Technological development and production processes require statistical process control in the use of alternative techniques to evaluate a productive process. This paper proposes an alternative procedure for monitoring a multivariate productive process using residuals obtained from the principal component scores modeled by the general class of autoregressive integrated moving average (ARIMA) and the generalized autoregressive conditional heteroskedasticity (GARCH) processes. We seek to obtain and investigate non-correlated and independent residuals 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 principal component analysis deals with the correlation among the variables and reduces the dimensions. The ARIMA-GARCH model estimates the mean and volatility of the principal components selected, providing independent residuals that are analyzed using control charts. Thus, a multivariate process can be assessed using univariate techniques, taking into account both the mean and the volatility behavior of the process. Therefore, we present an alternative procedure to evaluate a process with multivariate features to determine the level of volatility persistence in the productive process when an external action occurs.

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ARIMA models,Autocorrelated process,GARCH models,Multivariate statistical process control,Residual control chart,Statistical process control,Volatility

• Mathematics - Natural Sciences
• Civil Engineering - Engineering and Technology
• Mechanical Engineering - Engineering and Technology
• Chemical Engineering - Engineering and Technology
• Economics and Business - Social Sciences
• Other Social Sciences - Social Sciences