In this paper, we present a Bayesian framework for fault detection. Principal component analysis (PCA) technique and quadratic test statistics are incorporated under a Conditional Gaussian Network (CGN). The proposed network, given an observation, is able to project it into an orthogonal space and to give a decision about the system state (faulty or not). The paper demonstrate, the probability limits to use in order to match the decisions made by quadratic statistics. The equivalence between our method and PCA based fault detection is validated on the Tennessee Eastman process data sets.