A Model Averaging Prediction of Two-Way Functional Data in Semiconductor Manufacturing

Abstract

This paper proposes a linear regression model for scalar-valued responses and two-way functional (bivariate) predictors. Our motivation stems from the quality evaluation of products based on optical emission spectroscopy data from virtual metrology of semiconductor manufacturing. We focus on multivariate cases where the smoothness and shapes of the data vary significantly across variables. We propose a two-step solution to this problem, consisting of decomposition and prediction. First, we decompose the two-way functional data into pairs of component functions using functional singular value decomposition. Next, we build functional linear models for the decomposed functional variables and obtain the final predictor by averaging the models. Results from numerical studies, including simulation studies and real data analysis, demonstrate the promising empirical properties of the proposed approach, especially when the number of predictors is large.