An Area-based Methodology for the Monitoring of General Linear Profiles

Statistical profile monitoring has received much attention during recent years. While numerous contributions and applications have been demonstrated in the literature, the control statistics across many of the proposed methodologies have mainly remained unchanged, which somehow hinders further improvement of the monitoring schemes. In this paper, however, we propose a novel approach to leverage the information in the area formed between the sampled and in‐control profile to improve the monitoring scheme performance. Specifically, we develop a control statistic based on the convolution of the observed and in‐control profiles to monitor the shifts in the slope and intercept parameters. We also extend the mean square statistic to area weighted total sum of squares, to more effectively monitor the shift in the standard deviation. Extensive simulation studies are conducted to demonstrate the performance of the proposed methodology in comparison with some of the existing approaches.