Measurement Uncertainties Error Propagation Probabilistic Modelling Statistical Methods 1st Edition by Michael Krystek ISBN 3111453960 9783111453965

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ISBN 10: 3111453960 
ISBN 13: 9783111453965
Author: Michael Krystek

Measurement Uncertainties Error Propagation Probabilistic Modelling Statistical Methods 1st Table of contents:

1 Introduction
1.1 The importance of measurement uncertainty
1.2 The nature of measurement uncertainty
2 Fundamental terms of metrology
2.1 Quantities, quantity values and units
2.2 Measurement
2.3 The true value of a measured quantity
2.4 Principles, methods, procedures
2.5 Accuracy, trueness, precision, resolution
2.6 Measurement errors
2.7 Measurement uncertainty
3 Measurement models
3.1 Modelling methods
3.2 Model equations
3.3 Submodels
3.4 Modelling strategies
3.5 Linear approximation
3.6 Quadratic approximation
3.7 Graphical modelling
4 Basics of probability theory
4.1 Probability concepts
4.2 Events and outcomes
4.3 Mathematical probability
4.4 Conditional probability
4.5 Rules of probability calculations
4.6 The theorem of Bayes and Laplace
4.7 Stochastic independence
4.8 Random quantities
4.9 Probability distribution functions
4.10 Probability density functions
4.11 Transformations of random quantities
4.12 Expectations
4.13 Variances and standard deviations
4.14 Multivariate random quantities
4.15 Multivariate distribution functions
4.16 Multivariate density functions
4.17 Marginal distributions
4.18 Multivariate expectations
4.19 Covariances and correlations
4.20 Approximate estimations
4.21 Central limit theorem
5 Statistical methods
5.1 Populations and random sampling
5.2 Statistics
5.3 Estimators
5.4 Method of moments
5.5 Maximum likelihood method
5.6 Least squares method
5.7 Bayesian methods
5.8 Interval and region estimation
6 Measurement uncertainty concepts
6.1 The traditional method
6.2 The methods of the GUM
A From univariate to multivariate uncertainty
A.1 Introduction
A.2 Univariate uncertainty calculations
A.3 Multivariate uncertainty calculation
A.4 Matrix representation
A.5 Generalization
A.6 Coverage regions
A.7 Summary of multivariate calculations
A.8 Examples
B Dealing with systematic measurement errors
B.1 Introduction
B.2 Preliminary remarks
B.3 Ignoring an existing systematic error
B.4 Bayes’ theorem and marginalization
B.5 The principle of maximum entropy
B.6 A procedure to handle systematic errors
B.7 The influence of temperature on length
B.8 The cosine error in length measurement
B.9 The influence of form deviations on the distance
B.10 Noise as a systematic error
C Bayesian linking of key comparisons
C.1 Introduction
C.2 The scenario
C.3 The information available
C.4 Establishing key comparison reference values
C.5 Degrees of equivalence
C.6 Conformity tests
C.7 Examples
C.8 Uncorrelated measurement results
C.9 Conclusion

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Tags: Michael Krystek, Measurement Uncertainties, Error Propagation, Statistical Methods