Metrological data is known to be blurred by the imperfections of the measuring process. In retrospect, for about two centuries regular or constant errors were no focal point of experimental activities, only irregular or random error were. Today's notation of unknown systematic errors is in line with this. Confusingly enough, the worldwide practiced approach to belatedly admit those unknown systematic errors amounts to consider them as being random, too. This book discusses a new error concept dispensing with the common practice to randomize unknown systematic errors. Instead, unknown systematic errors will be treated as what they physically are- namely as constants being unknown with respect to magnitude and sign. The ideas considered in this book issue a proceeding steadily localizing the true values of the measurands and consequently traceability.
Author(s): Michael Grabe
Series: IOP Concise Physics
Publisher: IOP Publishing
Year: 2018
Language: English
Pages: 80
City: Bristol
PRELIMS.pdf
Preface
Acknowledgements
Author biography
Michael Grabe
CH001.pdf
Chapter 1 Basics of metrology
1.1 Regular or constant errors
1.2 Where traceability begins
1.3 Judging measurement results
1.4 True values and traceability
1.5 Consistency
1.6 Measuring errors
References
CH002.pdf
Chapter 2 Some statistics
2.1 Measurands and random variables
2.2 Fisher’s density
2.3 Confidence intervals
2.4 Non-uniqueness of the empirical covariance
2.5 Breakdown of statistical inference
2.6 Curing hypothesis testing
References
CH003.pdf
Chapter 3 Measurement uncertainties
3.1 One measurand
3.2 Two and more measurands
3.3 Random errors
3.4 Bias
3.5 Overall uncertainty
3.6 Error propagation at a glance
References
CH004.pdf
Chapter 4 Method of least squares
4.1 Geometry of adjustment
4.2 Linear systems
4.3 Quintessence of the method of least squares
References
CH005.pdf
Chapter 5 Fitting of straight lines
5.1 True straight line
5.2 Fitting conditions
5.3 Straight line (I)
Least squares estimators
Uncertainties of the input data
Uncertainties of the least squares estimators
Uncertainty band
EP-region
Security polygon
Data simulation
5.4 Straight line (II)
5.5 Straight line (III)
References
CH006.pdf
Chapter 6 Features of least squares estimators
6.1 Uncertainties
6.2 Weighted least squares
6.3 Transfer of true values
6.4 Fundamental constants of physics
References
CH007.pdf
Chapter 7 Prospects
7.1 Revising the error calculus
7.2 Redefining the SI base units
CH008.pdf
Chapter 8 Epilogue
8.1 Verification by experiment
8.2 Deciding by reasoning
8.3 What is right, what is wrong?
BIBLIO.pdf
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