## 3 Results and Discussion
### Strength Analysis
An examination of the graphs shown in Figures 8 and 9 suggests that despite the high-quality fit, the scattering of the points from the Weibull model reveals a characteristic feature--splitting data into three groups. Well-defined groups of the points suggest that the Weibull model consists of three components as shown in Figure 11 and listed in Table 5.  
The slope of all three lines shown in Figure 11 is positive, but only the slope of the points in the middle part, shown in solid red, resembles those of the whole Weibull distribution (dashed line). The three lower points delineate phase I, the subsequent seven points delineate phase II, and the final five points delineate phase III. The Weibull modulus is different for each phase, Table 5. In the lower range, m is nearly 21.84, in the middle, it does not exceed 14.76, and in the upper range, it reaches 26.4. Although the differences in the m values may seem large, a comparison of the differences between the slope of the total Weibull model and each linear fit (phase I, II, or III) converted to degrees (inclination angles in degrees), Am, shows that they are small. The percentages of phases are listed in the table. The characteristic strength values estimated based on these data are 432.31, 461.21, and 471.39 MPa, respectively. Thus, the three lower points (370, 390, and 400) reveal a greater influence of the m-phase, seven points in the middle of the graph reveal a mixture of the m-phase and t-phase, and the upper five (476, 480, 484, 490, and 494) reveal the larger influence of the t-phase. In each of them, the Weibull modulus is slightly different, the  
Figure 11: Three phases in the experimental bending strength for ZrO\({}_{2}\)-5 wt.% CeO\({}_{2}\) sintered sample. The black triangles in the graph represent high content of m-phase, the red points represent mixture of m-phase and t-phase, and the blue squares represent high content of t-phase. The solid lines represent the linear fits, while the dashed line represents the linear fit of the total Weibull model. \begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Phase**} & **Phase** & \multicolumn{3}{c}{**Fit Parameters**} & \multicolumn{3}{c}{**Statistics of the Fit**} & \multicolumn{3}{c}{**Weibull Distribution Parameters**} & \multirow{2}{*}{**Am \({}^{*}\), deg**} & \multirow{2}{*}{**Median**, **GPA**} \\ \cline{3-3} \cline{5-10}  & **Cont.** & & & & & & & & & & \\ \cline{1-1}  & **\%** & & & & & & & & & & \\ \hline I & 3.1\% & 21.838 \(\pm\) 0.027 & \(-\)132.538 \(\pm\) 0.162 & 1.000 & 0.0015 & 2.302 \(\times\) 10\({}^{-6}\) & 21.84 \(\pm\) 0.03 & 423.31 \(\pm\) 0.19 & 1.356 & 425.12 \\ \hline II & 92.5\% & 14.757 \(\pm\) 0.845 & \(-\)90.518 \(\pm\) 5.149 & 0.992 & 0.0657 & 0.0043 & 14.76 \(\pm\) 0.85 & 461.21 \(\pm\) 7.49 & 0.100 & 449.90 \\ \hline III & 4.4\% & 26.402 \(\pm\) 2.195 & \(-\)162.617 \(\pm\) 13.573 & 0.989 & 0.0667 & 0.0045 & 26.40 \(\pm\) 2.20 & 471.39 \(\pm\) 15.58 & 1.808 & 464.89 \\ \hline \hline \end{tabular} \({}^{*}\) The difference between the slope of the total Weibull model and linear fit (phase I, II, or III) converted to degrees.  
\end{table} 
Table 5: The results of the linear fitting of three phases, along with the Weibull distribution parameters. highest for the upper and the smallest for the middle part. The variation in the Weibull distribution parameters seems to be related to the temperature gradient during sintering, which in turn is related to the grain size.