Simultaneous monitoring of profile parameters using Bayesian methods

Industrial processes are often characterized by their associated quality characteristics, forming a profile that can exhibit linear or nonlinear patterns. While various methods have been proposed for monitoring simple linear profiles, Bayesian approaches are increasingly favoured for their ability to integrate prior knowledge, update beliefs, and provide superior inference compared to classical methods. This research introduces novel Bayesian control charts for simultaneous monitoring of simple linear profile parameters. These methods offer advantages such as requiring only a single charting constant, simplicity, efficiency and ease of application while effectively managing parametric uncertainty. Simulation results demonstrate that the proposed charting scheme outperforms existing methods. Specifically, newly designed control charts, such as Max-EWMA, SS-EWMA, EWMA-Max and EWMA-SS-3, implemented using methods A, B and C and based on Bayesian techniques, exhibit superior performance. The SS-EWMA-3-[A]-B chart is the most effective. Additionally, the significance of these charts was assessed using real chemical engineering data.