Process variations is one of the most challenging phenomena in deep submicron. Delay fault testing becomes more complicated because gate delays are not fixed but instead, they are statistical quantities due to the variations in the transistor characteristics. On the other hand, testing for hardware Trojan is also challenging in the presence of process variations because it can easily mask the impact of the inserted Trojan. This work consists of two parts. In the first part, an approach to detect ultra-low-power no-payload Trojans by analyzing IDDT waveforms at each gate in the presence of process variations is presented. The approach uses a novel ATPG to insert a small number of current sensors to analyze the behavior of individual gates at the IDDT waveform. The second part focuses on identifying a test set that maximizes the defect coverage for path delay fault. The proposed approach utilizes Monte-Carlo simulation efficiently and uses a machine-learning algorithm to select a small test set with high detect coverage.