A methodology is presented to solve multiple-objective system reliability design problems with some (or all) stochastic objectives. For these problems, the objective is to determine the maximum system reliability, but at a minimum cost and weight without explicit constraint limits. The reliability and cost objectives are not known exactly due to estimation uncertainties and cost fluctuations, respectively. Objective function variance measures are explicitly included in the formulation as additional objectives to be minimized for riskaverse decision makers. A multi-objective genetic algorithm is used to initially find Pareto optimal solutions, which are then prioritized based on the decision makers objective function preferences. The methodology is demonstrated on several test problems.