In the lower arm design process, a tolerance optimization of the variance of design variables should be preceded before manufacturing process, since it is very cost-effective compared to a strict management of tolerance of products. In this study, a design of experiment (DOE) based on response surface model (RSM) was carried out to find optimized design variables of the lower arm, which can meet a given requirement of probability constraint for the process capability index (Cpk) of the weight and maximum stress. Then, the design space was explored by using the central composite design method, in which the 2nd order Taylor expansion was applied to predict a standard deviation of the responses. The optimal solutions satisfying the probability constraint of the Cpk were found by considering both of the mean value and the standard deviation of the design variables.