A practical reference on theory and methods of estimating measurement errors and uncertainty for both scientists and engineers in industry and experimental research. Building on the fundamentals of measurement theory, this book offers a wealth of practial recommendations and procedures. It differs from the majority of books in that it balances coverage of probabilistic methods with detailed information on the characterization, calibration, standardization and limitations of measuring instruments, with specific examples from both electrical and mechanical systems. In addition to a general updating to reflect current research, new material in this edition includes increased coverage of indirect measurements, with a new, simpler, more efficient method for this class of measurements. 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
measurement Errors And Uncertainties Addresses The Most Important Problems That Physicists And Engineers Encounter When Estimating Errors And Uncertainty. Building From The Fundamentals Of Measurement Theory, The Author Develops The Theory Of Accuracy Of Measurements And Offers A Wealth Of Practical Recommendations And Examples Of Applications.
this New Edition Covers A Wide Range Of Subjects, Including:
- Basic Concepts Of Metrology
- Measuring Instruments Characterization, Standardization And Calibration
-estimation Of Errors And Uncertainty Of Single And Multiple Measurements
- Modern Probability-based Methods Of Estimating Measurement Uncertainty
with This New Edition, The Author Completes The Development Of The New Theory Of Indirect Measurements. This Theory Provides More Accurate And Efficient Methods For Processing Indirect Measurement Data. It Eliminates The Need To Calculate The Correlation Coefficient - A Stumbling Block In Measurement Data Processing - And Offers For The First Time A Way To Obtain The Confidence Intervals. In Other Words, This New Theory Provides Means To Calculate A Well-grounded Estimate Of Measurement Uncertainty For This Complex But Widely Used Type Of Measurements.
acclaim For Previous Editions:
extremely Useful To Metrologists And To Anyone Interested In Measurement Errors
(measurement Science And Technology)
i Suggest That Every Technical Library Should Own A Copy Of Measurement Errors. Serious Experimentalists Whose Interests Are Broad Will Surely Want To Examine The Book With The Intent Of Buying It.
(applied Mechanics Review)
The major objective of this book is to give methods for estimating errors and uncertainties of real measurements: measurements that are performed in industry, commerce, and experimental research. This book is needed because the existing theory of measurement errors was historically developed as an abstract mathematical discipline. As a result, this theory allows estimation of uncertainties of some ideal measurements only and is not applicable to most practical cases. In particular, it is not applicable to single measurements. This situation did not bother mathematicians, whereas engineers, not being bold enough to assert that the mathematical theory of errors cannot satisfy their needs, solved their particular problems in one or another ad hoc manner. Actually, any measurement of a physical quantity is not abstract, but it involves an entirely concrete procedure that is always implemented with concrete te- nical devices—measuring instruments—under concrete conditions. Therefore, to obtain realistic estimates of measurement uncertainties, mathematical methods must be supplemented with methods that make it possible to take into account data on properties of measuring instruments, the conditions under which measu- ments are performed, the measurement procedure, and other features of measu- ments. The importance of the methods of estimating measurement inaccuracies for practice can scarcely be exaggerated. Indeed, in another stage of planning a m- surement or using a measurement result, one must know its error limits or unc- tainty. Inaccuracy of a measurement determines its quality and is related to its cost. Measurement Errors and Uncertainties addresses the most important problems that physicists and engineers encounter when estimating errors and uncertainty. Building from the fundamentals of measurement theory, the author develops the theory of accuracy of measurements and offers a wealth of practical recommendations and examples of applications. This new edition covers a wide range of subjects, including: - Basic concepts of metrology - Measuring instruments characterization, standardization and calibration -Estimation of errors and uncertainty of single and multiple measurements - Modern probability-based methods of estimating measurement uncertainty With this new edition, the author completes the development of the new theory of indirect measurements. This theory provides more accurate and efficient methods for processing indirect measurement data. It eliminates the need to calculate the correlation coefficient - a stumbling block in measurement data processing - and offers for the first time a way to obtain the confidence intervals. In other words, this new theory provides means to calculate a well-grounded estimate of measurement uncertainty for this complex but widely used type of measurements. Acclaim for previous editions: "Extremely useful to metrologists and to anyone interested in measurement errors" (MEASUREMENT SCIENCE AND TECHNOLOGY) "I suggest that every technical library should own a copy of Measurement Errors. Serious experimentalists whose interests are broad will surely want to examine the book with the intent of buying it". (Applied Mechanics Review) This is a new edition of a best-selling reference on the theory and methods of estimating measurement errors and uncertainty. Building upon the fundamentals of measurement theory, the book offers a wealth of practical recommendations and procedures -- completely updated to include current research. Specific examples from both electrical and mechanical systems make the book useful to scientists and engineers.
