Post analysis on different operating time processes using orthonormal function approximation and multiway principal component analysis

In most batch process operations, operators often need to adjust the di€erent operating time in each batch run to get the desired product quality since the input speci®cations provided are di€erent. The proposed method is the combination of the orthonormal function approximation and the multiway principal component analysis (MPCA). It is used to analyze and monitor batch processes at the di€erent operating time. Like the philosophy of statistical process control in the traditional MPCA, this method leads to simple monitoring charts, easy tracking of the progress on each batch run and monitoring the occurrence of observable upsets. The only information needed to exploit the procedure is the historical data collected from the past successful batches. The methodology has been applied to two examples, a batch chemical reactor and a wafer plasma etching process, to illustrate the general use of this proposed method.