Process monitoring is becoming increasingly essential for ensuring safety in industrial production and maintaining product quality. In many real-world applications, processes consist of multiple interdependent stages, with the quality of each stage following a Poisson distribution. Autocorrelation is often a crucial element in Poisson-dependent multistage processes, and its omission leads to invalid conclusions. To effectively model the flexible autocorrelation, present in count data, state-space models are typically employed under specific conditions. This paper contributes to this area by presenting an effective deep learning approach, an autoencoder-based control chart, tailored for Poisson multistage processes. It presents a new training method based on an optimization problem for the stacked autoencoder, utilizing the Poisson state space representation. Numerical Phase II studies demonstrate that, compared to the state-of-the-art group EWMA control chart, the proposed monitoring scheme outperforms its competitor under various out-of-control situations. As another notable contribution, it also introduces a novel autoencoder-diagnostic approach to identify the stage responsible for any shifts. Additionally, comprehensive simulation results reveal a considerable difference in precision, with the autoencoder diagnosis classifier substantially exceeding the benchmarks. Furthermore, these findings are supported by a real-world application from the financial market.

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