Fault diagnosis and detection (FDD) improves product quality, process safety, and profitability in modern industrial plants. Faults can propagate between different parts of plants due to connections between devices and control loops. As a result, control room operators may receive multiple alarms that distract their attention from addressing the main causes of abnormal situations. Therefore, investigating causal relationships between process variables is essential in determining the root cause of faults. This study proposes a new systematic approach for causality analysis to identify the propagation path and root cause of faults in industrial plants. The research's innovations are categorized into two main parts. Initially, the study utilizes machine learning algorithms to identify causal relationships using probabilistic concepts. Additionally, it introduces a novel architecture by merging the generative adversarial network (GAN) with the variational auto-encoder (VAE). The process variables are mapped to a latent space, where an adversarial generative network will investigate the causal relationship between variables. Finally, the Tennessee Eastman Process simulation and gas turbine industrial data are used to evaluate the proposed algorithm.