Sequential Bayesian Monitoring for Recoverable and Drifting Processes
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.
Cite
@article{arxiv.2605.03326,
title = {Sequential Bayesian Monitoring for Recoverable and Drifting Processes},
author = {Gordon J. Ross},
journal= {arXiv preprint arXiv:2605.03326},
year = {2026}
}