## 3 Results  
The mean and standard deviation (SD) values for time to failure (in seconds) regarding the apical diameter and taper are displayed in Table 1 and Figure 5A,B. The ANOVA test showed statistically significant differences between the time to failure of the apical diameter (\(p<0.001\)) (Figure 5A) and taper (\(p<0.001\)) (Figure 5B) of the NiTi endodontic rotary files. The scale distribution parameter (\(\eta\)) of the Weibull statistics showed statistically significant differences between the time to failure of the 20.06 and 25.06 apical diameter study groups (\(p<0.001\)), 20.06 and 30.06 apical diameter study groups (\(p<0.001\)) and 25.06 and 30.06 apical diameter study groups (\(p<0.001\)). In addition, the shape distribution \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Study Group** & \(n\) & **Mean** & **SD** & **Minimum** & **Maximum** \\ \hline
20.06 & 10 & 361.91 & 18.07 & 328.18 & 382.91 \\
25.02 & 10 & 410.39 & 13.11 & 387.28 & 428.19 \\
25.04 & 10 & 294.27 & 10.50 & 279.87 & 310.33 \\
25.06 & 10 & 225.77 & 11.73 & 210.79 & 241.83 \\
30.06 & 10 & 102.91 & 15.41 & 81.29 & 127.91 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Descriptive statistics of the time to failure in relation to the apical diameter and taper study groups. Figure 5: Box plots of the time to failure for the (**A**) apical diameter and (**B**) taper study groups. The horizontal line in each box represents the respective median value. parameter (\(\beta\)) of the Weibull statistics showed statistically significant differences between the time to failure of the 20.06 and 25.06 apical diameter study groups (\(p<0.001\)) and 20.06 and 30.06 apical diameter study groups (\(p=0.002\)); however, it did not show statistically significant differences between the time to failure of the 25.06 and 30.06 apical diameter study groups (\(p=0.656\)) (Table 2, Figure 6A). The scale distribution parameter (\(\eta\)) of the Weibull statistics showed statistically significant differences between the time to failure of the 25.02 and 25.04 taper study groups (\(p<0.001\)), 25.02 and 25.06 taper study groups (\(p<0.001\)), and 25.04 and 25.06 taper study groups (\(p<0.001\)). However, the shape distribution parameter (\(\beta\)) of the Weibull statistics did not show statistically significant differences between the time to failure of the 25.02 and 25.04 taper study groups (\(p=0.148\)), 25.02 and 25.06 taper study groups (\(p=0.287\)), and 25.04 and 25.06 taper study groups (\(p=0.702\)) (Table 2, Figure 6B). The mean and SD values for number of cycles to failure regarding the apical diameter and taper are displayed in Table 3 and Figure 7A,B. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline  & \multicolumn{3}{c}{**Weibull Shape (\(\beta\))**} & \multicolumn{3}{c}{**Weibull Scale (\(\eta\))**} \\ \hline  & **Estimate** & **St Error** & **Lower** & **Upper** & **Estimate** & **St Error** & **Lower** & **Upper** \\ \hline
20.06 & 26.22 & 6.75 & 15.83 & 43.43 & 369.77 & 4.70 & 360.67 & 379.09 \\
25.02 & 37.02 & 9.08 & 22.89 & 59.86 & 416.37 & 3.76 & 409.05 & 423.81 \\
25.04 & 32.42 & 7.98 & 20.01 & 52.52 & 299.13 & 3.09 & 293.14 & 305.25 \\
25.06 & 22.37 & 5.53 & 13.78 & 36.31 & 231.14 & 3.46 & 224.45 & 238.02 \\
30.06 & 7.62 & 1.84 & 4.74 & 12.23 & 109.38 & 4.81 & 100.34 & 119.24 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: The Weibull statistics of the time to failure for the apical diameter and taper study groups. Figure 6: Weibull probability plots of the time to failure for the (**A**) apical diameter and (**B**) taper study groups. The ANOVA test showed statistically significant differences between the number of cycles to failure of the apical diameter (\(p<0.001\)) (Figure 7A) and taper (\(p<0.001\)) (Figure 7B) of NiTi endodontic rotary files.