The technological era has greatly promoted the informatization of the cigarette production process, making it a hotspot for research on how to use production data for quality management and correlation analysis. The article employs Pearson’s correlation coefficient and the Apriori algorithm to identify the frequent item set and correlation structure associated with the quality management of cigarette production, as well as to identify the key factors that influence this quality management. Then, we combined historical data and prioritized data points with Lajda’s law to split the distribution of events, enabling accurate construction of the item event library and single-point data factor search analysis. Finally, based on the results of correlation and causal analysis, the FDGM model for time series analysis is constructed using a priori knowledge combined with graph neural networks to realize causal learning and real-time prediction and evaluation of cigarette production quality management. The correlation coefficient between the total downtime and the production efficiency after removing the cumulative effect is 0.946, and the enhancement degree of the strong correlation rules is all greater than 1.55. The prediction F1 value of the FDGM model can be up to 0.910, and the importance of cigarette temperature in production quality is the largest at 90.62%. The evaluation score for silk production quality improved from 91.58 to 97.74, with an overall improvement of 6.73%. The combination of graph neural networks and correlation analysis algorithms can effectively detect abnormalities in cigarette production quality management and improve the quality of cigarette production.