An Improved Multivariate Chart Using Partial Least Squares With Continuous Ranked Probability Score
Reliable fault detection systems in industrial processes provide pertinent information for improving the safety and process reliability and reducing manpower costs. Here, we present a flexible and efficient fault detection approach based on the continuous ranked probability score (CRPS) metric to detect faults in multivariate data. This approach merges partial least squares (PLS) models and the CRPS metric to separate normal from abnormal features by simultaneously taking advantage of the feature representation ability of a PLS and the fault detection capacity of a CRPS-based scheme. The proposed approach uses PLS to generate residuals, and then apply the CRPS-based chart to reveal any abnormality. Specifically, two monitoring schemes based on the CRPS measure have been introduced in this paper. The first approach uses the Shewhart scheme to evaluate the CRPS of the response variables residuals from the PLS model. The second approach merges the CRPS into the exponentially weighted moving average monitoring chart. We assess the effectiveness of these approaches by using real and simulated distillation column data. We also compare the detection quality of PLS-based CRPS charts with that of PLS-based  $T^{2}$ ,  $Q$ , multivariate cumulative sum, and multivariate exponentially weighted moving average methods. Results show that the capacity of the proposed scheme can reliably detect faults in multivariate processes.