Table of Contents
Preface vii
Abbreviations xix
1 International measurement system 1
1.1 Principles underlying the international measurement system 1
1.2 Classification of key comparisons of national measurement standards 5
1.3 Basic approaches to evaluating key comparison data 9
1.4 Expression of the degree of equivalence of measurement standards on the basis of a mixture of distributions 12
1.5 Evaluation of regional key comparison data 15
1.5.1 Two approaches to interpreting and evaluating data of regional key comparisons 15
1.5.2 Equation of linking RMO and CJPM KC. Optimization of the algorithm of evaluating degrees of equivalence 18
1.5.3 Different principles for transforming the results of regional comparisons 22
1.6 Bayesian approach to the evaluation of systematic biases of measurement results in laboratories 27
1.7 Evaluation of measurement results in calibrating material, measures and measuring instruments 31
1.7.1 Formulating a measurement model 32
1.7.2 Evaluation of measurement uncertainty 39
1.7.3 Calculation of measurement uncertainty associated with a value of a material measure using Bayesian analysis 42
1.7.4 Determination of the linear calibration functions of measuring instruments 44
1.8 Summary 51
2 Systems of reproducing physical quantities units and transferring their sizes 53
2.1 Classification of reproducing physical quantities units and systems for transferring their sizes (RUTS) 53
2.1.1 General ideas 53
2.1.2 Analysis of the RUTS systems 55
2.1.3 Varieties of the elements of a particular RUTS system 74
2.1.4 Interspecific classification of particular RUTS systems 77
2.1.5 Some problems of the specific classification of particular RUTS systems 85
2.1.6 The technical-economic efficiency of various RUTS systems 92
2.2 Physical-metrological fundamentals of constructing the RUTS systems 96
2.2.1 General ideas 96
2.2.2 Analysis of the state of the issue and the choice of the direction for basic research 97
2.2.3 Foundations of the description of RUTS systems 108
2.2.4 Fundamentals of constructing a RUTS system 129
2.2.5 System of reproduction of physical quantity units 145
2.3 Summary 158
3 Potential measurement accuracy 164
3.1 System approach to describing a measurement 164
3.1.1 Concept of a system approach to the formalized description of a measurement task 164
3.1.2 Formalized description of a measurement task 166
3.1.3 Measurement as a process of solving a measurement task 167
3.1.4 Formalization of a measurement as a system 169
3.1.5 Target function of a system 170
3.2 Potential and limit accuracies of measurements 171
3.3 Accuracy limitations due to the components of a measurement task 173
3.3.1 Measurand and object models 173
3.3.2 Physical limitations due to the discontinuity of a substance structure 175
3.3.3 Quantum-mechanical limitations 183
3.4 Influence of external measurement conditions 189
3.5 Space-time limitations 190
3.6 Summary 194
4 Algorithms for evaluating the result of two or three measurements 197
4.1 General ideas 197
4.2 Evaluation problem and classical means 201
4.2.1 Classification of measurement errors 201
4.2.2 Problem definition and classification of evaluation methods 204
4.2.3 Classical means and their properties 207
4.2.4 Geometrical interpretation of the means 220
4.2.5 Relations of the means 224
4.2.6 Inverse problems in the theory of means 229
4.2.7 Weighted means 237
4.3 Algorithms of optimal evaluation 245
4.3.1 Probability approach 245
4.3.2 Deterministic approach 248
4.4 Heuristic methods for obtaining estimates 258
4.4.1 Principles of heuristic evaluation 258
4.4.2 Linear and quasi-linear estimates 263
4.4.3 Difference quasi-linear estimates 266
4.4.4 Heuristic means for n = 2 273
4.5 Structural and diagnostic methods for obtaining estimates 283
4.5.1 Structural means 283
4.5.2 Use of redundant variables to increase evaluation accuracy 285
4.5.3 Application of diagnostic algorithms for screening a part of measurements 289
4.5.4 Systematization and analysis of evaluation algorithms 292
4.6 Application of means for filtering problems 309
4.6.1 Digital filters with finite memory 309
4.6.2 Median filters 311
4.6.3 Diagnostic filters 314
4.6.4 Example of filtering navigational information 316
4.7 Summary 319
5 Metrological traceability of measurement results (illustrated by an example of magnetic recording instruments) 321
5.1 General ideas 321
5.2 Precise magnetic recording instruments (MRI) of analog electrical signals as a part of measuring systems; MRI metrological traceability 323
5.2.1 Application of recording/reproducing electrical signals on magnetic carriers in measurement technique and specific features of MRI as an object of metrological investigations 323
5.2.2 Main sources of distortions of measurement information signals in magnetic channels, and methods of their measurements 328
5.2.3 Problems of the metrological traceability of MRI 336
5.3 Methods of determining MRI metrological characteristics 340
5.3.1 Problems in developing metrological traceability systems 340
5.3.2 Metrological characteristics of MRI and their normalization 356
5.3.3 Methods for experimental evaluation of the basic error of measurement information signals registration in MRI channels 367
5.3.4 Methods for determining the dynamic characteristics of MRI channels 375
5.3.5 Methods for determining the nonlinear distortions and oscillations of a signal time delay in MRI channels 395
5.4 Hardware implementation of the methods for determining MRI metrological characteristics 401
5.4.1 Measuring instruments for experimentally determining MRI metrological characteristics 401
5.5 Summary 423
6 Validation of software used in metrology 425
6.1 General ideas 425
6.2 Tasks of the metrological validation of software (MVS) used in metrology 428
6.2.1 Classification of tasks for MVS used in metrology 428
6.2.2 State of affairs in this field in leading countries of the world, immediate tasks and ways for their solution 435
6.3 Approaches to evaluating precision parameters of software used in metrology 446
6.3.1 Sources of uncertainty and methods of their evaluation when applying data processing software for obtaining a measurement result 446
6.3.2 Methodology of algorithm validation for measurement data processing and its practical implementation 458
6.4 Requirements for software and methods for its validation 465
6.4.1 General requirements for measuring instruments with regard to the application of software 465
6.4.2 Requirements specific for configurations 472
6.4.3 Software validation methods 484
6.5 Type approval 492
6.5.1 Documentation for type approval 492
6.5.2 Requirements for the approval procedure 494
6.5.3 Verification 494
6.6 Assessment of severity (risk) levels 495
6.6.1 Brief review 495
6.6.2 Assessment of severity (risk) levels according to OIML Document D 31 497
6.6.3 Definition of risk classes according to the WELMEC Guide 7.2 500
6.6.4 Determination of severity degrees of software tests in Russia 502
6.7 Summary 504
Bibliography 512
Index 545
