Traditional solutions for test and reliability do not scale well for modern designs with their size and complexity increasing with every technology generation. Therefore, in order to meet time-to-market requirements as well as acceptable product quality, it is imperative that new methodologies be developed for quickly evaluating a system in the presence of faults. In this research, statistical methods have been employed and implemented to 1) estimate the stuck-at fault coverage of a test sequence and evaluate the given test vector set without the need for complete fault simulation, and 2) analyze design vulnerabilities in the presence of radiation-based (soft) errors. Experimental results show that these statistical techniques can evaluate a system under test orders of magnitude faster than state-of-the-art methods with a small margin of error. In this dissertation, I have introduced novel methodologies that utilize the information from fault-free simulation and partial fault simulation to predict the fault coverage of a long sequence of test vectors for a design under test. These methodologies are practical for functional testing of complex designs under a long sequence of test vectors. Industry is currently seeking efficient solutions for this challenging problem. The last part of this dissertation discusses a statistical methodology for a detailed vulnerability analysis of systems under soft errors. This methodology works orders of magnitude faster than traditional fault injection. In addition, it is shown that the vulnerability factors calculated by this method are closer to complete fault injection (which is the ideal way of soft error vulnerability analysis), compared to statistical fault injection. Performing such a fast soft error vulnerability analysis is very cruicial for companies that design and build safety-critical systems. / text