1. Introduction

Measurement uncertainty is a quantitative indication of the quality of measurement results, without which they could not be compared between themselves, with specified reference values or to a standard. Uncertainty evaluation is essential to guarantee the metrological traceability of measurement results and to ensure that they are accurate and reliable. In addition, measurement uncertainty must be considered whenever a decision has to be taken based on measurement results, such as in accept/reject or pass/fail processes.

Considering the context of globalization of markets, it is necessary to adopt a universal procedure for evaluating uncertainty of measurements, in view of the need for comparability of results between nations and for mutual recognition in metrology. As an example, laboratories accredited under the ISO/IEC 17025:2017 standard [1] need to demonstrate their technical

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competence and the ability to properly operate their management systems, and so they are required to evaluate the uncertainty for their measurement results.

EURACHEM/CITAC Measurement Uncertainty Working Group. This document was first published in 1995 and further revised in 2000 [14]. This last edition had a widespread implementation and is among the most highly cited publications in chemical metrology area [14]. Recently, a new revised edition was published in 2012 with improved content and added information on developments in uncertainty evaluation [14]. This document basically presents the uncertainty evaluation process following the suggestions of the GUM, but also contains

It must be clear to the analyst which quantity will be the final object of the measurement in question. This quantity is known as the measurand. In addition, it is important to identify all the variables that directly or indirectly influence the measurand. These variables are known as the input quantities. As an example, Eq. (1) shows a measurand y as a function of three

In this step, the measurement procedure should be modeled in order to have a functional relationship expressing the measurand as a result of all the input quantities. The measurand y

> <sup>y</sup> <sup>¼</sup> <sup>x</sup>1x<sup>2</sup> x2 3

The modeling step is critical for the uncertainty evaluation process as it defines how the input quantities impact the measurand. The better the model is defined, the better its representation of reality will be, including all the sources that impact the measurand on the uncertainty evaluation. The modeling process can be easily visualized by using a cause-effect diagram

Example: To illustrate these steps, let us consider a measurement model for a torque test. Torque is a quantity that represents the tendency of a force to rotate an object about an axis. It can be mathematically expressed as the product of a force and the lever-arm distance. In metrology, a practical way to measure it is by loading a known mass to the end of a horizontal

Note: This example is also presented, with a few adaptations, in other publications by the same

y ¼ f xð Þ <sup>1</sup>; x2; x<sup>3</sup> (1)

Methods for Evaluation of Measurement Uncertainty http://dx.doi.org/10.5772/intechopen.74873

(2)

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several examples in the analytical chemistry area.

3. Using the GUM approach on uncertainty evaluation

3.1. Definition of the measurand and of input quantities

different input quantities: x1, x2, and x<sup>3</sup>:

3.2. Modeling the measurement process

(Figure 1).

authors [15].

in Eq. (1) could be modeled, for example, as in Eq. (2)

arm while keeping the other end fixed (Figure 2).

The following main steps summarize the methodology presented by the GUM.

In addition, the use of uncertainty evaluation methods as a tool for technical management of measurement processes is extremely important to reduce, for example, the large number of losses that occurs in the industry, which can be highly significant in relation to the gross domestic product (GDP) of some countries. One of the probable causes of the waste can be attributed to instruments whose accuracy is inadequate to the tolerance of a certain measurement process.

In this chapter, detailed steps for uncertainty evaluation are given.
