Multi-dimensional nonlinear problems are often faced in automotive reliability analysis and optimal design. Among stochastic simulation methods, Monte Carlo and improved methods such as Importance Sampling, Subset Simulation, and directed sampling have some differences in their functional manipulation procedures and applicability due to the differences in their respective mathematical mechanisms. In order to clarify the applicability and characteristics of different methods on multi-dimensional nonlinear problems, this study explores the distribution features and propagation rules of random samples in the whole search space by using the Chi-square theory and the geometric properties of Gaussian space. Based on this, the directed sampling method is selected for reliability analysis, and solutions to improve efficiency and accuracy are proposed. Finally, it is validated by an automotive structural engineering problem, which provides a reference for the selection and improvement of reliability methods in practical applications.