Recent Advances in Multivariate Statistical Process Control: Improving Robustness and Sensitivity

Several extensions are made to the theory of multivariate process monitoring via Principal Components Analysis (PCA). An important robustness issue is addressed: the continued use of the PCA model after detection of a sensor failure. Without some adjustment, a single failed sensor can obscure other failures, thus rendering the monitoring method useless. It is shown here that one can calculate an estimate of the output of the failed sensor that is most consistent with the PCA model of the process. This estimate allows continued use of the model. Under some circumstances, replacing the failed output with this estimate is equivalent to rebuilding the entire PCA model. Partial Least Squares (PLS) regression can be used in a manner similar to PCA for process monitoring. It is shown that PLS is fundamentally more sensitive to sensor failures than PCA. Unlike PCA, however, the PLS monitoring scheme maps state information into the model residuals. For this reason, changes in the process state covariance and autocovariance can invalidate calculated PLS model residual limits. The failed sensor problem is also solved for the PLS monitoring method.