Franco (EDT)/ Forbes, Alistair B. (EDT) Pavese's Advances in Data Modeling for Measurements in the Metrology PDF

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

ISBN-10: 0817645926

ISBN-13: 9780817645922

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Extra info for Advances in Data Modeling for Measurements in the Metrology and Testing Fields

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The model, according to its author’s assumptions, can be simplified: – εi values “constitute a sample drawn randomly from a normal distribution with unknown variance σ 2 , possibly contaminated by outliers”. – E+E =ε+ε. 2 Thus, the expectation μ = a + ε + ε and Ei + E ∼ N(0, σi2 + σ ), with μ 2 and σ being unknown parameters. Nonprobabilistic systematic errors Opposite to the previous approach and to GUM, in [Gra01,Gra05] the systematic errors are preferred to be treated as nonprobabilistic, “to make allowance for them by introducing biases and worst–case estimations”.

For our purposes the original derivation is more significant, because it is grounded in probability. The theory of errors and the method of the least squares provided a great start for the theory of measurement and were the major results of the 19th century. At the beginning of the 20th century new ideas and methods became available to experimenters thanks to the contribution of ‘orthodox’ statistics [36]. 2 Orthodox statistics Experiments in metrology Orthodox or classic is the name given to the statistics developed in the first part of the 20th century and whose principal exponent was Ronald Aylmer Probability in Metrology 37 Fisher (1890–1962) [8, 11, 23, 36]4 .

Consider the measurement of a single constant quantity by a series of n repeated observations as described by model (5). This model assumes that systematic effects are negligible, as generally admitted in the classic theory of errors. Suppose now that we have a set of m measuring instruments of the same type, independently calibrated. If we want to apply model (5) to them, we should consider whether, for example, the residual calibration error, which could give rise to a systematic effect, is really negligible.

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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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