The stability and safety of industrial process operations have a decisive impact on the high-quality development of the economy and industry. However, the traditional model is difficult to adapt to the increasingly complex production process. In this paper, based on the probabilistic linear discriminant analysis model, we construct a fault monitoring model for industrial process operation, and through kernel density estimation, we judge whether the statistical indexes exceed the control limit so as to determine whether the industrial operation system has a fault. Using a genetic algorithm, the parameters of the model are optimized and modified to find the optimal value of the model. The performance of the model and its practical application were analyzed through the Tennessee-Istman process, and the effect of parameter modification was investigated. The experiments indicate that the KPLDA model’s parameter modification improves its ability to recognize faults with smaller amplitude, with only three minor errors, and provides more accurate fault reporting on data samples. The KPLDA model’s prediction range basically overlapped with the actual measurements until sample point 80, and the prediction trend of gray score values above 0.95 in the range of sample points 120-200 differed slightly from the actual measurements, with better prediction results overall.