SUMMARY

Because of the accuracy and ease of implementation, the Monte Carlo methodology is widely used in the analysis of nuclear systems. The estimated effective multiplication factor (keff) and flux distribution are statistical by their natures. Therefore, it is necessary to ensure that only the converged data are obtained for further analysis. Discarding a larger amount of initial histories could reduce the risk of contaminating the results by non-converged data, but increase the computational expense. This issue is amplified for large nuclear systems with slow convergence. One possible solution is to determine the convergence of keff or the flux distribution. Although several approaches have been developed, these methods are not always reliable, especially for slow convergence problems. As a result, this dissertation intends to attach this difficulty and achieve the objective using two independent but related methodologies. One path to the goal aims to find a more reliable and robust way to assess convergence by analyzing the local flux change. The other alternative solution is to increase the convergence rate and reduce the computational expense at the same time. Eventually, these two small topics will serve for the ultimate goal of this research—improving the reliability and efficiency of the Monte Carlo criticality calculations.