Abstract: The optimum design method based on the reliability is presented to the stochastic structure systems（i.e., the sectional area, length, elastic module and strength of the structural member are random variables）under the random loads.The sensitivity expression of system reliability index and the safety margins were presented in the stochastic structure systems. The optimum vector method was given.First,the expressions of the reliability index of the safety margins with the improved first-order second-moment and the stochastic finite element method were deduced, and then the expressions of the systemic failure probability by probabilistic network evaluation technique(PNET) method were obtained. After derivation calculus,the expressions of the sensitivity analysis for the system reliability were obtained.Moreover, the optimum design with the optimum vector algorithm was undertaken. In the optimum iterative procedure, the gradient step and the optimum vector step were adopted to calculate. At the last, a numerical example was provided to illustrate that the method is efficient in the calculation, stably converges and fits the application in engineering.

Key words: stochastic structure system, optimum vector method, optimum design, reliability, sensitivity analysis