## 2 Materials and Methods
### Statistical Analysis  
In terms of statistical analysis of the dataset, Figure 1 represents the step-by-step follow-up to the presented results. Initially, there is a verification of the dataset quantity and sampling available, leading to identifying its distribution. Normal distribution indicates a low standard deviation, while non-normal distribution refers to a dataset with a high standard deviation, i.e., dispersed from the central value. As shown in Figure 1, the Kolmogorov-Smirnov test is recommended when one has more than 50 data points, while the Shapiro-Wilk test is mostly implied when one has less \begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline
**Well** & & **DEPTH** & **TOR** & **RPM** & **FLOW** & **WOB** & **ROP** & **ECD** & **SR** & \(\phi\)**Bit** \\  & & **[m]** & **[kN-m]** & **[rev/min]** & **[L/min]** & **[tf]** & **[m/h]** & **[sg]** & **[\%]** & **[in]** \\ \hline
15\_9-F-1 & Min. & 2750 & 13.52 & 124.93 & 2367.36 & 1.44 & 16.81 & 1.34 & 0.02 & 8.50 \\  & Max. & 3090 & 22.45 & 161.03 & 2411.20 & 12.07 & 40.22 & 1.37 & 1.08 & 8.50 \\ \hline
15\_9-F-1 A & Min. & 2770 & 12.50 & 138.17 & 2343.60 & 0.37 & 9.17 & 1.34 & 0 & 8.50 \\  & Max. & 3209 & 23.87 & 161.08 & 2387.01 & 19.22 & 39.45 & 1.42 & 1.11 & 8.50 \\ \hline
15\_9-F-1 B & Min. & 2790 & 14.81 & 19.67 & 1840.03 & 1.03 & 1.82 & 1.29 & 0 & 8.50 \\  & Max. & 3300 & 26.08 & 150.28 & 4009.08 & 21.49 & 33.04 & 1.55 & 1.10 & 8.50 \\ \hline
15\_9-F-11 T2 & Min. & 2830 & 1.50 & 66.11 & 1996.22 & 0.54 & 4.83 & 1.34 & 0 & 8.50 \\  & Max. & 3980 & 24.78 & 180.57 & 2500.47 & 13.64 & 40.25 & 1.44 & 1.12 & 8.50 \\ \hline \end{tabular}
\end{table} 
Table 1: Dataset from the wells used. Figure 1: Statistical analysis appliance flowchart. than 50 data points under analysis. Additionally, if the dataset has a normal distribution (\(p\)-value \(>\) 0.05), the Pearson Correlation test is recommended. For non-normal distribution (\(p\)-value \(<\) 0.05), the Spearman test is recommended (36; 37). According to [PERSON] and [PERSON] (2016), [PERSON]'s correlation is a statistical measure that evaluates the strength and direction of a linear relationship between two continuous variables. The Pearson correlation coefficient, often represented by '\(\rho\)', ranges from \(-1\) to +1. The calculation of [PERSON]'s correlation involves the covariance between the two variables, divided by the product of the standard deviations of each variable, as indicated by Equation (2):  
\[\rho=\frac{\text{cov}(\text{X},\text{Y})}{\sigma\text{X}\cdot\sigma\text{Y}} \tag{2}\]  
where \(\text{cov}(\text{X},\text{Y})\) is the covariance between the variables X and Y; \(\sigma\text{X}\cdot\sigma\text{Y}\) are the standard deviations of X and Y, respectively. [PERSON]'s correlation assumes that the variables are normally distributed and that the relationship between them is linear. It is important to highlight that this correlation only assesses linear relations between variables, as it is incapable of capturing non-linear relations. If the relationship between the variables does not follow a linear pattern, [PERSON]'s correlation may underestimate the strength of the association. Additionally, this correlation is sensitive to outliers, meaning that extreme values can significantly influence the result. On the other hand, [PERSON]'s correlation, as described by [PERSON] and [PERSON] (2016), is a non-parametric statistical measure that evaluates the degree of correlation between two variables. Unlike [PERSON]'s correlation, which assumes a linear relationship between variables and is used for datasets with a normal distribution, [PERSON]'s correlation only assesses whether the variables have a monotonic relationship. That is, it measures the extent to which one variable tends to increase or decrease as the other varies. The advantage of [PERSON]'s correlation is its robustness to outliers and the non-linear nature of relationships between complex variables when analyzing drilling processes.