Abstract
Measurement provides objective and reliable support to decision-making [1, 2]. In manufacturing, for example, it is necessary to check workpieces for conformance to their design [3–5]. In mass production, as occurs, for example, in the automotive field, parts are produced independently and then assembled. In order to assemble properly, it is necessary that critical dimensions and forms are kept under control.
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Notes
- 1.
A numerical example will be provided in Sect. 11.4.
- 2.
- 3.
In this and in the following numerical examples, we mention some of the results that we extensively presented in Ref. [10]. Readers are referred to that paper for probing this subject further. The basic assumptions for this first example are taken from Ref. [11], a well and informative paper that we also recommend to read in full.
- 4.
See Ref. [12] for a discussion of the interpretation of \(e=\hat{x}-x\) as the measurement error, in particular Sect. 3 and footnote 10 in that paper.
- 5.
The gauging ratio is a parameter that relates measurement uncertainty to the characteristics of the production process, here summarised by parameter \(a\). A high gauging factor is typical of an accurate inspection process.
- 6.
In a more appropriate language, this concept should be expressed as “allowable (measurement) uncertainty”. Otherwise, apart from language subtleties, the metrological requirements are stated in a sound way.
- 7.
Note that here the “product” is a measuring device, so the production process is characterised by the measurement “error” of such devices, as detected in the testing process, and the measurement process is that performed by the testing device(s).
- 8.
Remember footnote 4.
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Rossi, G.B. (2014). Measurement-Based Decisions. In: Measurement and Probability. Springer Series in Measurement Science and Technology. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-8825-0_11
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