With the increase of complexity in industrial processes, it is necessary to ensure process safety and efficiency so that fault detection and diagnosis (FDD) plays an important role in process system. However, the characteristics of process data (high dimension and significant correlations) bring a lot of difficulties in FDD, because fault information is buried in the huge historical data. Hence, data-driven methods [1] [2] [3] are developed rapidly in this field. Generally, data-driven methods [4] such as principal component analysis (PCA) [5], partial least squares (PLS) [6] and fisher discriminant analysis (FDA) [7] can transform the highly correlated data into a low-dimensional subspace. With the evolution of data-driven methods, more and more machine learning algorithms have been introduced in FDD research area. Indeed, those algorithms exhibit improved performance in dealing with a large scale industrial process data. Among machine learning algorithms, Bayesian network classifier (BNC) [8] is famous for its capacity of causal analysis under system uncertainty. The Bayesian network (BN) [9] is a type of graphical model and able to model probabilistic influence, which based on a strong mathematical theory, named Bayesian Theorem. The application of BNC for FDD achieves some successes. Parteepasen [10] demonstrates the ability to combine signals from acoustic emission and vibration sensors for tool wear monitoring. Sylvain Verron [11] applied the Bayesian network in multivariate process for fault diagnosis. However, classical BNC only takes static distribution of fault data into consideration to complete the classification task in fault diagnosis, while ignores the importance of dynamic nature in fault data. The dynamic nature in fault data is reflected in temporal behaviors of process data. Therefore, the information extracted from this aspect is called dynamic information, which explicitly depicts some meaningful underlying fault characteristics [12]. More deeply, dynamic information and static information carry the different fault information, analogous to the concepts of position and velocity in physics, respectively. In terms of complex industrial process, there is usually a phenomenon where some faults are unable to be well classified by classifiers when they are put together. These faults are termed as inseparable faults. The reason of this phenomenon is various, such as co-linearity and the similar position distribution. Fortunately, extracting the dynamic information, as an alternative method, can tackle this problem. Because each fault has its own dynamic nature, the dynamic information can be used to divide the inseparable faults into different classifiers in order to achieve a better classification accuracy. One of the methods to extract dynamic information is slow feature analysis (SFA). The SFA [13] is a promising dimension reduction methodology that extracts slow varying features from temporal data. From 2002, SFA has received increasing attention in image recognition [14] and human action recognition [15]. Until 2015, it was found to be used in fault detection by Shang [16]. He has defined two new indices to detect anomalies in process dynamics through the SFA.