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

Abstract

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