Directional PCA for Fast Detection and Accurate Diagnosis: A Unified Framework.

Many methods for monitoring multivariate processes are built on principal component analysis (PCA), which, however, simply tells whether the process is faulty or not. In fact, there is still room for the improvement of the early detection performance by exploiting fully the information given by fault directions. To this end, this article proposes a novel directional PCA (diPCA) approach. First, by narrowing down faults to a specified direction or composite mutually orthogonal directions, diPCA can speed fault detection and facilitate accurate fault diagnosis. It also has good theoretical properties that guarantee concise control limits. Second, with appropriate fault directions, diPCA provides a unified framework for process monitoring and includes existing monitoring indices, such as Hotelling's T² and the squared prediction error (SPE), as special cases. Third, diPCA also naturally results in a new combined monitoring statistic, which is composed of both T² and SPE, and provides an optimal ratio of their combination. The Monte Carlo simulation results have demonstrated the power of the proposed monitoring and diagnostic methods stemming from diPCA. The proposed methods have also been implemented into the Tennessee Eastman process.