Sequential Bayesian Monitoring for Recoverable and Drifting Processes

2026-05-04

AI Summary

This study addresses the limitation of traditional statistical process control, which emphasizes detecting historical shifts while neglecting the acceptability of the current process state. To overcome this, the authors propose a Bayesian sequential monitoring framework tailored for recoverable processes subject to parameter drift. By recursively computing the posterior probability that the process is in-control at the current time, the method shifts the monitoring focus toward real-time state assessment. The framework integrates time-to-failure modeling, Gaussian and binomial tracking, and multivariate data analysis within a unified Bayesian formulation. Demonstrated through simulation studies and an application to white wine quality data, the approach effectively identifies the current operational status of dynamic recoverable processes, significantly enhancing both monitoring accuracy and practical applicability.

Abstract

In many Phase II statistical process control (SPC) problems, the main concern is not whether a monitored process has ever changed, but whether it is currently operating at an acceptable level. This distinction is especially important when monitoring continues after a signal, or when corrective action may restore the process. We develop Bayesian monitoring procedures for this formulation of the Phase II task. For recoverable processes that may alternate between in-control and out-of-control states, we derive recursions for the posterior probability that the process is presently in control. For sequential tracking problems in which a latent parameter evolves over time, we monitor the posterior probability that the parameter lies inside an acceptable region of behavior. The methods are studied through calibrated time-between-failure experiments, Gaussian and Binomial tracking examples, and a held-out multivariate data illustration using white wine quality measurements.

Problem

• Statistical Process Control
• Bayesian Monitoring
• Recoverable Processes
• Drifting Processes
• Phase II SPC

Innovation

• Bayesian monitoring
• recoverable processes
• drifting parameters
• posterior probability recursion
• statistical process control