A Statistical Process Control Framework for the Characterization of Variation in Batch Profiles

Abstract

An statistical process control framework for the characterization of the systematic variability in a historical database of batch profiles is proposed. The framework is geared toward facilitating an understanding of the sources of variability affecting the process. The overall variability in the profiles is categorized into two parts, systematic and unsystematic. The former is further divided, as along the time axis and the measurement axis. Scaling methods are applied to the profiles to obtain scale parameters that characterize the systematic time and measurement axis variability. The profile scaling is proposed so that each parameter has a very specific meaning in terms of the type of variability explained. Multivariate SPC charts on the scale parameters and also on the residuals remaining after scaling are developed for process monitoring. Profiles from two simulation examples, a simulated methyl methacralate polymerization reactor and a nylon-6,6 reactor, are used to demonstrate the application of the SPC framework. The examples demonstrate that a systematic study of the correlation structure of the scale parameters can reveal the signature of the primary disturbances affecting the process. Besides providing meaningful scale parameters, the framework also retains the power of projection methods for subtle special cause detection. The demonstration also highlights the importance of using the time variability information for final product quality predictions in batch data mining.