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| Main Author: | |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2605.03326 |
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Table of Contents:
- 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.