Deterministic design optimization (DO) does not explicitly deal with a variety of factors from inherent randomness and uncertainties. Reliability based design optimization(RBDO) is necessary to use in engineering systems in order to guarantee quality and performance of product. In this paper, design variables are considered as random variables. Standard deviation according to change of design variables have changed as much as coefficient of variation. And, if the standard deviation is error of manufacturing, standard deviation-mean relation is concave form. We obtain reliability index using advanced first order second moment method(AFOSM). This paper is examined by solving two examples and the results are compares with DO, RBDO and suggested RBDO.