Hierarchical process modeling: Describing within-run and between-run variations

Run-to-run variability is a common problem for modeling batch-wise and semi-continuous operated processes. Although observed reactor runs show the same trends in process behaviour, each specific reactor run also shows its own characteristics. Until now, available modeling methods were unable to describe the observed between run variance. In this paper, we present a hierarchical modeling method to solve this problem. A case study for a semi-continuous operated polymer process is analysed to illustrate the hierarchical modeling approach. It was shown that, using the applied modeling method, it is possible to obtain a model which is robust over several reactor runs and which provides a tool for process analysis. Also, the hierarchical model was shown to be superior to a model which lacked an appropriate description of the differences between reactor runs.