Published version of an article in the journal: Abstract and Applied Analysis. Also available from the publisher at: http://dx.doi.org/10.1155/2014/304754 Open Access ; Due to its simplicity and easy implementation, partial least squares (PLS) serves as an efficient approach in large-scale industrial process. However, like many data-based methods, PLS is quite sensitive to outliers, which is a common abnormal characteristic of the measured process data that can significantly affect the monitoring performance of PLS. In order to develop a robust prediction and fault detection method, this paper employs the partial robust M-regression (PRM) to deal with the outliers. Moreover, to eliminate the useless variations for prediction, an orthogonal decomposition is performed on the measurable variables space so as to allow the new method to serve as a powerful tool for quality-related prediction and fault detection. The proposed method is finally applied on the Tennessee Eastman (TE) process.