9
Abbreviations of Names of Organizations and Institutions 14
Chapter 1: General Concepts in the Theory of Measurements 15
1.1 Basic Concepts and Terms 15
1.2 The Basic Metrological Problems 18
1.3 New Forms of International Cooperation in Metrology 24
1.4 Postulates of the Theory of Measurements 26
1.5 Classification of Measurements 32
1.6 Classification of Measurement Errors 37
1.7 General Approach to Evaluation of Measurement Inaccuracy 39
1.8 Presentation of Measurement Results 41
Chapter 2: Measuring Instruments and Their Properties 44
2.1 Types of Measuring Instruments 44
2.2 Metrological Characteristics of Measuring Instruments 46
2.3 Rating of the Errors of Measuring Instruments 49
2.4 Dynamic Characteristics of Measuring Instruments 62
2.5 Calibration and Verification of Measuring Instruments 67
2.6 Designing a Calibration Scheme 72
2.7 Statistical Analysis of Measuring Instrument Errors 79
Chapter 3: Statistical Methods for Experimental Data Processing 84
3.1 Methods for Describing Random Quantities 84
3.2 Requirements for Statistical Estimates 88
3.3 Evaluation of the Parameters of the Normal Distribution 90
3.4 Elimination of Outlying Data 94
3.5 Construction of Confidence Intervals 96
3.6 Reliability of Estimation of the Variance of a Sample from a Normal Distribution 101
3.7 Reliability of Estimation of the Standard Deviation of the Mean of a Sample from a Normal Distribution 102
3.8 Testing Hypotheses About the Form of the Distribution Function 104
3.9 Testing for Homogeneity of Samples 106
3.10 Robust Estimates 113
3.11 Bootstrap Construction of Confidence Intervals 116
3.12 Application of the Bayes´ Theorem 117
Chapter 4: Direct Measurements 119
4.1 Relation Between Single and Multiple Measurements 119
4.2 Classification of Elementary Errors 122
4.3 Modeling of Elementary Errors 127
4.3.1 Absolutely Constant Errors 127
4.3.2 Conditionally Constant Errors 129
4.3.3 Purely Random Errors 130
4.3.4 Quasirandom Errors 130
4.4 Composition of Uniform Distributions 131
4.5 Methods for Precise Measurements 137
4.6 Accuracy of Single Measurements Using a Measuring Instrument Under Reference Conditions 139
4.7 Accuracy of Single Measurements Using a Measuring Instrument Under Rated Conditions 142
4.8 Comparison of Standard Deviation and Confidence Interval as Measurement Accuracy Indicators 148
4.9 Accuracy of Multiple Direct Measurements 151
4.10 Universal Method for Summation of Random and Systematic Errors 155
4.11 Analysis of the Accuracy of the Universal Method for Summation of Systematic and Random Errors 158
4.12 Comparison of Different Methods for Combining Systematic and Random Errors 161
Chapter 5: Indirect Measurements 166
5.1 Terminology and Classification 166
5.2 Correlation Coefficient and Its Calculation 168
5.3 Constructing the Composition of Histograms 170
5.4 Traditional Method of Measurement Data Processing 179
5.5 Shortcomings of the Traditional Method 184
5.6 Method of Reduction 187
5.7 Method of Enumeration 190
5.8 Accuracy of Single Indirect Measurements Under Reference Conditions for Instruments Involved 194
5.9 Accuracy of Single Indirect Measurements Under Rated Conditions for Instruments Involved 196
5.10 Accuracy of a Single Measurement with a Chain of Instruments 197
5.11 The Monte Carlo Method 199
Chapter 6: Combined and Simultaneous Measurements 201
6.1 General Remarks About the Method of Least Squares 201
6.2 Measurements with Linear Equally Accurate Conditional Equations 203
6.3 Measurements with Linear Unequally Accurate Conditional Equations 206
6.4 Linearization of Nonlinear Conditional Equations 208
6.5 Examples of the Application of the Method of Least Squares 210
6.6 General Remarks on Determination of the Parameters in Formulas From Empirical Data 215
6.7 Construction of Transfer Functions of Measuring Transducers 217
Chapter 7: Combining the Results of Measurements 222
7.1 Introductory Remarks 222
7.2 Theoretical Principles 223
7.3 Effect of the Error of the Weights on the Error of the Weighted Mean 227
7.4 Combining the Results of Measurements with Predominately Random Errors 229
7.5 Combining the Results of Measurements Containing Both Systematic and Random Errors 231
Chapter 8: Examples of Measurements and Measurement Data Processing 235
8.1 Voltage Measurement with a Pointer-Type Voltmeter 235
8.1.1 Single Measurement Under Reference Condition of the Voltmeter 236
8.1.2 Single Measurement Under Rated Condition of the Voltmeter 238
8.2 Voltage Measurement with a Potentiometer and a Voltage Divider 239
8.3 Comparison of Mass Measures 244
8.4 Measurement of Electric Power at High Frequency 246
8.5 An Indirect Measurement of the Electrical Resistance of a Resistor 247
8.5.1 Application of the Traditional Method 247
8.5.2 Application of the Method of Reduction 250
8.6 Measurement of the Density of a Solid Body 252
8.6.1 Application of the Traditional Method 252
8.6.2 Application of Method of Enumeration 255
8.7 Measurement of Ionization Current 258
8.8 Measurement of the Activity of a Radioactive Source 261
Chapter 9: The International Vocabulary of Metrology and the Guide to the Expression of Uncertainty in Measurement: Analysis, ... 264
9.1 Introduction 264
9.2 Critique of the ``International Vocabulary of Metrology´´ 266
9.3 Critique of the ``Guide to the Expression of Uncertainty in Measurement´´ 270
9.3.1 Scope of GUM 270
9.3.2 Philosophy of GUM 271
9.3.3 Terminology of the GUM 271
9.3.4 Evaluation of the Uncertainty in the GUM 273
9.4 Roots of the Drawbacks of GUM and VIM 274
9.5 Perspectives on Fixing GUM and VIM 276
Chapter 10: Step-by-Step Guide to the Evaluating of Measurement Accuracy 277
10.1 Introduction 277
10.2 Conventions for Expressing Accuracy of Measuring Instruments 277
10.2.1 Analog Instruments 278
10.2.2 Digital Instruments 278
10.3 Single Measurements 280
10.3.1 Direct Single Measurements Under Reference Conditions 280
10.3.2 Direct Single Measurements Under Rated Conditions 283
10.3.3 Indirect Single Measurements Under Reference Conditions 285
10.3.4 Indirect Single Measurements Under Rated Conditions 288
10.4 Multiple Measurements 290
10.4.1 Universal Method of Summation of Systematic and Random Errors 290
10.4.2 Direct Multiple Measurements 293
10.4.3 Linear Independent Indirect Multiple Measurements 294
10.4.4 Nonlinear Independent Indirect Multiple Measurements: Method of Linearization 296
10.4.5 Dependent Multiple Indirect Measurements: Method of Reduction 299
10.4.6 Independent Indirect Multiple Measurements: Method of Enumeration 301
Errata to: Evaluating Measurement Accuracy 305
Conclusion 306
Measurement Data Processing: Past, Present, and Next Steps 306
Appendix 310
Glossary 316
References 320
Standards and Recommendations 320
Books and Articles 321
Index 323