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.

翻译：在许多第二阶段统计过程控制问题中，主要关注的并非监控过程是否曾发生变化，而是其当前是否运行在可接受水平。这一区分在执行信号后持续监控或采取纠正措施可能恢复过程时尤为重要。我们针对这一第二阶段任务的定义开发了贝叶斯监控程序。对于可能在受控与失控状态间交替的可恢复过程，我们推导了过程当前处于受控状态的后验概率递推公式。针对潜参数随时间演化的序贯跟踪问题，我们监控参数位于可接受行为区域内的后验概率。通过校准的故障间隔时间实验、高斯与二项式跟踪示例，以及使用白葡萄酒质量测量数据的保留多变量数据示例，对这些方法进行了研究。