Sheet metal stamping processes have been widely implemented in many industries due to its repeatability and productivity. In general, the simulations for a sheet metal forming process involve nonlinearity, complex material behavior and tool-material interaction. Instabilities in terms of tearing and wrinkling are major concerns in many sheet metal stamping processes. In this work, a sheet metal stamping process of a mild steel for a wheelhouse used in automobile industry is studied by using an explicit nonlinear finite element code and incorporating failure analysis (tearing and wrinkling) and design under uncertainty. Margins of tearing and wrinkling are quantitatively defined via stress-based criteria for system-level design. The forming process utilizes drawbeads instead of using the blank holder force to restrain the blank. The main parameters of interest in this work are friction conditions, drawbead configurations, sheet metal properties, and numerical errors. A robust design model is created to conduct a probabilistic design, which is made possible for this complex engineering process via an efficient uncertainty propagation technique. The method called the weighted three-point-based method estimates the statistical characteristics (mean and variance) of the responses of interest (margins of failures), and provide a systematic approach in designing a sheet metal forming process under the framework of design under uncertainty.