## 1 Introduction
For example, the machining behavior of cast parts is very much related to the presence and quantity of the different intermetallics that can be formed during the solidification process of the alloy, promoting differences in the machinability in comparison with other manufacturing processes [6]. TA techniques can predict the presence and quantity of precipitated intermetallics, depending on the alloy composition. In TA, plotting temperature versus time, a curve is obtained that with its derivatives is used to characterize the solidification path of the alloy [7; 8; 9; 10]. To obtain the cooling curve, liquid aluminum is preheated approximately to 100 \({}^{\circ}\)C above its liquidus temperature, and then it is poured into a defined thermal analysis cup made from ceramic, steel, graphite, or sand. One, two, or more thermocouples are located in the analysis cup connected to data loggers, plotting the cooling curves. On observing only the cooling curve it is not possible to detect all the thermal events, especially when they are too weak. They are only detected using first and/or consecutive derivative curves of the cooling curve. There are four main processes for the determination of RPT temperature. The first, the mechanical-rheological method, is based on the continuous recording of the torque required to produce the rotation of a disc or paddle in a liquid metal [11; 12], until the dendrite structure becomes mechanically rigid, stopping the rotation of the impeller. The temperature at which this occurs is defined as the RPT. The second is based on the in-situ study of neutron diffraction during casting. However, this system needs a large detector to obtain enough resolution of the diffraction peak in the semi-solid state [13]. The third method corresponds to the two thermocouples thermal analysis technique [14] to determine the temperature data at the center (T\({}_{c}\)) and at a nearby inner wall (T\({}_{w}\)) with two thermocouples. The RPT is determined with the second minimum on the \(\Delta\)T versus time curve (\(\Delta\)T = \(\mathrm{Tw}-\mathrm{Tc}\)) and its projection on the Tc cooling curve. Due to the difference in the thermal conductivity in the solid and liquid phases, there is a minimum on the \(\Delta\)T versus time curve. There are other methods that are based on employing only one thermocouple to decrease costs and to increase productivity of the data analysis. However, there is no work in which this method has been applied to aluminum alloys. It seems that the application of these methods is not suitable when thermal signal of the cooling curve is weak and also in the case of hypereutectic aluminum alloys, which are studied in the following section. It has been demonstrated that the use of a derivative beyond the first derivative could extend the use of thermal analysis techniques allowing new properties related to the solidification process to be obtained. This work suggests that the application of Taguchi techniques to obtain new regressions models based on alloy composition to determine the rigidity point for AlSi\({}_{10}\)Mg alloy could be a more precise and cheaper way through the advanced thermal analysis techniques. The Taguchi method has been quite often applied in the improvement and control of industrial processes in different sectors, no application of the Taguchi method has been observed in the literature. In addition, this method could also be used to analyze other types of aluminum alloys. In the present study, a design of experiments based on the Taguchi method was employed to compare the effect of the major and minor alloying elements over the obtained RPT values, and to evaluate the accuracy of every studied method for AlSi\({}_{10}\)Mg alloys by employing only one thermocouple to register the solidification.