Piecewise regression model construction with sample efficient regression tree (SERT) and applications to semiconductor yield analysis

Forward stepwise regression analysis selects critical attributes all the way with the same set of data. Regression analysis is, however, not capable of splitting data to construct piecewise regression models. Regression trees have been known to be an effective data mining tool for constructing piecewise models by iteratively splitting data set and selecting attributes into a hierarchical tree model. However, the sample size reduces sharply after few levels of data splitting causing unreliable attribute selection. In this research, we propose a method to effectively construct a piecewise regression model by extending the sample-efficient regression tree (SERT) approach that combines the forward selection in regression analysis and the regression tree methodologies. The proposed method attempts to maximize the usage of the dataset's degree of freedom and to attain unbiased model estimates at the same time. Hypothetical and actual semiconductor yield-analysis cases are used to illustrate the method and its effective search for critical factors to be included in the dataset's underlying model.