Adaptive control chart mechanisms through Bayesian updating with normal prior distributions

Abstract:

Adaptive control charts that modify their parameters in response to incoming process data represent an important advancement in engineering process monitoring. This critical review examines the role of Bayesian updating with normal prior distributions as a mechanism for achieving adaptive behavior in control chart systems. The review encompasses published research from 2000 through 2022 that addresses the theoretical foundations, algorithmic implementations, and engineering performance evaluations of Bayesian adaptive control charts. The analysis identifies three principal adaptive mechanisms enabled by Bayesian updating: sequential narrowing of control limits as posterior precision increases, dynamic adjustment of sampling intervals based on posterior process state probabilities, and automatic recalibration of chart parameters following detected process changes. Performance evaluations across the reviewed literature demonstrate that Bayesian adaptive charts achieve average run length reductions of twenty to forty-five percent for small shifts while maintaining in-control ARL performance within five percent of the design target. The review further assesses the computational requirements of different Bayesian updating algorithms, ranging from closed-form conjugate updates requiring minimal processing overhead to particle filter implementations demanding substantial computational resources.