## 3 Results and Discussion
### Control

Table 9: _Cont._  
As can be seen, the values obtained after implementing the LSS framework fall within the range of the estimated values required to achieve a 50% reduction in variability. This proves the effectiveness of the improvement actions proposed, successfully fulfilling the research objective. Table 12 shows the upper limits (ULs), lower limits (LLs), average values (\(\overline{\chi}\)), and standard deviations (\(\sigma\)) for each parameter obtained using the data from Tables 9-11. The experimental composition values for P\({}_{1}\) and P\({}_{3}\) (Y\({}_{11R}\)', Y\({}_{31R}\)') exhibited a significant decrease in variability, with reductions of 50% and 40%, respectively, compared to the estimated values (Y\({}_{11R}\)*, Y\({}_{31R}\)*). Additionally, the average value (\(\overline{\chi}\)) for P\({}_{1}\) and P\({}_{3}\) decreased by 1.89% and 11.77%, respectively. These results led to a 38% decrease in global material overuse costs. The standard deviations and mean values of the data define the arguments of the normal distributions, enabling the determination of the probability of each data occurrence, as expressed by Equation (12). \[\varphi_{\overline{\chi},\sigma}(x)=\frac{1}{\sigma\sqrt{2\pi}}e^{-\frac{(x- \overline{\chi})^{2}}{2\sigma^{2}}} \tag{11}\] \begin{table}
\begin{tabular}{c c c c c c c c} \hline  & \(\mathbf{D_{1R}}\)* & \(\mathbf{Y_{11R}}\)* & \(\mathbf{D_{1R}}\)* & \(\mathbf{Y_{11R}}\)* & \(\mathbf{D_{3R}}\)* & \(\mathbf{Y_{31R}}\)* & \(\mathbf{D_{3R}}\)* & \(\mathbf{Y_{31R}}\)* \\ \hline UL & 1.223 & 0.056 & 1.225 & 0.054 & 1.175 & 0.057 & 1.175 & 0.049 \\ LL & 1.197 & 0.046 & 1.195 & 0.049 & 1.138 & 0.042 & 1.140 & 0.043 \\ \(\overline{\chi}\) & 1.211 & 0.053 & 1.209 & 0.052 & 1.153 & 0.051 & 1.158 & 0.045 \\ \(\sigma\) & 0.007 & 0.002 & 0.010 & 0.001 & 0.010 & 0.004 & 0.009 & 0.002 \\ \hline \end{tabular}
\end{table} 
Table 12: Upper limits (UL), lower limits (LL), average values (\(\overline{\chi}\)), and standard deviations (\(\sigma\)) for each parameter. \begin{table}
\begin{tabular}{c c c c} \hline  & \(\mathbf{P_{1}}\) & & \(\mathbf{P_{3}}\) \\ \hline \(\mathbf{D_{1R}}\)* & \(\mathbf{Y_{11R}}\)* & \(\mathbf{D_{3R}}\)* & \(\mathbf{Y_{31R}}\)* \\ kg/L & kg C\({}_{11}\)/kg T & kg/L & kg C\({}_{31}\)/kg T \\ \hline
1.215 & 0.050 & 1.141 & 0.044 \\
1.209 & 0.050 & 1.141 & 0.043 \\
1.216 & 0.056 & 1.158 & 0.046 \\
1.219 & 0.055 & 1.138 & 0.049 \\
1.217 & 0.056 & 1.138 & 0.049 \\
1.214 & 0.051 & 1.1 where \(\varphi_{\Xi,\sigma}(x)\) represents the density function. The graphical representation of this normal distribution can be expressed in terms of n\(\sigma\), where \(-6<\) n \(<\) 6 covers the behavior of the data within the Six Sigma range and is also standardized by dividing by the maximum value of the density function obtained (N(X, n\(\sigma\))). Figure 7 presents the normal distribution plots for the experimental values of P\({}_{1}\) (I, II) and P\({}_{3}\) (III, IV) products before and after LSS application, along with the target values to achieve a 50% reduction in variability. It is evident that the experimental data obtained after the application of the LSS tools (dotted line) closely align with the target values necessary to achieve the desired reduction in variability (orange line). Additionally, the experimental data obtained after the application of LSS tools (dotted line) show a narrower amplitude of the typical Gaussian curve than those obtained prior to the implementation of LSS tools (blue line). In the case of Y\({}_{1}\) and Y\({}_{3}\) values (Figure 7 II,IV), the experimental data obtained after implementing LSS tools show a distribution nearly identical to the target data required to achieve a 50% reduction in product variability; however, there are slight variations in the values of D\({}_{1}\) and D\({}_{3}\) (Figure 7,III). Thus, it can be stated that the improvement actions had a greater influence on composition (Figure 7,III) than on density (Figure 7 II,IV).