Design optimization is a method to find optimum point which minimizes the objective function while satisfying design constraints. The conventional optimization does not consider the uncertainty originated from modeling or manufacturing process, so optimum point often locates on the boundaries of constraints. Reliability based design optimization includes optimization technique and reliability analysis that calculates the reliability of the system. Reliability analysis can be classified into simulation method, fast probability integration method, and moment-based reliability method. In most generally used MPP based reliability analysis, which is one of fast probability integration method, if many MPP points exist, cost and numerical error can increase in the process of transforming constraints into standard normal distribution space. In this paper, multiplicative decomposition method is used as a reliability analysis for RBDO, and sensitivity analysis is performed to apply gradient based optimization algorithm. To illustrate whole process of RBDO mathematical and engineering examples are illustrated.