## 4 Discussion  
In this study we compared the different methods in order to determine the best method to obtain the RPT of AlSi\({}_{10}\)Mg alloys. **Method 1** sometimes is not suitable for the determination of RPT, because in the second derivation curve two minimum can be presented, as is shown in Figure 1.  
**Method 2** was designed for hypereutectic alloys, and it is sometimes difficult to determine the exact point for the RP of the hypoeutectic aluminum alloys. The difficulties in determining the exact point reduces the accuracy of the calculations, and for example magnesium has no statistical signification after analyzing the t student coefficient. **Method 3** is based on the application of higher order derivatives of the temperature curve with respect to time, with a very similar coefficient of determination in comparison to those of Method 1 and Method 2. However, neither of these methods reflects the effect of magnesium over on the RCP values in the regression models. The reason seems to be that the application of the method is not as accurate because the size of the thermal cup plotting the dT/dt curve vs. time is not considered. Figure 8: Effect of Mg percentage over RPT employing Method 5. \begin{table}
\begin{tabular}{c c c c c c c c c c c c} \hline \hline
**Meth.** & **Si** & **Mg** & **Fe** & **Cu** & **Ni** & **Cr** & **Mn** & **Ti** & **Zn** & **Pb** & **Sn** & **Sr** \\ \hline
1 & 1.65 & 2.14 & 1.21 & 0.95 & 0.04 & 0.47 & 1.78 & 1.37 & 0.64 & 0.13 & 0.27 & 0.00 \\ \hline
2 & 1.48 & 2.05 & 1.18 & 0.91 & 0.05 & 0.45 & 1.75 & 1.32 & 0.69 & 0.17 & 0.27 & 0.07 \\ \hline
3 & 1.40 & 1.99 & 1.41 & 1.11 & 0.29 & 0.50 & 1.62 & 1.12 & 0.80 & 0.05 & 0.17 & 0.18 \\ \hline
4 & 1.53 & 2.21 & 1.54 & 1.11 & 0.00 & 0.56 & 2.00 & 1.37 & 0.82 & 0.16 & 0.01 & 0.41 \\ \hline
5 & 2.22 & 3.09 & 0.83 & 0.55 & 0.33 & 0.11 & 0.92 & 0.66 & 0.02 & 0.31 & 0.61 & 0.76 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Student t values for regression models for calculation of RPT. **Method 4** is based on the use of a derivative curve but plotting dT/dt versus temperature, and the rest of the methods are based on the moment when the cooling rate is constant, so that all the dendrites touch each other, compared with the concept of acceleration in Method 4, where only a limited number of dendrites touch each other, which may promote an increase in the cooling rate of the sample. It is proven that temperature is a more reliable parameter because it is not influenced by the cup size. Thus, it has the smallest standard error (1.29 \({}^{\circ}\)C). However, the rest of the results are very similar to those of Method 1, 2, and 3, because it is quite difficult to define the exact RPT value, as the acceleration of the cooling rate is the base to determine the exact point where the RPT starts. It is not so easy to determine the exact point where the tangent is in the elbow area of the curve. **Method 5** is the most accurate process for determining the RPT values, with the highest coefficient of regression, combined with a small error. In addition to using higher order derivatives, it uses the dT/dt derivative curve with respect to the temperature in order to define the RPT. It is similar to Method 3 in using higher order derivatives to determine the RPT but in this case the temperature derivative curve with respect to the time is in a way similar to Method 4, thus the coefficient of regression is reduced. By the study of student t results, we can observe that the method with the highest values is obtained for Method 5. The results obtained show a result that is consistent with previous results in the literature, since it has been determined that magnesium is the main element that influences the RPT values and is the element with the highest student t coefficient [20]. This method is the only one that indicates that silicon also has a statistical effect on the RPT values.