A new approach to fault detection and isolation that combines principal component analysis (PCA) and Bayesian classification is proposed. For a given set of training data, a PCA subspace is constructed, and the score vectors are classified by solving the Bayesian classification problem with the deterministic annealing expectation maximization (DAEM) and robust mixture decomposition (RMD) algorithms. If data for new events do not belong to the existing subspace, the PCA subspace must be rebuilt to include the new events. Whereas new data form their own classes in the new subspace, existing classifications of the old data must also be updated in the newer subspace. This can be done using a simple translation and rotation if the dimensionality of the new subspace is the same as that of the old subspace. If the new subspace is of higher dimension, a good initial estimate is generated using translation and rotation. This estimate ensures convergence within a few expectation maximization steps. The proposed methodology is applied to the monitoring of a high-pressure polyethylene process with multiple operating modes. Results show that the fault detection capability can be expanded incrementally as operating data accumulate.