To measure the variation of device Vt requires long test for conventional WAT test structures. This paper presents a framework that can efficiently and effectively obtain the mean and variance of Vt for a large number of DUTs. The proposed framework applies the model-based random forest as its core model-fitting technique to learn a model that can predict the mean and variance of Vt based on only the combined Id measured from parallel connected DUTs. The experimental results based on the SPICE simulation of a UMC 28nm technology demonstrate that the proposed model-fitting framework can achieve a more than 99% R-squared for predicting both of Vt mean and variance. Compared to conventional WAT test structures using binary search, our proposed framework can achieve 42.9X speedup in turn of the required iterations of Id measurement per DUT.