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This book recasts the classical Gaussian error calculus from scratch, the inducements concerning both random and unknown systematic errors. The idea of this book is to create a formalism being fit to localize the true values of physical quantities considered – true with respect to the set of predefined physical units. Remarkably enough, the prevailingly practiced forms of error calculus do not  feature this property which however proves in every respect, to be physically indispensable. The amended formalism, termed Generalized Gaussian Error Calculus by the author, treats unknown systematic errors as biases and brings random errors to bear via enhanced confidence intervals as laid down by students. The significantly extended second edition thoroughly restructures and systematizes the text as a whole and illustrates the formalism by numerous numerical examples. They demonstrate the basic principles of how to understand uncertainties to localize the true values of measured values - a perspective decisive in view of the contested physical explorations.

Measurement --- Error analysis (Mathematics) --- History. --- Errors, Theory of --- Instrumental variables (Statistics) --- Mathematical statistics --- Numerical analysis --- Statistics --- Engineering mathematics. --- Mathematical physics. --- Measurement Science and Instrumentation. --- Mathematical and Computational Engineering. --- Mathematical Methods in Physics. --- Engineering --- Engineering analysis --- Mathematical analysis --- Physical mathematics --- Physics --- Mathematics --- Physical measurements. --- Measurement   . --- Applied mathematics. --- Physics. --- Natural philosophy --- Philosophy, Natural --- Physical sciences --- Dynamics --- Measuring --- Mensuration --- Technology --- Metrology --- Physical measurements --- Measurements, Physical --- Mathematical physics

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Error analysis (Mathematics). --- Instrumental variables (Statistics). --- Measurement.

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This book recasts the classical Gaussian error calculus from scratch, the inducements concerning both random and unknown systematic errors. The idea of this book is to create a formalism being fit to localize the true values of physical quantities considered – true with respect to the set of predefined physical units. Remarkably enough, the prevailingly practiced forms of error calculus do not  feature this property which however proves in every respect, to be physically indispensable. The amended formalism, termed Generalized Gaussian Error Calculus by the author, treats unknown systematic errors as biases and brings random errors to bear via enhanced confidence intervals as laid down by students. The significantly extended second edition thoroughly restructures and systematizes the text as a whole and illustrates the formalism by numerous numerical examples. They demonstrate the basic principles of how to understand uncertainties to localize the true values of measured values - a perspective decisive in view of the contested physical explorations.

Mathematics --- Measuring methods in physics --- Mathematical physics --- Physics --- Chemical laboratory practice --- Applied physical engineering --- Engineering sciences. Technology --- procescontrole --- laboratoriuminstrumenten --- analyse (wiskunde) --- meetkundige instrumenten --- economie --- wiskunde --- ingenieurswetenschappen --- fysica --- micro-elektronica --- elektrische meettechniek

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For the first time in 200 years Generalized Gaussian Error Calculus addresses a rigorous, complete and self-consistent revision of the Gaussian error calculus. Since experimentalists realized that measurements in general are burdened by unknown systematic errors, the classical, widespread used evaluation procedures scrutinizing the consequences of random errors alone turned out to be obsolete. As a matter of course, the error calculus to-be, treating random and unknown systematic errors side by side, should ensure the consistency and traceability of physical units, physical constants and physical quantities at large. The generalized Gaussian error calculus considers unknown systematic errors to spawn biased estimators. Beyond, random errors are asked to conform to the idea of what the author calls well-defined measuring conditions. The approach features the properties of a building kit: any overall uncertainty turns out to be the sum of a contribution due to random errors, to be taken from a confidence interval as put down by Student, and a contribution due to unknown systematic errors, as expressed by an appropriate worst case estimation.

Mathematical physics --- Physics --- Applied physical engineering --- Engineering sciences. Technology --- systeemtheorie --- wiskunde --- systeembeheer --- ingenieurswetenschappen --- fysica

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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 practised approach to belatedly admit those unknown systematic errors amount to considering 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.

Measurement. --- Physics. --- Metrology. --- Uncertainty. --- Mensuration & systems of measurement. --- SCIENCE / Weights & Measures.