Aiming at the problem of low probability of occurrence events such as coal mill failures that are difficult to extract and used for machine learning classification, resulting in low fault diagnosis accuracy, a PCA-FINCH high-precision fault diagnosis method for small samples is proposed. Firstly, based on principal component analysis PCA, fault detection is carried out on the historical data that characterizes the operating state of the equipment, and the occurrence of faults is detected and the fault samples are identified through the T² control limit and the Q control limit, and the fault samples are extracted to form a small sample fault set; Secondly, based on the FINCH classifier, the obtained small sample fault set is accurately classified to realize the fault diagnosis of the equipment. Finally, the method is verified using a historical data set containing coal mill faults. The results show that the PCA-FINCH fault diagnosis method proposed can achieve high-precision classification of small-sample faults, and its accuracy is 2.61 percentage points, 1.74 percentage points and 1.85 percentage points higher than that of decision tree CART, random forest RF and support vector machine SVM, respectively, and its convergence speed is excellent.