TIME-ADAPTIVE BAYESIAN QUALITY CONTROL (TABQC): A STATE-SPACE FRAMEWORK FOR DYNAMIC PROCESS MONITORING

Abstract

Modern industrial production systems increasingly exhibit autocorrelation, structural breaks, heavy-tailed disturbances, and time-varying process parameters, conditions that violate the assumptions underlying classical statistical process control (SPC) methods. This study develops a Time-Adaptive Bayesian Quality Control (TABQC) framework for monitoring dynamic industrial processes. The framework integrates Bayesian hierarchical inference with state-space time-series modelling to generate adaptive predictive control limits that evolve as new data become available. In the proposed approach, process parameters are treated as latent dynamic states and are updated sequentially using Bayesian learning techniques. Posterior predictive distributions are then used to construct monitoring limits that incorporate parameter uncertainty, temporal dependence, and structural changes. Theoretical relationships between TABQC and classical control charts, including Shewhart, CUSUM, EWMA, and ARIMA-residual monitoring are established.Monte-Carlo simulation experiments and an industrial case application are conducted to evaluate the performance of the framework under autocorrelation, gradual drift, structural breaks, and heavy-tailed disturbances. Results indicate that TABQC provides improved detection of process changes while maintaining stable false-alarm behaviour compared with traditional monitoring schemes. The study demonstrates that Bayesian predictive monitoring offers a flexible and robust foundation for quality control in modern Industry 4.0 environments characterised by dynamic and data-intensive production systems.