Abstract: To address the issues low-amplitude characteristics of minor faults in industrial processes and the inadequate adaptability of traditional fixed-threshold methods under multiple operating conditions, a minor fault detection method based on state exception analysis using nonnegative matrix factorization (NMF) was proposed in this paper. From a data-driven perspective, the operational data of complex industrial processes were systematically modeled to achieve effective extraction and identification of weak anomaly information. First, NMF was applied to obtain a low-dimensional representation of the high-dimensional process data, extracting the primary features characterizing the system's operational state. Second, the Wasserstein distance was introduced to measure the discrepancy between feature probability distributions, constructing distribution characteristics that describe subtle system state changes. Based on this, a dissimilarity statistic was defined to enhance the monitoring index’s sensitivity to early anomalies and minor faults. Furthermore, an adaptive threshold adjustment strategy based on data volatility was designed to achieve dynamic optimization of the threshold under varying operating conditions. Finally, experimental validation was conducted using multiple typical minor fault scenarios from the Tennessee–Eastman chemical process. The results indicate that, compared with traditional statistical process monitoring methods, significant advantages are exhibited by the proposed method in terms of fault detection rate, false alarm rate, and monitoring stability. The accuracy and robustness of minor fault detection are effectively improved, and its effectiveness and engineering application potential in complex industrial process monitoring are validated.