Historically, metrology emerged as a science of measures. Even in the middle of the last century, metrology was considered to be the science of measurements concerning the creation and maintenance of measurement standards . With this approach, the theory of accuracy of measurements was limited to the problems of estimation of the accuracy of multiple measurements and only to random errors. Math statistics was a natural fit for these problems. As a result, the science of measurement data processing was in essence the reformulation of math statistics in the context of random errors.
This state of affairs can be clearly seen by examining relatively recent books on the subject, for example, Data Analysis for Scientists and Engineers by S. Meyer (1975), Data Reduction and Error Analysis for Physical Sciences by Ph. Bevington and D. Robinson (1992), and Measurement Theory for Engineers by I. Gertsbakh (2003). Even the book The Statistical Analysis of Experimental Data (National Bureau of Standards, 1964) by J. Mandel, which stands out by considering concrete measurement problems, remained within the above confines. Nevertheless, because this purely mathematical theory found practical applications, even in a restricted case of random errors in multiple measurements, this theory obtained the status of the classical theory of measurement data processing.
In the meantime, this theory did not satisfy practical needs. In particular, every practitioner knew that in addition to random errors, there are systematic errors, and the overall inaccuracy of the measurement result combined both of these components. But the classical theory ignored this fact and, furthermore, not so long ago considered it incorrect to combine these two components. There were other practical problems ignored by the classical theory. As a result, those who encountered these problems in their practice resorted to ad hoc and often incorrect methods. For example, in the case of single measurements, the measurement errors were often equated to the fiducial error of the measuring device used (see Chap. 2Measuring Instruments and Their Propertieschapter.2.26), which is wrong. To account for systematic errors in a multiple measurement, people often simply added them to the random errors, which overestimated the inaccuracy of the result.
KeywordsRandom Error Classical Theory Measured Quantity Multiple Measurement Standard Uncertainty
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