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In this paper we propose a novel statistical framework to model the impact of process variations on semiconductor circuits through the use of process sensitive test structures. Based on multivariate statistical assumptions, we propose the use of the expectation-maximization algorithm to estimate any missing test measurements and to calculate accurately the statistical parameters of the underlying multivariate distribution. We also propose novel techniques to validate our statistical assumptions and to identify any outliers in the measurements. Using the proposed model, we analyze the impact of the systematic and random sources of process variations to reveal their spatial structures. We utilize the proposed model to develop a novel application that significantly reduces the volume, time, and costs of the parametric test measurements procedure without compromising its accuracy. We extensively verify our models and results on measurements collected from more than 300 wafers and over 25 thousand die fabricated at a state-of-the-art facility. We prove the accuracy of our proposed statistical model and demonstrate its applicability towards reducing the volume and time of parametric test measurements by about 2.5 - 6.1times at absolutely no impact to test quality.