A Stochastic-Adaptive Quality Control Framework for Non-Stationary Manufacturing Processes

Traditional Statistical Process Control (SPC) methods are grounded in stationarity assumptions that are inconsistent with the dynamic operating conditions of modern manufacturing. This paper develops the Stochastic-Adaptive Quality Control (SAQC) framework as a rigorous classical conceptual and mathematical foundation for quality control in non-stationary processes. The framework is motivated through a targeted review of theoretical and methodological gaps in existing approaches, particularly the lack of unified integration among stochastic process modeling, adaptive parameter estimation, uncertainty quantification, and control decision-making. SAQC addresses these gaps by combining stochastic differential equation (SDE) modeling, recursive Bayesian estimation, and optimal control principles within a single coherent architecture. The framework further introduces adaptive predictive control limits, belief-dependent decision rules, and a hierarchical multi-time-scale structure for monitoring, estimation, and control adaptation. The contribution of this paper lies in establishing a coherent theoretical basis for adaptive quality control under evolving process conditions, while explicitly identifying the assumptions, limitations, and validation requirements necessary for future empirical assessment. In this form, SAQC is positioned as a standalone theoretical foundation for subsequent methodological and computational extensions.