Sequential Bayesian Monitoring for Recoverable and Drifting Processes

TL;DR

This paper introduces Bayesian methods for real-time monitoring of processes to determine if they are currently operating acceptably, especially when processes can recover or drift over time.

Contribution

It develops recursive Bayesian procedures for detecting current process states in recoverable and drifting scenarios, extending traditional SPC methods.

Findings

Effective in tracking process recoverability and drift in simulated experiments.

Applicable to Gaussian, Binomial, and multivariate data examples.

Provides a framework for ongoing process assessment beyond initial change detection.

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.