Multivariate Batch Process Monitoring Utilizing Summary Variables With An Application To Semiconductor Etch

摘要

Monitoring and fault detection of batch chemical processes is complicated by stretching of the time axis, resulting in batches of different length. Previously, we have considered the use of PARAFAC2 for modeling this type of data. In this paper we consider the use of Correlation Optimized Warping (COW) and summary variables. Summary variables are an alternative to using the original process data. The batch production time is broken into sub-segments and parameters are derived which describe each segment, such as mean, variance, slope, etc. The summary variables are then used for monitoring, in this case as input variables in Principal Components Analysis (PCA). It is shown that PCA model based on summary variables have approximately the same or slightly better sensitivity to faults as other competing methods, including PCA on batch means, un-fold PCA (often referred to as Multi-way PCA), Parallel Factor Analysis (PARAFAC) and PARAFAC2. The advantage of summary variables relative to MPCA and PARAFAC is that the effective number of variables is in the analysis is smaller and models are somewhat less cumbersome and easier to interpret. Unlike PCA on the batch means, some amount of time information is retained.