🤖 AI Summary
This paper addresses online change detection for binary (conforming/non-conforming) responses in multi-production-line systems. We propose a dynamic monitoring method based on adaptive sampling. Our approach innovatively formulates change detection as a Markov decision process (MDP) with average reward, where the reward function jointly incorporates the likelihood ratio test statistic and sampling information; the optimal sampling policy is derived via Bellman iteration. The method enables real-time identification of potentially out-of-control lines and prioritizes sampling accordingly. Experimental results demonstrate that, when sample size ≥ 20, the proposed method achieves significantly higher statistical power than proportional random sampling. Moreover, both the average sampling proportion allocated to anomalous lines and overall detection performance improve monotonically with increasing sample size or greater disparity in out-of-control/ in-control probabilities across lines.
📝 Abstract
We propose using an adaptive sampling method to detect changes for a system with multiple lines. The adaptive sampling utilizes the information in responses to learn on which line is more likely to have a change thus allocating more units to the line. The learning process is formatted as a Markov decision process by integrating sampling information with likelihood ratio for changes to define rewards and the optimal sampling is approximated by using the Bellman operator iteratively based on the average reward criterion. We demonstrate the performance of the proposed method for binary responses using the exact distribution method for adaptive sampling. Our numeric results show that the adaptive sampling samples more often the line that has a change and the statistical power to detect a change is better than those with the equal randomization for sample sizes of 20 or higher. When sample sizes increase or the difference between out-of-control and in-control probabilities increases, the adaptive sampling allocates higher proportion of units averagely to the line with a change and the statistical power to detect a change increases.