## 1 Introduction  
In the eighteenth century, the first industrial revolution used steam as a source of power and brought major changes to industry. The second industrial revolution used electricity and assembly lines for mass production. The third industrial revolution witnessed the integration of information technology and computers in manufacturing. Now, with the proposal of \"Industry 4.0\" in Germany, the industry is currently undergoing the \"fourth industrial revolution\", marking the integration of processing equipment systems and data in the production process, which will take us to a new level [1]. Modern manufacturing enterprises focus their attention on the intelligent management of production, including the material supply chain, manufacturing process technology, intelligent warehousing, and quality control. Among these, quality control has always been a core concern. The rate of product renewal in modern manufacturing is accelerating, and large-scale and unitary product production cannot meet the differentiated needs of the market. Enterprises adapt to market changes while reducing operating costs to gain advantages in competition, and an increasing number of enterprises have established flexible production lines, seeking to build a small-batch production mode. According to recent statistics from the United States, Japan, and other countries, small and medium-sized enterprises represent 75% of all enterprises. Multivarieties and small-batch production is rapidly becoming the main production mode, representing more than 90% of China's manufacturing industry. Multivarieties and small-batch production models require parallel production and production flexibility [2]. This production mode brings high-dimensional, small-sample quality information data. In the context of \"Industry 4.0\", it is necessary to further pursue high-quality output. However, in this production mode, with its continuous decline in single batch production, it is difficult to extract a large amount of quality information, quality data are relatively scarce, and the composition of the generated data information is also more complex. This production mode brings high-dimensional, small-sample quality information data. In reference to the quality control of manufacturing processes in the literature, some researchers used data processing technology to expand the dataset, thereby expanding the sample size. Other researchers identified the quality of products by methods such as the multivariate control chart of T2 statistics [3], multivariate statistical process control (MSPC) [4], fuzzy autoregressive moving average (FARMA) [5], and multivariate exponentially weighted moving average (MEWMA) [6]. If there are systematic errors in the production process, the production process will be out of control, and the control chart will no longer be stable. The above methods have good results for specific products, but for high-dimensional, small-sample manufacturing processes, there is insufficient product data with similar characteristics. Different products have different influencing factors. The factors that determine quality are high dimensionality, multivariability, small sample size, time varying, and other characteristics that have greater uncertainty and limitations. Artificial intelligence technology has brought a new development direction to the manufacturing industry and has attracted the attention of an increasing number of industrial enterprises. Intelligent manufacturing has gradually entered the stage of modern advanced manufacturing. Traditional statistical process quality-control technology has gradually added intelligent quality-control technology, especially prediction technology based on machine learning, which has become one of the key directions of current quality-control technology. Enterprises can collect multisource data from the production process, including data anomalies, processing parameters, and processing data.