The relationship between quality abnormality and anomalous causes in the assembly process of CNC machine was described by fuzzy relation equations, because they were not one to one. The fuzzy relation equations were established according to the fuzzy relation matrix and membership degree of abnormality mode and were translated into optimal solution problems by fuzzy deconvolution method. The interval solution of the fuzzy relation equation was obtained by minimal mean square error of BP algorithm, realizing section locating of the contribution of anomalous causes to quality abnormality for a given problem, thereby gaining the optimal solution. Finally, the viability and effectiveness of this method were verified by the quality abnormity diagnosis in the assembly process of a NC rotary table. 1. Introduction Assembly is the last link in the product-form process and also is the key important link determining the product quality [1]. Different assembly control methods may cause products of different quality using the same parts. Some domestic high-grade CNC machine tool manufacturers purchase high quality parts and components from abroad to assemble, but the product reliability can hardly reach the level of foreign countries. Practice shows that scientific assembly technology can greatly improve the product quality with the same parts [2]. The foreign research about the assembly quality control has provided valuable methods and means for the prevention and control of products quality. Wang and Geng [3] predicted and evaluated the potential quality loss in the preparation stage before the assembly of mechanical product. Zhang and Ge [4] proposed the concept of defects source entropy that target assembly quality in the assembly process of mechanical product. Liu et al. [5] categorized the anomalous causes of assembly quality abnormality and analyzed the collected information that abnormality control required. Literatures [6–8] applied the decision tree, expert system, and artificial neural network to the quality diagnosis and control in manufacturing process. Literature [9] showed an evaluation method of assembly quality for automotive BIW. Literature [10] presented a quality control method for a mixed model assembly line. Assembly is a very complicated process, which includes a lot of factors probably causing abnormal quality. To improve the reliability, accuracy, accuracy preservation, and other key quality characteristics of a machine, it is important to match quality abnormality with the anomalous cause. However, there are few studies concerning the
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