On the Use of Copula for Quality Control Based on an AR(1) Model

Manufacturing for a multitude of continuous processing applications in the era automation and ‘Industry 4.0? is focused on rapid throughput while producing products acceptable quality that meet customer specifications. Monitoring stability or statistical control key process parameters using data acquired from online sensors fundamental to successful manufacturing applications. This study addresses significant problem positive autocorrelation collected sensors, which may impair assessment control. Sensor at short time intervals typically have autocorrelation, traditional (SPC) techniques cannot be deployed. There plethora literature SPC presence autocorrelation. paper contributes this area by investigating performance ‘Copula’ based charts assessing average run length (ARL) when subsequent observations are correlated follow AR(1) model. The conditional distribution yt given yt?1 used deriving chart limits three different categories Copulas: Gaussian, Clayton, Farlie-Gumbel-Morgenstern Copulas. Preliminary results suggest overall Clayton Copula better compared other Archimedean more robust with respect changes standard deviation as correlation coefficient increases.