# Application of Machine Learning to Express Measurement Uncertainty
## 2 Methods
### Measurement Uncertainty  
It is impossible to determine the exact value of the measured quantity because the results of actual measurements contain a certain degree of uncertainty. Measurement error is the difference between the measured value and the \"true value.\" \"True value\" means a value measured by a reference standard, i.e., an available standard with the highest level of accuracy. The disadvantage of the given approach (error theory) in the processing and expressing measurement results is the absence of uniformity and the impossibility of comparing the same types of measurements from different institutions (researchers). To introduce standardization in the field of processing and expression of measurement results, the leading institutions of the international metrology system published the first version of the instructions for the expression of measurement uncertainty in 1993 [32].  
When processing and expressing measurement results, it is necessary to determine three quantities: measurement result, measurement uncertainty, and statistical certainty. The measurement result is the mean value of repeated measurements (\(x_{s}\)). Measurement uncertainty (dispersion or scattering of measurement results) is expressed as an interval around the mean value in which the  
Type B measurement uncertainty is determined by all methods other than the statistical analysis of repeated measurement results. Considering that the set of methods for determining type B measurement uncertainty is not defined, the choice of procedures depends on the requirements, knowledge, and experience of the measurer. The given measurement uncertainty can also be specified in the case when the measurement was performed only once.  
Sources of information on type B measurement uncertainty can be data on the operational measurement procedure, data on the measuring equipment (manufacturer's instructions, calibration certificates), knowledge about the influence of the environment on the measurement process (temperature, humidity), knowledge about the impact of disturbances (electromagnetic, mechanical), results of previous measurements, variability of personnel performing the same type of measurement, etc. The standard measurement uncertainty of type B, \(u_{B}\), is equal to the standard deviation due to the influence of the quantity from which it originates. In most cases, due to the lack of data, the measurement uncertainty of type B has an assumed uniform distribution [32; 33; 34].  
In uniform distribution, the values of the measurement results belong to the limited interval (\(x_{s}-a\), \(x_{s}+a\)). All values within the interval have an equal probability, i.e., \(p(x)=1/(2a)\), where \(a\) is the half-width of the distribution. The standard deviation is \(s=a/\sqrt{3}\), where approximately \(57.7\%\) of the measurement results are in the interval (\(x_{s}-s\), \(x_{s}+s\)) (Figure 1). The given distribution is applied when there is insufficient information about the measurement instrument [33].  
The result of the measurement uncertainty calculation should be presented transparently, i.e., in such a way as to show all the relevant facts related to the procedure of determining the measurement uncertainty. The tabular representation of the given data is called the measurement uncertainty budget. The data in the measurement uncertainty budget are significant measurement quantities, their distribution functions with standard measurement uncertainties, appropriate coverage factors, etc. [33].