# Design Optimization of the Aeronautical Sheet Hydroforming Process Using the Taguchi Method
## 2 [PERSON]'s Robust Design Method  
The classical analysis of conducting trials to optimize production processes by analyzing several factors is usually a complex process with high time consumption [12]. In the case of statistically designed experiments, several individual experiments are performed simultaneously. However, there are problems such as the sequence of the experiments to be performed and the analysis of the influence of different independent variables analyzed during the trials. Given these aspects, [PERSON] established a methodology for the design of factorial experiments that would allow optimizing productive processes [7; 8]. This methodology emphasizes the use of fractional factorial designs and other orthogonal matrices in novel ways with the purpose of achieving four aspects [13]; (i) manufacture products that are robust to environmental conditions; (ii) make the products insensitive to the variation of components; (iii) minimizing the mean square error over an objective value; and (iv) greater reliability and product life. The experiments planned statistically with the Taguchi methodology allow one to recognize and characterize those parameters of the analyzed process that reduce the variation of their performance [14]. Additionally, the Taguchi methodology has been widely applied in developmental trials, consisting of the detection of the optimal configurations of the analyzed parameters of a process through a reduced number of experiments [7]. Therefore, the application of the Taguchi methodology allows one to optimize the process quickly [15]. The experiments are designed in the form of orthogonal matrices. These experiments include several individual experiments that should be performed in a random manner. In this way the error is reduced, and the efficiency of the results is improved. For identification, the level indicator \"L\" and the number of trials performed are used. Thus, experiments of type L4, L9, and L18 can be configured with 4, 9, and 18 trials, respectively. To understand the methodology, it is fundamental to distinguish two types of factors. All the processes analyzed by the Taguchi methodology are affected by a series of controllable and noncontrollable factors. Noncontrollable factors (also known as noise factors) make it difficult to achieve desirable quality levels. In practice, they are usually factors whose control requires high economic investment. The main aim of the robust design of a process is to reduce the sensitivity of noise factors [16]. The signal-to-noise index (SN) establishes the quality and shows the relationship between control factors and noise factors, allowing one to determine the most robust design [17]. The use of orthogonal arrays allows analyzing different combinations of control factors and noise factors. To determine the effect of each factor, SN should be calculated in each experiment. For this, the following equations are used:  
\[SN_{i}=10\log\frac{y^{2}}{s^{2}} \tag{1}\]  
\[y_{i}=\frac{1}{N_{i}}\sum_{u=1}^{N_{i}}y_{i,u} \tag{2}\]  
\[s_{i}=\frac{1}{N_{i}-1}\sum_{u=1}^{N_{i}}\left(y_{i,u}-\overline{y}_{i}\right) \tag{3}\]  
where \(i\) is the experiment number, \(y_{i}\) is the value of the behavioural characteristic for a given experiment, \(\overline{y}_{i}\) is the average value, \(s_{i}\) is the variance, \(N_{i}\) is number of trials for experiment i, and \(u\) is the trial number. Depending on the process analyzed, it should be sought to minimize or maximize the performance characteristic.