By Franco (EDT)/ Forbes, Alistair B. (EDT) Pavese
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Extra info for Advances in Data Modeling for Measurements in the Metrology and Testing Fields
3 Instead √ of considering the standard deviation, Gauss elicits a precision measure, h = 2σ −1 and discusses how interpercentile ranges depend upon it. Probability in Metrology 35 Laplace’s approach and the theory of errors A near contemporary to the Theoria motus was Pierre-Simon Marquis de Laplace’s (1749–1827) Th´eorie analytique des probabilit´es, published in 1812 . He derived the normal distribution in another way . Let us consider again the case of repeated measurement, as described by model (5).
Eve81, McLP00]). The probabilistic model, called the mixture model, can provide a characterisation of the overall stochastic variability of the population of a comparison involving Class 2 standards, that is, when not involving artefacts (Class 1) [CCPR04]. In fact, the mixture density function represents the total variability of a super-population comprising several populations, each one identiﬁed by a speciﬁc pdf. It is often used in the statistical quality control of an industrial process, for example, when nominally identical electronic components have various lifetime constants.
We consider the contributions of Helmholtz and Campbell and the debate on the possibility of the measurement of ‘sensory events’, promoted by the British Association for the Advancement of Science in the 1930s, which has had consequences up to the present day. Then we present the representational approach to measurement and some criticism of it. We discuss the role of the measuring instrument in a formal theory and the beneﬁt of a probabilistic approach. This part concludes with a brief outline of a probabilistic theory of measurement that we have recently proposed and published and also with an attempt to make some previsions on the possible future role of probability in the science of measurement.
Advances in Data Modeling for Measurements in the Metrology and Testing Fields by Franco (EDT)/ Forbes, Alistair B. (EDT) Pavese