An alternative method for the evaluation of a multivariate productive process in the presence of volatility

Technological development and production processes require that the statistical process control uses alternative techniques for the evaluation of a productive process. This paper proposes an alternative procedure to the monitoring of a multivariate productive process using residuals obtained from principal component scores modeled by the general class of AutoRegressive Integrated Moving Average (ARIMA) and the Generalized AutoRegressive Conditional Heteroskedasticity - (GARCH) processes. Non-correlated and independent residuals are sought to be obtained and investigated by means of X-bar and Exponentially Weighted Moving Average (EWMA) charts as a way to capture large and small variations in the productive process. The level of volatility persistence in the productive process is intended to be determined when an external action occurs. The principal component analysis deals with the correlation among the variables and provides the dimensionality reduction. The ARIMA-GARCH model estimates jointly the mean and volatility of the principal components selected, providing independent residuals that are analyzed by means of control charts. Thus, a multivariate process can be assessed by univariate techniques, with the advantage of taking into account both the mean and the volatility behavior of the process. Therefore, we emphasize that an alternative procedure is presented to evaluate a process with multivariate features.