## 3 Results and Discussions
### Practical Application  
A practical/applicative example will be presented next, for the dental bur of the type in Figure 8, where \(x=t\) is the time of good operation of the dental bur, so \(x_{i}=t_{i}\); \(X=t_{d}\) is also the specified limit of the duration of good operation, or the operation time until the first system failure (here the dental bur active part). Figure 8: Conical–cylindrical dental bur: 1— dental bur active part; 2— dental bur neck; 3— dental bur foot. Figure 6: Interval with bilateral symmetric risk. Note: \(a_{0}\)—the true value of the estimated parameter; \(a\)—the probability of the analyzed parameter; \((a_{1},a_{2})\)—the confidence interval. Figure 7: Interval with bilateral asymmetric risk. Note: \(a_{0}\)—the true value of the estimated parameter; \(a\)—the probability of the analyzed parameter; \((a_{1},a_{2})\)—the confidence interval. These dental burs are made of a metallic mixture in which tungsten carbide (WC) dominates together with other carbides of Cr, Mn, Fe, etc., with the medium graining on the active part. They are used for processing Co-Cr alloys, as well as metals, both semi-precious and precious metals. Such a dental bur is provided with a blue ring for identification, marked on position 2 in Figure 8, and works at speeds up to 35,000 rpm. At the same time, on the active part of the dental burs there are cutting lamellae wounds, arranged equidistantly and oriented to the right, with a pitch of about 0.65 mm, seating angle of 47.740 degrees, sharpening angle of 61.480 degrees, clearance angle of 9.900 degrees, maximum diameter of 6.20 mm, average diameter of 5.40 mm, length of the active part of 14.50 mm, total length of 52.75 mm, and average mass of 4.701 g.  
The conventional lifetime (conventional durability), \(t_{\mu}\), of the dental bur active part in Figure 8 was estimated using the formula for calculating the working time (optimal functioning), given the relationship [9; 29] as follows:  
\[t_{\mu}=\frac{\ln\frac{1}{\Gamma-\mu}}{\omega\cdot d} \tag{10}\]  
where \(\mu\) is a fraction from the dental bur active part total mass, established conventionally and lost during the work/functioning process; \(\omega\) is the dental bur angular speed; \(d\) is the model parameter (\(d\) = 3.5 \(\times\) 10\({}^{-5}\)) dependent on the lost mass through the dental bur active part wear and tested on the angular space (circular friction length), \(\varphi\) = \(\omega\cdot t\). The critical fraction of material, \(\mu\), which is lost in the work process from the dental bur active part was established, starting from about 65% of the approximate circular crown mass, determined experimentally through the active part total wear (as mass lost). Then, by weighing and calculating the difference compared to the dental bur specimen (Figure 9) the value of 0.408 g was obtained. It is mentioned that milling wear is estimated by the reduction in the tool diameter (bur) on a certain contact width [30] and is consistent with the weight loss, as a result of wear, in the dental bur work process. Thus, Table 1 presents the dental bur characteristics taken as a specimen. The lifetime results (calculated with relation (10) and presented as average values) for the dental burs of the same type, in number of 16, tested in the laboratory (see Figure 7), for \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Type of** & **Mass [g]** & **Total Length,** & **Length of the Active** & **Average** & **Maximum** \\
**Bur/Features** & & **[mm]** & **[mm]** & **[mm]** & **Diameter,** & **Diameter,** \\ \hline Specim & & & & & \\ dental bur & 4.701 & 52.750 & 14.500 & 5.400 & 6.200 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Mass and dimensions of the dental bur specimen. Figure 9: Methodology of establishing the circular crown mass of the dental bur active part: (a) specimen dental bur, after 1 h of operation; (b) worn dental bur after 4 h of operation; (c) dental bur with the circular crown of the active part, completely worn.