THE THEORY OF MEASUREMENTS
CHAPTER 1: GENERAL CONCEPTS IN THE THEORY OF MEASUREMENTS 11 BASIC CONCEPTS AND TERMS 12 THE BASIC METROLOGICAL PROBLEMS 13 NEW FORMS OF INTERNATIONAL COOPERATION IN METROLOGY 14 POSTULATES OF THE THEORY OF MEASUREMENTS 15 CLASSIFICATION OF MEASUREMENTS 16 CLASSIFICATION OF MEASUREMENT ERRORS 17 GENERAL APPROACH TO EVALUATION OF MEASUREMENT INACCURACY 18 PRESENTATION OF MEASUREMENT RESULTS CHAPTER 2: MEASURING INSTRUMENTS AND THEIR PROPERTIES 21 TYPES OF MEASURING INSTRUMENTS 22 METROLOGICAL CHARACTERISTICS OF MEASURING INSTRUMENTS 23 RATING OF THE ERRORS OF MEASURING INSTRUMENTS 24 DYNAMIC CHARACTERISTICS OF MEASURING INSTRUMENTS 25 CALIBRATION AND VERIFICATION OF MEASURING INSTRUMENTS 26 DESIGNING A CALIBRATION SCHEME 27 STATISTICAL ANALYSIS OF MEASURING INSTRUMENT ERRORS CHAPTER 3: STATISTICAL METHODS FOR EXPERIMENTAL DATA PROCESSING 31 METHODS FOR DESCRIBING RANDOM QUANTITIES 32 REQUIREMENTS FOR STATISTICAL ESTIMATES 33 EVALUATION OF THE PARAMETERS OF THE NORMAL DISTRIBUTION 34 ELIMINATION OF OUTLYING DATA 35 CONSTRUCTION OF CONFIDENCE INTERVALS 36 RELIABILITY OF ESTIMATION OF THE VARIANCE OF A SAMPLE FROM A NORMAL DISTRIBUTION 37 RELIABILITY OF ESTIMATION OF THE STANDARD DEVIATION OF THE MEAN OF A SAMPLE FROM A NORMAL DISTRIBUTION 38 TESTING HYPOTHESES ABOUT THE FORM OF THE DISTRIBUTION FUNCTION 39 TESTING FOR HOMOGENEITY OF SAMPLES 310 ROBUST ESTIMATES 311 BOOTSTRAP CONSTRUCTION OF CONFIDENCE INTERVALS 312 APPLICATION OF THE BAYES´ THEOREM CHAPTER 4: DIRECT MEASUREMENTS 41 RELATION BETWEEN SINGLE AND MULTIPLE MEASUREMENTS 42 CLASSIFICATION OF ELEMENTARY ERRORS 43 MODELING OF ELEMENTARY ERRORS 431 ABSOLUTELY CONSTANT ERRORS 432 CONDITIONALLY CONSTANT ERRORS 433 PURELY RANDOM ERRORS 434 QUASIRANDOM ERRORS 44 COMPOSITION OF UNIFORM DISTRIBUTIONS 45 METHODS FOR PRECISE MEASUREMENTS 46 ACCURACY OF SINGLE MEASUREMENTS USING A MEASURING INSTRUMENT UNDER REFERENCE CONDITIONS 47 ACCURACY OF SINGLE MEASUREMENTS USING A MEASURING INSTRUMENT UNDER RATED CONDITIONS 48 COMPARISON OF STANDARD DEVIATION AND CONFIDENCE INTERVAL AS MEASUREMENT ACCURACY INDICATORS 49 ACCURACY OF MULTIPLE DIRECT MEASUREMENTS 410 UNIVERSAL METHOD FOR SUMMATION OF RANDOM AND SYSTEMATIC ERRORS 411 ANALYSIS OF THE ACCURACY OF THE UNIVERSAL METHOD FOR SUMMATION OF SYSTEMATIC AND RANDOM ERRORS 412 COMPARISON OF DIFFERENT METHODS FOR COMBINING SYSTEMATIC AND RANDOM ERRORS CHAPTER 5: INDIRECT MEASUREMENTS 51 TERMINOLOGY AND CLASSIFICATION 52 CORRELATION COEFFICIENT AND ITS CALCULATION 53 CONSTRUCTING THE COMPOSITION OF HISTOGRAMS 54 TRADITIONAL METHOD OF MEASUREMENT DATA PROCESSING 55 SHORTCOMINGS OF THE TRADITIONAL METHOD 56 METHOD OF REDUCTION 57 METHOD OF ENUMERATION 58 ACCURACY OF SINGLE INDIRECT MEASUREMENTS UNDER REFERENCE CONDITIONS FOR INSTRUMENTS INVOLVED 59 ACCURACY OF SINGLE INDIRECT MEASUREMENTS UNDER RATED CONDITIONS FOR INSTRUMENTS INVOLVED 510 ACCURACY OF A SINGLE MEASUREMENT WITH A CHAIN OF INSTRUMENTS 511 THE MONTE CARLO METHOD CHAPTER 6: COMBINED AND SIMULTANEOUS MEASUREMENTS 61 GENERAL REMARKS ABOUT THE METHOD OF LEAST SQUARES 62 MEASUREMENTS WITH LINEAR EQUALLY ACCURATE CONDITIONAL EQUATIONS 63 MEASUREMENTS WITH LINEAR UNEQUALLY ACCURATE CONDITIONAL EQUATIONS 64 LINEARIZATION OF NONLINEAR CONDITIONAL EQUATIONS 65 EXAMPLES OF THE APPLICATION OF THE METHOD OF LEAST SQUARES 66 GENERAL REMARKS ON DETERMINATION OF THE PARAMETERS IN FORMULAS FROM EMPIRICAL DATA 67 CONSTRUCTION OF TRANSFER FUNCTIONS OF MEASURING TRANSDUCERS CHAPTER 7: COMBINING THE RESULTS OF MEASUREMENTS 71 INTRODUCTORY REMARKS 72 THEORETICAL PRINCIPLES 73 EFFECT OF THE ERROR OF THE WEIGHTS ON THE ERROR OF THE WEIGHTED MEAN 74 COMBINING THE RESULTS OF MEASUREMENTS WITH PREDOMINATELY RANDOM ERRORS 75 COMBINING THE RESULTS OF MEASUREMENTS CONTAINING BOTH SYSTEMATIC AND RANDOM ERRORS CHAPTER 8: EXAMPLES OF MEASUREMENTS AND MEASUREMENT DATA PROCESSING 81 VOLTAGE MEASUREMENT WITH A POINTER-TYPE VOLTMETER 811 SINGLE MEASUREMENT UNDER REFERENCE CONDITION OF THE VOLTMETER 812 SINGLE MEASUREMENT UNDER RATED CONDITION OF THE VOLTMETER 82 VOLTAGE MEASUREMENT WITH A POTENTIOMETER AND A VOLTAGE DIVIDER 83 COMPARISON OF MASS MEASURES 84 MEASUREMENT OF ELECTRIC POWER AT HIGH FREQUENCY 85 AN INDIRECT MEASUREMENT OF THE ELECTRICAL RESISTANCE OF A RESISTOR 851 APPLICATION OF THE TRADITIONAL METHOD 852 APPLICATION OF THE METHOD OF REDUCTION 86 MEASUREMENT OF THE DENSITY OF A SOLID BODY 861 APPLICATION OF THE TRADITIONAL METHOD 862 APPLICATION OF METHOD OF ENUMERATION 87 MEASUREMENT OF IONIZATION CURRENT 88 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, 91 INTRODUCTION 92 CRITIQUE OF THE ``INTERNATIONAL VOCABULARY OF METROLOGY´´ 93 CRITIQUE OF THE ``GUIDE TO THE EXPRESSION OF UNCERTAINTY IN MEASUREMENT´´ 931 SCOPE OF GUM 932 PHILOSOPHY OF GUM 933 TERMINOLOGY OF THE GUM 934 EVALUATION OF THE UNCERTAINTY IN THE GUM 94 ROOTS OF THE DRAWBACKS OF GUM AND VIM 95 PERSPECTIVES ON FIXING GUM AND VIM CHAPTER 10: STEP-BY-STEP GUIDE TO THE EVALUATING OF MEASUREMENT ACCURACY 101 INTRODUCTION 102 CONVENTIONS FOR EXPRESSING ACCURACY OF MEASURING INSTRUMENTS 1021 ANALOG INSTRUMENTS 1022 DIGITAL INSTRUMENTS 103 SINGLE MEASUREMENTS 1031 DIRECT SINGLE MEASUREMENTS UNDER REFERENCE CONDITIONS 1032 DIRECT SINGLE MEASUREMENTS UNDER RATED CONDITIONS 1033 INDIRECT SINGLE MEASUREMENTS UNDER REFERENCE CONDITIONS 1034 INDIRECT SINGLE MEASUREMENTS UNDER RATED CONDITIONS 104 MULTIPLE MEASUREMENTS 1041 UNIVERSAL METHOD OF SUMMATION OF SYSTEMATIC AND RANDOM ERRORS 1042 DIRECT MULTIPLE MEASUREMENTS 1043 LINEAR INDEPENDENT INDIRECT MULTIPLE MEASUREMENTS 1044 NONLINEAR INDEPENDENT INDIRECT MULTIPLE MEASUREMENTS: METHOD OF LINEARIZATION 1045 DEPENDENT MULTIPLE INDIRECT MEASUREMENTS: METHOD OF REDUCTION 1046 INDEPENDENT INDIRECT MULTIPLE MEASUREMENTS: METHOD OF ENUMERATION CONCLUSION MEASUREMENT DATA PROCESSING: PAST, PRESENT, AND NEXT STEPS APPENDIX GLOSSARY 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