## 3 Results and Discussions
### Practical Application
4 h and at 4 rotation speeds are those presented in Table 2, the column \"Lifetime (Duration) calculated, hours\". The wear was evaluated by the mass loss of the dental bur active part by weighing, during 4 h of operation, at each of the rotation speeds of 7000, 12,000, 20,000, and 35,000 rpm and presented graphically in Figure 10.  
Initially, the dental bur mass was 4701 g, and after 4 h of operation and at four different rotation speeds, it reached the value of 4360 g (see Figure 10). Given the experimental results, respectively, by the user consultation of dental burs (doctors and dental technicians) with those who use/consume them a lot, the following was found:  
* Failure probability in the work process of the dental bur active part is very low until a minimum time, \(t_{1}\), and then it grows rapidly up to a maximum time, \(t_{2}\), when practically, in general, no bur is usable anymore;
* Time range, \(t_{2}\)-\(t_{1}\), when the dental bur active part is taken out of operation, is due to the small differences between parameters (with masses, angles, etc., being a little different) of the same active parts. Finally, these differences influence the lifetime, a thing observable from the durability calculation (see Table 2). The range [\(t_{1}\), \(t_{2}\)] of increase in the failure probability is greater by how much the differences between active parts from the same set, or type, are bigger. Based on these findings, for the operation of dental burs without defects, the following reliability function is proposed [31; 32]:  
\[R(t)=\left\{ \begin{array}{ll}\exp\biggl{(}\frac{1}{t_{2}^{2n}}\biggr{)} \cdot\exp\biggl{(}\frac{1}{t^{2n}-t_{2}^{2n}}\biggr{)},\ 0\leq t\leq t_{2}\\ 0,\qquad t>t_{2}\end{array} \right. \tag{11}\]  
where \(t_{2}\) is the maximum time after which the dental bur active part of the same type and brand was damaged, in the experiment time, and \(m\) is an exponent parameter, chosen so  
Figure 10: Variation in time of the lost mass in the dental bur work process. Note: the points in the graph represent the average value of the cumulative mass loss in time for the 4 rotation speeds and 5 repetitions considered in the experiment. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Values** & **Selected and** & **Rotation Speed of** & **Lifetime (Durability)** \\
**Calculated Sizes** & **Dental Bur, rpm** & **Calculated, Hours** \\ \hline \hline  & 7000 & 20.433 \\ \cline{2-3} Average time values of calculated & 12,000 & 11.919 \\ \cline{2-3} lifetime, hours & 20,000 & 7.151 \\ \cline{2-3}  & 35,000 & 4.086 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Average lifetime calculated for the dental bur active part, researched experimentally. that the time, \(t_{1}\), at which failure probability (reliability), \(R(t)\), begins to grow exponentially can be estimated as best as possible. A satisfactory estimate is obtained for \(m=0.75\), in this case, and the reliability function variation, \(R(t)\), in time (according to the relationship (11)) is represented graphically in Figure 11. Thus, for dental burs of the same type, whose lifetime at the rotation speed of 7000 rpm is 20,526 h after 1 operating hour, 19,265 h after 2 h of operation, 21,573 h after 3 h of operation, and 20,368 after 4 h of operation, respectively, the average value of the lifetime is 20,433 h and is presented in Table 2. It turns out that the estimated minim and maxim times (according to the above) are \(t_{1}=19,265\) h and \(t_{2}=21,573\) h, respectively, obtained by calculation from the experimental determinations. In Figure 11, the failure function plot, \(F(t)\), is also shown, and in Figure 12 the frequency function plot, \(f(t)\), which corresponds to the reliability function, \(R(t)\), from relation (11). Analyzing Figures 10 and 11, it can be seen that \(R(t)\) is monotonically decreasing, and instead \(F(t)\) is increasing.