By Franco (EDT)/ Forbes, Alistair B. (EDT) Pavese

ISBN-10: 0817645926

ISBN-13: 9780817645922

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The plurality of “unknown systematic errors” are supposed to bring to an overall effect, a constant-in-time unknown systematic error f , whose value is supposed to fall into a confining interval f1 ≤ f ≤ f2 . This interval is defined as the bound for the values of f , is not a confidence interval, and its width is matter of expert (metrologist) judgement only. The corresponding model is written as model (4), but in this case b ≡ f is not a random variable. A full exploitation of the concept of using bounding intervals, particularly useful in the treatment of systematic errors, is developed in Chapter 4 of this book.

Should randomisation of systematic effects truly occur, both εij and ηij would be really zero-mean errors. In [KDP03, Kak04] (see also [For06b]) this model is called the “random laboratory-effects model”, written as model (2), where (adapting to the chapter notation) bi = (Xi − Yj ) is the laboratory effect in xij (‘bias’ in the NIST terminology) and εij = (xij – Xi ) is the intralaboratory error in xij . Capital letters indicate the random variables from which the samples, written in lowercase letters, are drawn.

B. Rossi Note that, as already pointed out by Gauss, the same phenomenon, the residual calibration error θ, gives rise to a systematic error if we consider as ‘observations of the same class’ the indications of a single instrument (index i fixed to, say, i0 ), whilst it becomes a random variation if we sample instruments from the class of all the instrument of the same type (index i varying from 1 to m). Consider the following averages. – Grand average, y¯ = 1/N ij yij , which is an estimate of x.

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Advances in Data Modeling for Measurements in the Metrology and Testing Fields by Franco (EDT)/ Forbes, Alistair B. (EDT) Pavese


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