## 1 Introduction  
Coronavirus disease 2019 has severely affected manufacturing and service industries worldwide, which has prompted corporations to focus on ensuring the stable delivery of orders. Consequently, equipment stability has become a key problem. In general, data on equipment failure are sparse. Given the high level of imbalance between failure data and regular-operation data, failure data cannot be effectively classified and predicted. Moreover, machine equipment is limited by its replacement cycles, which further increases the difficulty in collecting failure data [1, 2]. Such data, which are time-limited and rare, are referred to as \"limited data\" [3]. Due to the properties of limited data sets, learning models often categorize the big data according to the normal operation conditions and do not diagnose fault type, which is crucial in the manufacturing industry. Applications of the categorization and prediction of limited data include cancer diagnosis, scam trading identification, and equipment fault diagnosis. The failure comes from mechanical issues or abnormal data [4, 5, 6], and we discuss the data from mechanical issues in this study. Among these three applications, equipment fault diagnosis is the most difficult. Since equipment must be replaced periodically, with the new machine often having different operating procedures from the previous machine, the fault diagnosis model of the previous machine becomes outdated. Therefore, a new diagnosis model must be developed, which requires new failure data to be accumulated. Limited data has become a hot topic recently, and such data are analyzed using two methods. The first method is few-shot learning, which is a learning method aimed at overcoming the difficulties involved in classifying minority class data. In few-shot learning, small data are used to identify minority classes, and a feature extractor is used to perform small-sample tasks, thereby effectively extracting valuable information from small samples. In [7, 8, 9, 10, 11], few-shot learning was adopted to detect the manufacturing data of the minority class. By ensuring that no new data are generated, this method effectively prevents overfitting. The second method used to analyze limited data involves generating additional minority data or reducing the quantity of majority data to balance the data, increase the focus of the classifier on minority data, and enhance the accuracy of minority prediction. The most representative algorithm of this method is the synthetic minority oversampling technique (SMOTE) [12], in which simulated minority data are used to achieve data balance. [PERSON] et al. employed a generative adversarial network (GAN) to simulate equipment failure data and adopted a long-short term memory network for fault prediction [13; 14]. In [15; 16; 17], a hybrid approach that involves combining a GAN with the SMOTE was adopted for processing limited data. This approach solved the overfitting problem of the SMOTE and fulfilled the requirement of a GAN-based training model for considerable data. However, advancements in sensor technology and the Internet of Things (IoT) have increased the complexity of the status of environmental data obtained in machine operation processes, which has resulted in the emergence of data consisting of hybrid features (i.e., categorical and numerical features). The aforementioned methods are inapplicable to such data [18]. Machines have complicated structures and are vulnerable to various types of faults. The nonlinear relationship between performance parameters and faults increases the difficulty in overcoming the imbalanced nature of a data set containing limited data with hybrid features. In [12], a SMOTE-based technique (i.e., Synthetic Minority Over-Sampling Technique for Nominal and Continuous (SmoteNC)) was proposed to balance and process data with continuous and categorical features. In [19], an approach named Conditional Tabular Generative Adversarial Network (ctGAN) was used to establish an adversarial network with hybrid features.