BAYESIAN STOCHASTIC VOLATILITY–DRIVEN CONTROL CHARTS FOR NON-STATIONARY PRODUCTION PROCESSES

Abstract

Traditional statistical process control (SPC) methods rely on constant-variance assumptions that are frequently violated in modern production, service, and financial systems. Empirical evidence shows that process variability often evolves, exhibiting persistence, clustering, and abrupt bursts. Under such conditions, fixed-limit control charts such as Shewhart, Exponentially Weighted Moving Average (EWMA), and Cumulative Sum (CUSUM) control charts suffer from inflated false alarm rates and delayed detection. This paper propose a Bayesian Statistical Process Control (SPC) framework that explicitly models time-varying process variance using stochastic volatility dynamics within a state-space formulation. Posterior predictive distributions used to construct adaptive control limits that respond automatically to changes in uncertainty. Simulation studies demonstrate superior detection performance and improved false alarm stability under joint mean–variance shifts and volatility persistence. An application to Nigerian Stock Exchange 30 index returns was used to illustrate the practical relevance of the approach in environments characterized by volatility clustering. The results showed that incorporating stochastic volatility into Bayesian SPC provide interpretable, uncertainty-aware monitoring decisions and constitutes a robust alternative to classical fixed-variance charts.