However, the integration of multivariate graphs with memory for process monitoring and variability analysis using multilayer perceptron artificial neural network and support vector machines (SVM) is not addressed. This research work proposes the development of an efficient methodology for the interpretation and analysis of out-of-control signals in a multivariate production system working in two phases. The first phase is carried out by the multivariate control chart that responds to the task of monitoring and surveillance of quality in the production system, and once a mismatch occurs in the process and an out-of-control signal is presented in the multivariate chart, phase two is used. The second phase is aimed at analyzing the source of variation by means of the artificial neural network (ANN). In this way, the procedure will allow the users of the production system to locate the variable(s) that cause(s) the lack of control in the process, being able to employ corrective actions that manage to reduce the production of out-of-specification products early on. The multivariate control and classification methods will be defined from experiments where they demonstrate their efficiency for the task of monitoring and interpretation of the variation generated in the manufacturing processes. Figure 1 shows the steps to develop the proposed methodology. After an introduction and bibliographic review of the subject to be dealt with in Section 1, the paper is organized as follows: Sections 2 and 3 are composed of the materials and methods used for the development of the proposed methodology, respectively. The results of the experiments and validation are shown in Section 4. Finally, the discussion of the procedure generated is presented in Section 5. \begin{table}
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**Authors** & **Year** & **Methods** & **Contribution** & **Limitations** \\ \hline \multirow{4}{*}{[PERSON] et al. [14]} & \multirow{2}{*}{2023} & \(\bullet\) & Multivariate control charts, MCUSUM, MEWMA, and Hotelling’s T\({}^{2}\) & The approach used for process monitoring is pattern recognition in multivariate control charts. & The research does not present a proposal to analyze the source of process variation beyond associating a lack of control in the manufacturing process to patterns generated in the multivariate plots. \\ \cline{1-1}  & & \(\bullet\) & Univariate control charts, CUSUM and EWMA. Support vector machines (SVMs). & A control chart more sensitive to changes in the mean vector is proposed compared to the MCUSUM and MEWMA control charts. \\ \cline{1-1}  & & \(\bullet\) & Hotelling’s T\({}^{2}\) multivariate control chart using a multilayer artificial neural network & Interprets out-of-control signals in the multivariate T\({}^{2}\) Hotelling chart using a multilayer artificial neural network. & The use of multivariate graphs with memory was not considered in defining the methodology. \\ \hline \multirow{4}{*}{[PERSON] et al. [17]} & \multirow{2}{*}{2024} & \(\bullet\) & Independent component analysis & Independent component analysis is combined with an SVM to implement multivariate process monitoring. & For implementation, the condition of statistical independence between variables must be met. \\ \cline{1-1}  & & \(\bullet\) & Independent component analysis & Independent component analysis is combined with an SVM to implement multivariate process monitoring. & For implementation, the condition of statistical independence between variables must be met. \\ \cline{1-1}  & & \(\bullet\) & Support vector machine (SVM) & Independent component analysis is combined with an SVM to implement multivariate process monitoring. & For implementation, the condition of statistical independence between variables must be met. \\ \hline \end{tabular}
\end{table} 
Table 1: _Cont._