## 4 Results and Discussion
### Linear Regression Model for Reliability Prediction  
A linear regression model was adjusted considering all 12 process variables obtained. To determine the best set of predictors in the model, Table 3 presents the correlation matrix of predictors and responses to avoid collinearity effects. In which  
* R(t) is the exponential model for the reliability of ceramic plates;
* U129_IIT is the electrical current in the drive motor of the backwash pump;
* U129 is the frequency inverter control of the backwash pump motor;
* U009_IIT is the electrical current in the motor of the drum drive;
* PT325 is the vacuum pressure in the second cake-formation section;
* PT225 is the vacuum pressure in the first cake-formation section; \begin{table}
\begin{tabular}{c||c||c||c||c||c||c||c||c} \hline  & **U129\_IIT** & **U129** & **U009\_IIT** & **PT325** & **PT225** & **PT125** & **PT101** & **KPV325** & **PT329** & **PT129** & **FT129** & **Delta P** \\ \hline U129 & 0.114 & & & & & & & & \\ U009\_IIT & 0.355 & 0.073 & & & & & & & \\ PT325 & 0.061 & 0.09 & 0.039 & & & & & & \\ PT225 & 0.015 & 0.009 & 0.021 & 0.351 & & & & & \\ PT125 & \(-\)0.036 & \(-\)0.026 & 0.057 & 0.021 & 0.489 & & & & \\ PT101 & \(-\)0.045 & \(-\)0.093 & 0.022 & \(-\)0.055 & 0.454 & 0.794 & & & \\ KPV325 & \(-\)0.037 & \(-\)0.068 & \(-\)0.02 & \(-\)0.091 & \(-\)0.383 & \(-\)0.028 & 0.038 & & \\ PT329 & 0.132 & 0.526 & 0.031 & \(-\)0.01 & \(-\)0.018 & \(-\)0.013 & \(-\)0.004 & \(-\)0.001 & & \\ PT129 & \(-\)0.011 & 0.014 & \(-\)0.02 & 0.039 & \(-\)0.267 & \(-\)0.429 & \(-\)0.465 & \(-\)0.019 & 0.029 & \\ FT129 & 0.158 & 0.212 & 0.13 & 0.137 & \(-\)0.098 & \(-\)0.391 & \(-\)0.447 & \(-\)0.1 & 0.122 & 0.329 & \\ Delta P & 0.133 & 0.52 & 0.033 & \(-\)0.015 & 0.021 & 0.05 & 0.064 & 0.002 & 0.989 & \(-\)0.119 & 0.072 & \\ R(t) & 0.046 & 0.002 & \(-\)0.007 & 0.197 & 0.186 & \(-\)0.008 & \(-\)0.008 & \(-\)0.149 & \(-\)0.045 & 0.005 & 0.044 & \(-\)0.045 \\ \hline \end{tabular} Colors gradients indicate the magnitude of correlation coefficients, where red represents negative correlation and green positive.  
\end{table} 
Table 3: Predictor correlation matrix. Figure 9: Exponential model for ceramic plate failure data. * PT125 is the vacuum pressure in the cake-drying section;
* PT101 is the vacuum pressure in the vacuum pump;
* KPV325 is the percentage of valve opening in the second cake-formation section;
* PT329 is the pressure in the backwash pipeline before bag filtration;
* PT129 is the pressure in the backwash pipeline after the bag is filtered;
* FT129 is the backwash flow rate;
* Delta P is the pressure variation in bag filters. The correlation matrix can also be assessed by Figure 10, where the eigenvalue profiles of the first three components are responsible for explaining 81.9% of the variance. Figure 11 indicates a distribution of predictor candidates regarding their first two components, where some groups of variables can be determined. Three groups can be clearly distinguished: one representing vacuum pressure measurements (PT101, PT125, PT325 and PT225), a second one representing backwash pressure and flow measurements (PT129, PT329, U129_IIT, FT129), and one variable being strongly relevant to component number 2: second-cake-formation valve opening (KPV325). A similar grouping is noted in Table 3.  
An iterative procedure was performed to verify the best set of predictors by obtaining multiple regression models with different combinations of predictor groups to obtain the  
Figure 11: Loading plot of predictor candidates. Figure 10: Eingenvalue profiles for predictor candidates. R(t) response. The multicollinearity between predictors was verified and is presented in Table 3, in addition to the \(p\) values considering a significance level of 0.05 and the variance inflation factors (VIFs).