Measurement Errors and Uncertainties: Theory and Practice

Preface......Page 5
Contents......Page 9
1.1. Basic Concepts and Terms......Page 13
1.2. Metrology and the Basic Metrological Problems......Page 15
1.3. Initial Points of the Theory of Measurements......Page 22
1.4. Classification of Measurements......Page 27
1.5. Classification of Measurements Errors......Page 32
1.6. Principles of Estimation of Measurement Errors and Uncertainties......Page 34
1.7. Presentation of Results of Measurements; Rules for Rounding Off......Page 36
1.8. Basic Conventional Notations......Page 39
2.1. Types of Measuring Instruments......Page 41
2.2. The Concept of an Ideal Instrument: Metrological General Information About
Measurements......Page 44
2.3. Standardization of the Metrological Characteristics of Measuring Instruments......Page 48
2.4. Some Suggestions for Changing Methods of Standardization of Errors of Measuring Instruments and Their Analysis......Page 60
2.5. Dynamic Characteristics of Measuring Instruments and Their Standardization......Page 64
2.6. Statistical Analysis of the Errors of Measuring Instruments Based on Data Provided by Calibration Laboratories......Page 69
3.1. Relationship Between Error and Uncertainty......Page 73
3.2. Classification of Elementary Errors......Page 74
3.3. Mathematical Models of Elementary Errors......Page 76
3.4. Methods for Describing Random Quantities......Page 78
3.5. Construction of the Composition of Uniform Distributions......Page 82
3.6. Universal Method for Constructing the Composition of Distributions......Page 86
3.7. Natural Limits of Measurements......Page 93
4.1. Requirements for Statistical Estimations......Page 103
4.2. Estimation of the Parameters of the Normal Distribution......Page 104
4.3. Outlying Results......Page 107
4.4. Construction of Confidence Intervals......Page 109
4.5. Methods for Testing Hypotheses About the Form of the Distribution Function of a Random Quantity......Page 113
4.6. Methods for Testing Sample Homogeneity......Page 115
4.7. Trends in Applied Statistics and Experimental Data Processing......Page 121
4.8. Example: Analysis of Measurement Results in Comparisons of Measures of Mass......Page 124
5.1. Relation Between Single and Multiple Measurements......Page 127
5.2. Identification and Elimination of Systematic Errors......Page 130
5.3. Estimation of Elementary Errors......Page 136
5.4. Method for Calculating the Errors and Uncertainties of Single Measurements......Page 140
5.5. Example: Calculation of Uncertainty in Voltage Measurements Performed with a Pointer-Type Voltmeter......Page 144
5.6. Methods for Calculating the Uncertainty in Multiple Measurements......Page 150
5.7. Comparison of Different Methods for Combining Systematic and Random Errors......Page 161
5.8. Essential Aspects of the Estimation of Measurement Errors when the Number of Measurements Is Small......Page 165
5.9. General Plan for Estimating Measurement Uncertainty......Page 167
6.1. Basic Terms and Classification......Page 171
6.2. Correlation Coefficient and its Calculation......Page 172
6.3. The Traditional Method of Experimental Data Processing......Page 174
6.4. Shortcomings of the Traditional Method......Page 178
6.5. The Method of Reduction......Page 180
6.6. The Method of Transformation......Page 181
6.7. Errors and Uncertainty of Indirect Measurement Results......Page 186
7.1. An Indirect Measurement of the Electrical Resistance of a Resistor......Page 191
7.2. The Measurement of the Density of a Solid Body......Page 194
7.3. The Measurement of Ionization Current by the Compensation Method......Page 201
7.4. The Measurement of Power at High Frequency......Page 204
7.5. The Measurement of Voltage with the Help of a Potentiometer and a Voltage Divider......Page 205
7.6. Calculation of the Uncertainty of the Value of a Compound Resistor......Page 209
8.1. General Remarks About the Method of Least Squares......Page 213
8.2. Measurements with Linear Equally Accurate Conditional Equations......Page 215
8.3. Reduction of Linear Unequally Accurate Conditional Equations to Equally Accurate Conditional Equations......Page 217
8.4. Linearization of Nonlinear Conditional Equations......Page 218
8.5. Examples of the Applications of the Method of Least Squares......Page 220
8.6. Determination of the Parameters in Formulas from Empirical Data and Construction of Calibration Curves......Page 225
9.2. Theoretical Principles......Page 231
9.3. Effect of the Error of the Weights on the Error of the Weighted Mean......Page 235
9.4. Combining the Results of Measurements in Which the Random Errors Predominate......Page 237
9.5. Combining the Results of Measurements Containing both Systematic and Random Errors......Page 238
9.6. Example: Measurement of the Activity of Nuclides in a Source......Page 245
10.1. The Problems of Calculating Measuring Instrument Errors......Page 249
10.2. Methods for Calculating Instrument Errors......Page 250
10.3. Calculation of the Errors of Electric Balances (Unique Instrument)......Page 261
10.4. Calculation of the Error of ac Voltmeters (Mass-Produced Instrument)......Page 263
10.5. Calculation of the Error of Digital Thermometers (Mass-Produced Instrument)......Page 270
11.1. Types of Calibration......Page 275
11.2. Estimation of the Errors of Measuring Instruments in Verification......Page 277
11.3. Rejects of Verification and Ways to Reduce Their Number......Page 281
11.4. Calculation of a Necessary Number of Standards......Page 287
12.1. Measurement Data Processing: Past, Present, and Future......Page 295
12.2. Remarks on the “International Vocabulary o fBasic and General Terms in Metrology”......Page 297
12.3. Drawbacks of the “Guide to the Expression of Uncertainty in Measurement”......Page 298
Appendix......Page 301
Glossary......Page 307
References......Page 311
Index......Page 315