Conventional methods are under the assumption that a process is driven by either non-Gaussian or Gaussian essential variables. However, many complex processes may be simultaneously driven by these two types of essential source. This paper proposes a novel independent component analysis and factor analysis (ICA-FA) method to capture the non-Gaussian and Gaussian essential variables. The non-Gaussian part is first extracted by ICA and support vector data description is utilized to obtain tight confidence limit. A probabilistic approach is subsequently incorporated to separate the residual Gaussian part into latent influential factors and unmodeled uncertainty. By retrieving the underlying process data generating structure, ICA-FA facilitates the diagnosis of process faults that occur in different sources. A further contribution of this paper is the definition of a new similarity factor based on the ICA-FA for fault identification. The efficiency of the proposed method is shown by a case study on the TE benchmark process.