Measurement uncertainties: physical parameters and calibration of instruments
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| Format: | Book |
| Language: | English |
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Berlin [u.a.]
Springer
2012
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| Online Access: | Inhaltstext Inhaltsverzeichnis |
| Physical Description: | XIX, 321 S. graph. Darst. |
| ISBN: | 9783642209888 |
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| 100 | 1 | |a Gupta, S. V. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Measurement uncertainties |b physical parameters and calibration of instruments |c S. V. Gupta |
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 2012 | |
| 300 | |a XIX, 321 S. |b graph. Darst. | ||
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IMAGE 1
CONTENTS
SOME IMPORTANT DEFINITIONS 1
1.1 INTRODUCTION 1
1.2 TERMS PERTAINING TO QUANTITY 2
1.2.1 QUANTITY 2
1.2.2 SYSTEM OF BASE QUANTITIES 2
1.2.3 DERIVED QUANTITY 2
1.2.4 QUANTITY EQUATION 3
1.2.5 DIMENSION OF A QUANTITY 3
1.2.6 MEASURAND 4
1.2.7 TRUE VALUE OF A QUANTITY 4
1.2.8 CONVENTIONAL TRUE VALUE OF A QUANTITY 4
1.2.9 MEASURED VALUE 5
1.2.10 RELATION IN BETWEEN MEASURED VALUE AND TRUE OR CONVENTIONAL TRUE
VALUE 5
1.3 TERMS PERTAINING TO MEASUREMENT 5
1.3.1 MEASUREMENT 5
1.3.2 METHOD OF MEASUREMENT 5
1.3.3 SUBSTITUTION METHOD 5
1.3.4 DIFFERENTIAL METHOD 6
1.3.5 NULLMETHOD 6
1.3.6 MEASUREMENT PROCEDURE 6
1.3.7 RESULT OF MEASUREMENT 6
1.3.8 ERROR 6
1.3.9 SPURIOUS ERROR 7
1.3.10 RELATIVE ERROR 7
1.3.11 RANDOM ERROR 7
1.3.12 SYSTEMATIC ERROR 7
1.3.13 ACCURACY OF MEASUREMENT 8
1.3.14 PRECISION OF MEASUREMENT RESULT 8
1.3.15 REPEATABILITY 8
BIBLIOGRAFISCHE INFORMATIONEN HTTP://D-NB.INFO/1010922378
DIGITALISIERT DURCH
IMAGE 2
CONTENTS
1.3.16 REPRODUCIBILITY (OF MEASUREMENT RESULTS) 9
1.3.17 CORRECTION 9
1.4 TERMS PERTAINING TO STATISTICS 9
1.4.1 OBSERVATION 9
1.4.2 INDEPENDENT OBSERVATIONS 9
1.4.3 POPULATION 10
1.4.4 SAMPLE 10
1.4.5 MEASUREMENT 10
1.4.6 POPULATION OF MEASUREMENT 10
1.4.7 SAMPLE OF MEASUREMENTS 11
1.4.8 FREQUENCY/RELATIVE FREQUENCY 11
1.4.9 MEAN 11
1.4.10 SAMPLEMEAN 11
1.4.11 POPULATION MEAN 11
1.4.12 MERITS AND DEMERITS OF ARITHMETIC MEAN [3] 12 1.4.13 MEDIAN 12
1.4.14 QUARTILES 12
1.4.15 DISPERSION 13
1.4.16 STANDARD DEVIATION 13
1.4.17 VARIANCE 13
1.4.18 SAMPLE STANDARD DEVIATION 14
1.4.19 POPULATION STANDARD DEVIATION 14
1.4.20 ESTIMATE OF POPULATION STANDARD DEVIATION 14 1.4.21 ESTIMATE OF
POPULATION AND SAMPLE STANDARD DEVIATIONS-RELATION 15
1.4.22 INDEPENDENT VARIABLE 15
1.4.23 DEPENDENT VARIABLE OR RESPONSE VARIABLE 15 1.4.24 CORRELATION 15
1.4.25 CORRELATION COEFFICIENT 15
1.4.26 COVARIANCE 16
1.4.27 RANDOM VARIABLE 16
1.4.28 DISCRETE RANDOM VARIABLE 16
1.4.29 CONTINUOUS RANDOM VARIABLE 16
1.4.30 PROBABILITY 16
1.4.31 PROBABILITY DISTRIBUTION 17
1.4.32 NORMAL DISTRIBUTION 17
1.4.33 PROPERTIES OF NORMAL DISTRIBUTION 18
1.4.34 PROBABLE ERROR 18
1.4.35 RANGE 18
1.4.36 CONFIDENCE LEVEL 18
1.4.37 CONFIDENCE INTERVAL 19
1.4.38 OUTLIER 19
1.4.39 PARAMETER 19
1.4.40 RANDOM SELECTION 19
1.4.41 SAMPLE STATISTIC 19
IMAGE 3
CONTENTS
1.4.42 ERROR 20
1.4.43 STANDARD ERROR, OR STANDARD DEVIATION OF THE MEAN 20
1.4.44 UNCERTAINTY 20
1.4.45 EVALUATIONS OF UNCERTAINTY 20
1.4.46 RANDOM UNCERTAINTY(E R ) 21
1.4.47 SYSTEMATIC UNCERTAINTY(/ S ) 22
1.4.48 STANDARD UNCERTAINTY 22
1.4.49 EXPANDED UNCERTAINTY 22
1.4.50 EXPRESSING UNCERTAINTY OF MEASUREMENT 22 1.4.51 COVERAGE INTERVAL
22
1.4.52 COVERAGE PROBABILITY 23
1.4.53 CENTRAL LIMIT THEOREM 23
1.5 INFLUENCE QUANTITY 23
1.6 INSTRUMENTS AND STANDARDS 24
1.6.1 REPEATABILITY OF AN INSTRUMENT 24
1.6.2 PRECISION OF THE INSTRUMENT 24
1.6.3 ACCURACY OF AN INSTRUMENT 24
1.6.4 ACCURACY OF A STANDARD 25
1.6.5 DIFFERENCE BETWEEN UNCERTAINTY AND ACCURACY 25
1.6.6 DIFFERENCE BETWEEN THE CORRECTION, ERROR AND UNCERTAINTY 25
1.6.7 CORRECTION FACTOR 26
1.6.8 DISCRIMINATION THRESHOLD 26
1.7 SOME SPECIAL INTEGRALS AND FUNCTIONS 26
1.7.1 GAMMA FUNCTION 26
1.7.2 BETA FUNCTION OF FIRST KIND B(M,N) 27
1.7.3 ALTERNATIVE FORM OF BETA FUNCTION 27
1.7.4 BETA FUNCTION OF SECOND KIND B (M,N) 28
1.7.5 CAUCHY DISTRIBUTION 28
1.7.6 ARC SINE(U-SHAPED) DISTRIBUTION 29
REFERENCES 29
DISTRIBUTION FUNCTIONS 31
2.1 INTRODUCTION 31
2.2 RANDOM VARIABLE 31
2.3 DISCRETE AND CONTINUOUS VARIABLES 32
2.4 DISCRETE FUNCTIONS 32
2.4.1 PROBABILITY DISTRIBUTION OF A RANDOM VARIABLE 32 2.4.2 DISCRETE
PROBABILITY FUNCTION 32
2.5 DISTRIBUTION FUNCTION 33
2.5.1 CONTINUOUS DISTRIBUTION FUNCTION 33
2.5.2 DISCRETE DISTRIBUTION 33
IMAGE 4
CONTENTS
2.6 PROBABILITY DENSITY FUNCTION 33
2.6.1 DISCRETE PROBABILITY FUNCTION 34
2.7 DISCRETE PROBABILITY FUNCTIONS 34
2.7.1 BINOMIAL PROBABILITY DISTRIBUTION 34
2.7.2 POISSON'S DISTRIBUTION 36
2.8 CONTINUOUS PROBABILITY DISTRIBUTIONS 38
2.8.1 NORMAL PROBABILITY FUNCTION 38
2.8.2 CUMUL ATIVE DISTRIBUTION OF THE NORMAL PROBABILITY FUNCTION 39
2.8.3 NORMAL DISTRIBUTION AND PROBABILITY TABLES 40
2.8.4 MEAN AND VARIANCE OF A LINEAR COMBINATION OF NORMAL VARIATES 41
2.8.5 STANDARD DEVIATION OF MEAN 41
2.8.6 DEVIATION FROM THE MEAN 42
2.8.7 STANDARD DEVIATION OF STANDARD DEVIATION 43
2.8.8 NOMENCLATURE FOR NORMAL DISTRIBUTION 46
2.8.9 PROBABILITY FUNCTION OF THE RATIO OF TWO NORMAL VARIATES [ 1 ] 46
2.8.10 IMPORTANCE OF NORMAL DISTRIBUTION 48
2.8.11 COLLATION OF DATA FROM VARIOUS LABORATORIES [2] 48
REFERENCES 51
OTHER PROBABILITY FUNCTIONS 53
3.1 INTRODUCTION 53
3.2 IMPORTANT DISTRIBUTIONS 53
3.2.1 RECTANGULAR DISTRIBUTION 53
3.2.2 TRIANGULAR PROBABILITY FUNCTION 55
3.2.3 TRAPEZOIDAL PROBABILITY FUNCTION 56
3.3 SMALL SAMPLE DISTRIBUTIONS 58
3.3.1 THE STUDENT'S T DISTRIBUTION 59
3.3.2 THE X 2 DISTRIBUTION 66
3.3.3 THE F-DISTRIBUTION 69
3.3.4 UPPER AND LOWER PERCENTAGE POINTS 71
3.3.5 APPLICATION OF F-TEST 72
3.3.6 FOR EQUALITY OF SEVERAL MEANS 73
3.4 COMBINING OF VARIANCES OF VARIABLES FOLLOWING DIFFERENT PROBABILITY
DISTRIBUTION FUNCTIONS 73
REFERENCES 74
EVALUATION OF MEASUREMENT DATA 75
4. 1 INTRODUCTION 75
4.2 EVALUATION OF VALIDITY OF EXTREME VALUES OF MEASUREMENT RESULTS 75
4.2.1 OUTLINE (DIXON)TEST 76
IMAGE 5
CONTENTS
4.3 EVALUATION OF THE MEANS OBTAINED FROM TWO SETS OF MEASUREMENT
RESULTS 77
4.3.1 TWO MEANS COMING FROM THE SAME SOURCE 78
4.3.2 TEST FOR TWO MEANS COMING FROM DIFFERENT SOURCES 83 4.4 COMPARISON
OF VARIANCES OF TWO SETS OF MEASUREMENT RESULTS 85
4.4.1 NUMERICAL EXAMPLE 86
4.5 MEASUREMENTS CONCERNING TRAVELLING STANDARDS 86
4.5.1 MEAN AND STANDARD DEVIATION FOR EACH LABORATORY 89 4.5.2
INTER-LABORATORIES STANDARD DEVIATION 91
4.5.3 INTRA-LABORATORY STANDARD DEVIATION 91
4.6 F-TEST FOR INTERNAL AND EXTERNAL CONSISTENCY 92
4.6.1 F-TEST FOR INTER- AND INTRA-LABORATORY VARIANCES 92 4.6.2 WEIGHT
FACTORS 94
4.6.3 F-TEST FOR VARIANCES 97
4.7 STANDARD ERROR OF THE OVERALL MEAN 97
4.7.1 RESULTS INCONSISTENT 97
4.8 ANALYSIS OF VARIANCE 98
4.8.1 ONE-WAY ANALYSIS OF VARIANCE 98
4.9 TESTS FOR UNIFORMITY OF VARIANCES 105
4.9.1 BARTLETT'S TEST FOR UNIFORMITY OF MANY VARIANCES 105 4.9.2 COCHRAN
TEST FOR HOMOGENEITY OF VARIANCES 107 REFERENCES 108
PROPAGATION OF UNCERTAINTY 109
5.1 MATHEMATICAL MODELLING 109
5.1.1 MEAN OF MEASURAND (DEPENDENT VARIABLE) 110 5.1.2 FUNCTIONAL
RELATIONSHIP AND INPUT QUANTITIES 110 5.1.3 EXPANSION OF A FUNCTION I LL
5.1.4 COMBINATION OF ARITHMETIC MEANS 113
5.1.5 COMBINATION OF VARIANCES 113
5.1.6 VARIANCE OF THE MEAN 113
5.2 UNCERTAINTY 114
5.2.1 COMBINED STANDARD UNCERTAINTY 114
5.2.2 EXPANDED UNCERTAINTY 115
5.3 TYPE A EVALUATION OF UNCERTAINTY 116
5.3.1 NUMERICAL EXAMPLE FOR CALCULATION OF TYPE A EVALUATION OF STANDARD
UNCERTAINTY 117
5.4 POOLED VARIANCE 118
5.4.1 VALIDITY 118
5.4.2 APPLICABLE 118
5.4.3 USES 118
5.4.4 NEED 119
5.4.5 CALCULATION OF POOLED VARIANCE 119
5.4.6 USES OF POOLED VARIANCE 121
5.4.7 CONCLUDING REMARKS 124
IMAGE 6
XIV CONTENTS
5.5 TYPE B EVALUATION OF STANDARD UNCERTAINTY 125
5.5.1 TYPE B EVALUATION OF UNCERTAINTY 125
5.5.2 COMMON UNCERTAINTIES EVALUATED BY TYPE B 126 5.6 VARIANCE AND
UNCERTAINTY RANGE 126
5.6.1 NORMAL DISTRIBUTION 126
5.6.2 RECTANGULAR DISTRIBUTION 126
5.6.3 TRIANGULAR DISTRIBUTION 127
5.6.4 TRAPEZOIDAL DISTRIBUTION 127
REFERENCES 129
6 UNCERTAINTY AND CALIBRATION OF INSTRUMENTS 131
6.1 INTRODUCTION 131
6.2 LINEAR RELATION 132
6.2.1 THE CLASSICAL METHOD ,. 133
6.2.2 MATRIX METHOD 135
6.3 UNCERTAINTY 137
6.4 NUMERICAL EXAMPLE 138
6.4.1 CALIBRATION OF A PROVING RING 138
6.4.2 CALIBRATION OF A GLASS SCALE 141
6.5 OTHER FUNCTIONS 142
6.5.1 EXPONENTIAL FUNCTION 143
6.6 POWER FUNCTION 145
6.6.1 UNCERTAINTY 146
6.6.2 NUMERICAL EXAMPLE 147
6.6.3 SAME DATA FITTED TO TWO FUNCTIONS 147
6.7 METHOD OF LEAST SQUARES 148
REFERECE 151
7 CALCULATION OF UNCERTAINTY 153
7.1 IMPORTANCE OF CORRECT MEASUREMENT 153
7.1.1 DISCOVERY OF INERT GASES 153
7.1.2 CORRECTION IN COMPOSITION OF AIR 154
7.1.3 MEANING OF QUANTITY BEING EXACT 154
7.1.4 INTERNATIONAL AGREEMENT WITH UNCERTAINTY 154
7.1.5 INITIATION BY BIPM 155
7.2 CLASSICAL PROCEDURE FOR UNCERTAINTY CALCULATIONS 155
7.2.1 RANDOM ERROR 155
7.2.2 SYSTEMATIC ERROR 156
7.2.3 CALCULATION OF RANDOM UNCERTAINTY (U R ) 156
7.2.4 COMBINATION OF RANDOM UNCERTAINTIES (W R ) 157 7.3 SOURCES OF
SYSTEMATIC UNCERTAINTY (/ S ) 158
7.4 COMBINATION OF SYSTEMATIC UNCERTAINTY 159
7.5 DOMINANT TERM 159
7.6 TOTAL OVERALL UNCERTAINTY U 160
7.7 OBJECTIONS TO THE ABOVE METHOD 160
IMAGE 7
CONTENTS
7.8 THE BIPM RECOMMENDATIONS 1980 BASIS OF ISO GUIDE (GUM) 161
7.9 ISO GUM-STEP-BY-STEP PROCEDURE FOR CALCULATION OF UNCERTAINTY 162
7.10 CALCULATION OF UNCERTAINTY 164
7.10.1 PROCEDURE FOR CALCULATION 164
7.10.2 RELATION BETWEEN RANGE AND STANDARD UNCERTAINTY 165 7.10.3
APPLICABILITY OF ISO GUM 166
7.11 PROPAGATION OF PROBABILITY DENSITY FUNCTION 167
7.11.1 STEP-BY-STEP PROCEDURE FOR MONTE-CARLO METHOD 167 7.11.2
TWO-STAGE BOOTSTRAP PROCEDURE 168
7.12 BAYESIAN STATISTICS 169
7.13 EXAMPLE FOR CALCULATIONS OF UNCERTAINTY 169
7.13.1 CALCULATION OF RANDOM UNCERTAINTY 170
7.13.2 SYSTEMATIC UNCERTAINTY 172
7.14 MERITS AND LIMITATIONS OF ISO GUM METHOD 174
7.14.1 MERITS OF ISO GUM 174
7.14.2 LIMITATIONS OF ISO GUM 175
REFERENCES 175
UNCERTAINTY IN CALIBRATION OF A SURFACE PLATE (FITTING A PLANE) 177 8.1
INTRODUCTION 177
8.2 PROCEDURE 178
8.3 DERIVATION OF FORMULAE FOR HEIGHT 180
8.3.1 HEIGHT OF A POINT ON THE DIAGONAL AC 180
8.3.2 HEIGHT OF A POINT ON THE DIAGONAL BD 181
8.3.3 HEIGHT OF A POINT ON THE SIDES AB 182
8.3.4 HEIGHT OF A POINT ON THE SIDE DC 183
8.3.5 HEIGHT OF A POINT ON THE SIDES AD 183
8.3.6 HEIGHT OF A POINT ON THE SIDE BC 184
8.3.7 HEIGHT OF A POINT ON THE MIDDLE SIDE GH 184
8.3.8 HEIGHT OF A POINT ON THE MIDDLE SIDE EF 185
8.3.9 HEIGHTS OF SOME IMPORTANT POINTS 186
8.4 NUMERICAL EXAMPLE 187
8.4.1 FOR DIAGONALS BD OR AC 187
8.4.2 FOR LONGER PARALLEL SIDES BA OR CD 188
8.4.3 FOR SIDES BC OR AD 189
8.4.4 FOR MIDDLE PARALLEL SIDES EF AND GH 190
8.5 FITTING A PLANE TO THE GIVEN DATA 191
8.5.1 STANDARD DEVIATION FROM THE MEAN PLANE 195
8.6 UNCERTAINTY IN MEASUREMENTS 195
8.6.1 UNCERTAINTY IN MEASURED HEIGHT OF A POINT 195
8.6.2 UNCERTAINTY IN DIFFERENCE IN HEIGHTS OF TWO POINTS ON THE DIAGONAL
199
8.6.3 POINTS ARE ON THE SAME STRAIGHT LINE 200
8.6.4 POINTS ON TWO DIFFERENT LINES 205
IMAGE 8
XVI CONTENTS
8.7 TYPE A EVALUATION OF UNCERTAINTY 209
8.8 TYPE B EVALUATION OF STANDARD UNCERTAINTY 209
8.8.1 UNCERTAINTY DUE TO THE FINITE DIGITAL READOUT OF THE MEASURING
INSTRUMENT 209
8.8.2 UNCERTAINTY DUE TO CERTIFIED ACCURACY OF THE MEASURING INSTRUMENT
210
8.8.3 UNCERTAINTY DUE TO UNSTABILITY OF THE INSTRUMENT 210 8.8.4 THE
ERROR IN NON-UNIFORMITY OF TEMPERATURE 210 8.8.5 EFFECTIVE DEGREES OF
FREEDOM 211
8.8.6 EXTENDED UNCERTAINTY 211
REFERENCES 211
9 UNCERTAINTY IN MASS MEASUREMENT 213
9.1 BALANCES 213
9.2 CHOICE OF STANDARD WEIGHTS 213
9.3 CALIBRATION OF BALANCE 214
9.3.1 REPEATABILITY 214
9.3.2 CALIBRATION OF SMALLEST SCALE INTERVAL 215
9.3.3 CALIBRATION OF BUILT-IN WEIGHT 216
9.3.4 UNCERTAINTY IN BALANCE CALIBRATION 217
9.3.5 LINEARITY CHECK 218
9.3.6 CHECK FOR OFF-CENTRE PLACEMENT OF WEIGHT/CORNER TEST 219
9.3.7 DISCRIMINATION TEST 219
9.4 UNCERTAINTY IN CALIBRATION OF WEIGHTS 220
9.5 MEASUREMENT REQUIREMENTS FOR VARIOUS CORRECTIONS 221 9.5.1 BUOYANCY
CORRECTION 221
9.5.2 MPE AND CORRECTION 221
9.5.3 CALIBRATION OF WEIGHTS AGAINST PT-IR STANDARD 222 9.5.4 COMPONENTS
OF RELATIVE UNCERTAINTY FOR AIR DENSITY . 222 9.6 MEASUREMENT
REQUIREMENTS FOR P, T, AND H 225
9.6.1 FOR 10 JIG UNCERTAINTY IN LKG 225
9.6.2 FOR 1 U,G UNCERTAINTY IN 1 KG 225
9.6.3 MEASUREMENT REQUIREMENT FOR CO2 225
9.7 UNCERTAINTY IN CALIBRATION OF WEIGHTS UNDER LEGAL METROLOGY. 226
9.7.1 REFERENCE STANDARD WEIGHTS (CLASS E2) 226
9.7.2 SECONDARY STANDARD WEIGHTS (CLASS FL). 227
9.7.3 WORKING STANDARD WEIGHTS (CLASS F2) 227
9.7.4 COMMERCIAL WEIGHTS (CLASS ML) 227
REFERENCES 228
10 UNCERTAINTY IN VOLUMETRIC MEASUREMENT 229
10.1 INTRODUCTION 229
10.2 UNCERTAINTY USING GRAVIMETRIC METHOD 230
10.2.1 TYPE A EVALUATION OF STANDARD UNCERTAINTY 230 10.2.2 TYPE B
EVALUATION OF STANDARD UNCERTAINTY 230
IMAGE 9
CONTENTS XVII
10.2.3 MATHEMATICAL MODEL FOR VOLUME (GRAVIMETRIC METHOD) 231
10.3 EXAMPLES OF A FEW MEASURES 233
10.3.1 UNCERTAINTY IN CALIBRATION OF CAPACITY OF A ONE-MARK PIPETTE 233
10.3.2 CALIBRATION OF A BURETTE 237
10.4 UNCERTAINTY USING VOLUMETRIC COMPARISON 238
10.4.1 MULTIPLE AND ONE-TO-ONE TRANSFER METHODS 238 10.4.2 CORRECTIONS
APPLICABLE IN VOLUMETRIC METHOD 238 10.4.3 REFERENCE TEMPERATURES 238
10.5 UNCERTAINTY IN CALIBRATION OF STORAGE TANKS 241
10.5.1 STORAGE TANKS 242
10.5.2 SOME IMPORTANT TERMS 242
10.5.3 MAXIMUM PERMISSIBLE ERROR IN STORAGE TANKS 242 10.5.4 MAXIMUM
PERMISSIBLE ERRORS IN TAPE MEASURES 243 10.5.5 MAXIMUM PERMISSIBLE
ERRORS IN CIRCUMFERENCE MEASUREMENT 243
10.6 PRINCIPLE OF PREPARING GAUGE TABLE (CALIBRATION TABLE) 243 10.6.1
EXTERNAL STRAPPING 244
10.6.2 INTERNAL STRAPPING 248
10.7 TANK DEFORMATION 249
10.8 UNCERTAINTY IN CALIBRATION OF A HYDROMETER BY COMPARISON METHOD 250
REFERENCES 252
11 UNCERTAINTY IN CALIBRATION OF SOME MORE PHYSICAL INSTRUMENTS 253 11.1
UNCERTAINTY IN CALIBRATION OF SLIP GAUGES 253
11.1.1 FRINGE FRACTION 254
11.1.2 ACTUAL AND AMBIENT TEMPERATURES OF THE SLIP GAUGE . 255 11.1.3
COEFFICIENT OF LINEAR EXPANSION 255
11.1.4 REFRACTIVITY OF AIR 256
11.1.5 PHASE CHANGE DUE TO REFLECTIONS FROM THE PLATEN AND END FACE OF
THE GAUGE 257
11.1.6 WRINGING OF THE GAUGE WITH THE PLATEN 257
11.1.7 INTERFEROMETER PARAMETER 257
11.1.8 PARALLELISM OF END FACES AND THEIR FLATNESS 258 11.2 UNCERTAINTY
IN CALIBRATION OF A MICROMETER AGAINST A STANDARD SLIP GAUGE 260
11.2.1 PARTICULARS OF STANDARD GAUGE AND MICROMETER UNDER-TEST 260
11.2.2 MATHEMATICAL MODEL 260
11.2.3 SOURCES OF UNCERTAINTY AND VALUES OF UNCERTAINTY COMPONENTS 261
11.2.4 COMBINED STANDARD UNCERTAINTY 263
IMAGE 10
XVIUE CONTENTS
11.2.5 EFFECTIVE DEGREE OF FREEDOM 263
11.2.6 EXPANDED UNCERTAINTY 263
11.3 UNCERTAINTY IN PRESSURE MEASURING INSTRUMENTS 263
11.3.1 PRIMARY STANDARD OF PRESSURE 263
11.3.2 TRANSFER STANDARDS 267
11.3.3 DEAD WEIGHT PRESSURE GAUGE TESTER 269
11.4 UNCERTAINTY IN TEMPERATURE MEASUREMENT AND INSTRUMENTS 270
11.4.1 UNCERTAINTY IN TRIPLE POINT AND OTHER FIXED POINTS 271 11.4.2
TEMPERATURE SCALE AND PRIMARY STANDARDS 271 11.4.3 DISSEMINATION OF
TEMPERATURE SCALE 272
11.4.4 THERMOCOUPLES AS TEMPERATURE MEASURING INSTRUMENTS 272
11.4.5 CALIBRATION OF A DIGITAL THERMOMETER 273
11.5 UNCERTAINTY IN LUMINOUS FLUX MEASUREMENT 275
11.5.1 PRINCIPLE 275
11.5.2 PROCEDURE FOR CALIBRATION 275
11.5.3 EXPRESSION FOR UNCERTAINTY 275
11.5.4 EXAMPLE 276
11.5.5 COMBINED RELATIVE UNCERTAINTY 277
11.5.6 EXPRESSION OF RESULTS WITH UNCERTAINTY 278
REFERENCES 278
12 UNCERTAINTY IN CALIBRATION OF ELECTRICAL INSTRUMENTS 279 12.1
UNCERTAINTY IN CALIBRATION OF RF POWER SENSOR 279
12.1.1 PRINCIPLE OF CALIBRATION 279
12.1.2 MATHEMATICAL MODELLING 279
12.1.3 TYPE A EVALUATION OF UNCERTAINTY 280
12.1.4 TYPE B EVALUATION OF UNCERTAINTY 281
12.1.5 COMBINED STANDARD AND EXPANDED UNCERTAINTY 283 12.1.6 STATEMENT
OF RESULT WITH UNCERTAINTY 283
12.2 UNCERTAINTY IN CALIBRATION OF A DIGITAL MULTI-METER 283 12.2.1
EQUIPMENT AND PRINCIPLE OF CALIBRATION USED 283 12.2.2 MATHEMATICAL
MODEL 284
12.2.3 TYPE A EVALUATION OF UNCERTAINTY 284
12.2.4 TYPE B EVALUATION OF UNCERTAINTY 285
12.2.5 COMBINED STANDARD UNCERTAINTY U C AND EXPANDED UNCERTAINTY 286
12.2.6 STATEMENT OF RESULTS 286
12.3 UNCERTAINTY IN CALIBRATION OF A DIGITAL INSTRUMENT 287 12.3.1
PRINCIPLE OF CALIBRATION 287
12.3.2 TYPE A EVALUATION OF UNCERTAINTY 287
12.3.3 TYPE B EVALUATION OF UNCERTAINTY 288
12.3.4 COMBINED UNCERTAINTY 289
12.3.5 EXPANDED UNCERTAINTY 289
12.3.6 STATEMENT OF RESULTS 289
IMAGE 11
CONTENTS XIX
12.4 UNCERTAINTY CALCULATION FOR CORRELATED INPUT QUANTITIES 289 12.4.1
TYPE A EVALUATION OF UNCERTAINTY 290
12.4.2 TYPE B EVALUATION OF UNCERTAINTY 290
12.5 VECTOR MEASURANDS 290
12.5.1 MATHEMATICAL MODEL 291
12.5.2 COMBINED UNCERTAINTY 291
12.5.3 CORRELATION COEFFICIENTS 292
REFERENCES 294
APPENDIX A 295
BIBLIOGRAPHY 309
INDEX 317 |
| any_adam_object | 1 |
| author | Gupta, S. V. |
| author_facet | Gupta, S. V. |
| author_role | aut |
| author_sort | Gupta, S. V. |
| author_variant | s v g sv svg |
| building | Verbundindex |
| bvnumber | BV039688736 |
| classification_rvk | UX 1100 UX 1300 ZQ 3100 ZQ 3115 |
| ctrlnum | (OCoLC)725083461 (DE-599)DNB1010922378 |
| dewey-full | 530.8 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 530 - Physics |
| dewey-raw | 530.8 |
| dewey-search | 530.8 |
| dewey-sort | 3530.8 |
| dewey-tens | 530 - Physics |
| discipline | Physik Mess-/Steuerungs-/Regelungs-/Automatisierungstechnik / Mechatronik |
| format | Book |
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| id | DE-604.BV039688736 |
| illustrated | Illustrated |
| indexdate | 2024-07-21T00:15:10Z |
| institution | BVB |
| isbn | 9783642209888 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-024537570 |
| oclc_num | 725083461 |
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| physical | XIX, 321 S. graph. Darst. |
| publishDate | 2012 |
| publishDateSearch | 2012 |
| publishDateSort | 2012 |
| publisher | Springer |
| record_format | marc |
| spelling | Gupta, S. V. Verfasser aut Measurement uncertainties physical parameters and calibration of instruments S. V. Gupta Berlin [u.a.] Springer 2012 XIX, 321 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Kalibrieren Messtechnik (DE-588)4198763-9 gnd rswk-swf Messunsicherheit (DE-588)4210374-5 gnd rswk-swf Messunsicherheit (DE-588)4210374-5 s Kalibrieren Messtechnik (DE-588)4198763-9 s DE-604 Erscheint auch als Online-Ausgabe 978-3-642-20989-5 X:MVB text/html http://deposit.dnb.de/cgi-bin/dokserv?id=3710624&prov=M&dok_var=1&dok_ext=htm Inhaltstext DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=024537570&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Gupta, S. V. Measurement uncertainties physical parameters and calibration of instruments Kalibrieren Messtechnik (DE-588)4198763-9 gnd Messunsicherheit (DE-588)4210374-5 gnd |
| subject_GND | (DE-588)4198763-9 (DE-588)4210374-5 |
| title | Measurement uncertainties physical parameters and calibration of instruments |
| title_auth | Measurement uncertainties physical parameters and calibration of instruments |
| title_exact_search | Measurement uncertainties physical parameters and calibration of instruments |
| title_full | Measurement uncertainties physical parameters and calibration of instruments S. V. Gupta |
| title_fullStr | Measurement uncertainties physical parameters and calibration of instruments S. V. Gupta |
| title_full_unstemmed | Measurement uncertainties physical parameters and calibration of instruments S. V. Gupta |
| title_short | Measurement uncertainties |
| title_sort | measurement uncertainties physical parameters and calibration of instruments |
| title_sub | physical parameters and calibration of instruments |
| topic | Kalibrieren Messtechnik (DE-588)4198763-9 gnd Messunsicherheit (DE-588)4210374-5 gnd |
| topic_facet | Kalibrieren Messtechnik Messunsicherheit |
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