## 3 Results
### Taguchi Analysis  
The Taguchi analysis for the friction coefficient between rubber samples and granite tiles was conducted in several iterations. In the first design of the Taguchi method, all parameters (variables) were used, and the analysis revealed that hardness had a strong correlation with the other parameters, so it was excluded from further analysis. In the second analysis, the parameters used were hysteresis, speed, roughness, and substrate condition. The design of the Taguchi experiment in this specific case was not orthogonal. This study evaluated the coefficient of friction using the nominally best characteristic.  
\begin{table}
\begin{tabular}{c c c c c} \hline \multicolumn{5}{c}{**Regression Statistics**} \\ \hline Multiple R & & 0.880958 & \\ \hline R-Squared & & 0.776087 & \\ \hline Adjusted R-Squared & & 0.764145 & \\ \hline Standard Error & & 0.043438 & \\ \hline Observations & & 80 & \\ \hline  & _df_ & \(SS\) & \(MS\) & \(F\) & _Significance F_ \\ \hline Regression & 4 & 0.490486 & 0.122622 & 64.98802 & \(1.28\times 10^{-23}\) \\ \hline Residual & 75 & 0.141513 & 0.001887 & \\ \hline Total & 79 & 0.631999 & \\ \hline  & _Coefficients_ & _Standard Error_ & _t-Stat_ & _p-value_ \\ \hline Intercept & \(-0.8275\) & 0.241086 & \(-3.43238\) & 0.000977 \\ \hline Hysteresis & 0.5 & 0.095243 & 5.249705 & \(1.37\times 10^{-6}\) \\ \hline Hardness & 0.0249 & 0.003341 & 7.452363 & \(1.31\times 10^{-10}\) \\ \hline Roughness & \(-0.00013\) & \(3.89\times 10^{-5}\) & \(-3.21735\) & 0.001911 \\ \hline Speed & \(-0.13525\) & 0.009713 & \(-13.9247\) & \(1.73\times 10^{-22}\) \\ \hline \end{tabular}
\end{table}
Table 7: Anti-slip tile regression data (wet, soapy).  
\begin{table}
\begin{tabular}{c c c c c} \hline \multicolumn{5}{c}{**Regression Statistics**} \\ \hline Multiple R & & 0.788303 & \\ \hline R-Squared & & 0.621422 & \\ \hline Adjusted R-Squared & & 0.600094 & \\ \hline Standard Error & & 0.04788 & \\ \hline Observations & & 76 & \\ \hline  & _df_ & \(SS\) & \(MS\) & \(F\) & _Significance F_ \\ \hline Regression & 4 & 0.267175 & 0.066794 & 29.13597 & \(2.44\times 10^{-14}\) \\ \hline Residual & 71 & 0.162767 & 0.002292 & \\ \hline Total & 75 & 0.429942 & \\ \hline  & _Coefficients_ & _Standard Error_ & _t-Stat_ & _p-value_ \\ \hline Intercept & 0.600628 & 0.276521 & 2.172091 & 0.03319 \\ \hline Hysteresis & \(-0.45165\) & 0.109357 & \(-4.1301\) & 9.76E-05 \\ \hline Hardness & 0.000105 & 0.003858 & 0.027102 & 0.978454 \\ \hline Roughness & \(-0.00024\) & \(4.39\times 10^{-5}\) & \(-5.46229\) & \(6.57\times 10^{-7}\) \\ \hline Speed & \(-0.07286\) & 0.01103 & \(-6.60523\) & \(6.17\times 10^{-9}\) \\ \hline \end{tabular}
\end{table}
Table 8: Smooth tile regression data (wet, soapy).  
Table 9 presents the means of the responses for different surface conditions, rubber hysteresis, roughness, and speeds obtained by the Taguchi method. The delta values were used to determine the ranking of these factors in terms of their influence on the coefficient of friction (COF). The analysis revealed that for all surface conditions, the most significant factor influencing the COF was the surface conditions, followed by hysteresis, roughness, and speed.  
Figure 5 shows the main effects on the COF obtained by the Taguchi method. The figure highlights the parameters influencing the COF: increasing the hysteresis and roughness decreased the COF, while increasing the speed slightly raised it. Altering the substrate conditions from dry to wet or soapy significantly reduced the COF.  
Table 10 shows the response table for means under wet and soapy conditions. Under these conditions, the roughness and surface conditions were the most influential parameters on the COF, followed by rubber hysteresis and speed.  
Figure 6 emphasizes the main effects on COF under wet and soapy conditions obtained by Taguchi method. Notably, as the surface roughness increased, the COF also rose, contrary to the behavior observed with speed, where an increase in speed resulted in a decrease in the COF.