Logistic Regression for Crystal Growth Process Modeling through Hierarchical Nonnegative Garrote based Variable Selection

Logistic Regression for Crystal Growth Process Modeling through Hierarchical Nonnegative Garrote based Variable Selection Hongyue Sun, Xinwei Deng, Kaibo Wang, and Ran Jin Grado Department of Industrial and Systems Engineering, Virginia Tech., Blacksburg, VA 24061, USA Department of Statistics, Virginia Tech., Blacksburg, VA 24061, USA Department of Industrial Engineering, Tsinghua University, Beijing 100084, China Abstract Single-crystal silicon ingots are produced from a complex crystal growth process. Such a process is sensitive to subtle process condition changes, which may easily become failed and lead to the growth of a polycrystalline ingot instead of the desired monocrystalline ingot. Therefore, it is important to model this polycrystalline defect in the crystal growth process and identify key process variables and their features. However, to model the crystal growth process poses great challenges due to complicated engineering mechanisms and a large amount of functional process variables. In this paper, we focus on modeling the relationship between a binary quality indicator for polycrystalline defect and functional process variables. We propose a logistic regression model with hierarchical nonnegative garrote based variable selection method, which can accurately estimate the model, identify key process variables, and capture important features. Simulations and a case study are conducted to illustrate the merits of the proposed method in prediction and variable selection. [Supplemental materials are available for this article. Go to the publisher’s online edition of IIE Transactions for the supplemental materials.]