Abstract
The evaluation of measurement uncertainty is a main task in measurement, as we have amply discussed in Chap. 2, and one of the main aims of this book is to provide a sound foundation for that. We have already taken some steps in this direction: in Chap. 5, we have presented a general probabilistic model of the measurement process which provides the basic theoretical framework for the evaluation. In Chap. 6, we have started to consider the application of that framework, discussing the logical steps involved, by means of simple illustrative examples.
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Notes
- 1.
This and the following two sections are amply based on Ref. [2], to which the reader is referred for additional details.
- 2.
For understanding this result without performing analytical calculation, consider the following geometrical argument. Multiplying the argument of a function by a constant factor \(k\) is equivalent to scaling the function along the abscissa by the same factor. For example, if \(k>1\), the result is a contraction of the graph of the function. The integration is equivalent to calculating the area under the graph, which, after contraction, is reduced by the factor \(k\). To restore a unit area, it is thus necessary to further multiply by \(k\). A similar argument holds true for \(k<1\), which corresponds to a dilation.
- 3.
Numerical values are assumed to be expressed in arbitrary consistent units.
- 4.
Hysteresis occurs when the behaviour of a system depends on its past environment. This happens because the system can be in more than one internal state. Prediction of its future development would require knowledge either of its internal state or of its history. In typical measurement conditions, such a prediction is impossible and thus hysteresis constitutes a source of uncertainty.
- 5.
- 6.
Legal metrology will be briefly addressed in Chap. 11.
- 7.
- 8.
The term \(\mathbf{a}\cdot \mathbf{v}^{T}\) is the scalar product of \(\mathbf{a}\) times \(\mathbf{v}\) and the operator \(T\) superscript denotes transposition.
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Rossi, G.B. (2014). The Evaluation of Measurement Uncertainty. In: Measurement and Probability. Springer Series in Measurement Science and Technology. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-8825-0_9
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