Rabinovich Measurement Errors and Uncertainties

Theory and Practice
3rd Auflage 2005
ISBN: 978-0-387-29143-7
Verlag: Springer US
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 308 Seiten, eBook

The major objective of this book is to give methods for estimating errors and uncertainties of real measurements: measurements that are performed in industry, commerce, and experimental research. This book is needed because the existing theory of measurement errors was historically developed as an abstract mathematical discipline. As a result, this theory allows estimation of uncertainties of some ideal measurements only and is not applicable to most practical cases. In particular, it is not applicable to single measurements. This situation did not bother mathematicians, whereas engineers, not being bold enough to assert that the mathematical theory of errors cannot satisfy their needs, solved their particular problems in one or another ad hoc manner. Actually, any measurement of a physical quantity is not abstract, but it involves an entirely concrete procedure that is always implemented with concrete te- nical devices—measuring instruments—under concrete conditions. Therefore, to obtain realistic estimates of measurement uncertainties, mathematical methods must be supplemented with methods that make it possible to take into account data on properties of measuring instruments, the conditions under which measu- ments are performed, the measurement procedure, and other features of measu- ments. The importance of the methods of estimating measurement inaccuracies for practice can scarcely be exaggerated. Indeed, in another stage of planning a m- surement or using a measurement result, one must know its error limits or unc- tainty. Inaccuracy of a measurement determines its quality and is related to its cost.

Zielgruppe

Research

Autoren/Hrsg.

Rabinovich, Semyon G.

Inhaltsverzeichnis

General Information About Measurements.- Measuring Instruments and Their Properties.- Prerequisites for the Analysis of the Inaccuracy of Measurements and for Synthesis of Their Components.- Statistical Methods for Experimental Data Processing.- Direct Measurements.- Indirect Measurements.- Examples of Measurements and Measurement Data Processing.- Combined Measurements.- Combining the Results of Measurements.- Calculation of the Errors of Measuring Instruments.- Problems in the Theory of Calibration.- Conclusion.

Leseproben

5 Direct Measurements (p. 115-116)

5.1. Relation Between Single and Multiple Measurements

The classical theory of measurement errors is constructed based on the welldeveloped statistical methods and pertains to multiple measurements. In practice, however, the overwhelming majority of measurements are single measurements, and however strange it may seem, for this class of measurements, there is no accepted method for estimating errors.

In searching for a solid method for estimating errors in single measurements, it is first necessary to establish the relation between single and multiple measurements. At first glance, it seems natural to regard single measurements as a particular case of multiple measurements, when the number of measurements is equal to 1. Formally this is correct, but it does not give anything, because statistical methods do not work when n = 1. In addition, the question of when one measurement is suf.cient remains open. In the approach examined, to answer this question—and this is the fundamental question—it is first necessary to perform a multiple measurement, and then, analyzing the results, to decide whether a single measurement was possible. But such an answer is in general meaningless: A multiple measurement has already been performed, and nothing is gained by knowing, for example, that in a given case, one measurement would have suf.ced. Admittedly, it can be objected that such an analysis will make it possible not to make multiple measurements when future such measurements are performed. Indeed, that is what is done, but only when preliminary measurements are performed, i.e., in scientific investigations when some new object is studied. This is not done in practical measurements.

When it is necessary to measure, for example, the voltage of some source with a given accuracy, a voltmeter with suitable accuracy is chosen and the measurement is performed. If, however, the numbers on the voltmeter indicator dance about, then it is impossible to perform a measurement with the prescribed accuracy, and the measurement problem must be reexamined rather than performing a multiple measurement. For practical applications, we can state the opinion that single measurements are well founded by experience, concentrated in the construction of the corresponding measuring instruments, and that measuring instruments are manufactured so that single measurements could be performed.

From the foregoing assertion a completely different point of view follows regarding the relationship between single and multiple measurements, namely, that single measurements are the primary, basic form of measurement, whereas multiple measurements are derived from single measurements. Multiple measurements are performed when necessary, based on the formulation of the measuring problem. It is interesting that these problems are known beforehand, they can even be enumerated. Namely, multiple measurements are performed as follows: (a) When investigating a new phenomenon or a new object and relationships between the quantities characterizing the object, as well as their connection with other physical quantities, are being determined, or briefiy, when preliminary measurements, according to the classification given in Chapter 1, are performed.

(b) When measuring the average value of some parameter, corresponding to the goal of the measuring problem.
(c) When the effect of random errors of measuring instruments must be reduced.
(d) In measurements for which measuring instruments have not yet been developed.

Of the four cases presented above, the first is typical for investigations in science and the third is typical for calibration practice. There is another point of view, namely, that any measurement must be a multiple measurement, because otherwise it is impossible to judge the measurement process and its stability and to estimate its inaccuracy.

Über Autor(innen)

Rabinovich was head of the Laboratory of Theoretical Metrology at the All-Union State Research Institute of Metrology in the former Soviet Union. His theory of galvanometrical self-balancing instruments led to the creation of numerous new measuring devices.