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An optimal network design model is formulated providing a set of link investment pattern for the most reliable network with highest network performance under uncertain conditions. The connectivity probability of a link is assumed to be improved by the investment to the link. The object function is represented as the expected performance measure. The formulated model is categorized in a group of stochastic network design problem in which the existence of a link is probabilistic. The characteristics of the gradient vector of the objective function are analyzed. The derivatives of the objective function can be approximately evaluated without enumerating all possible network state vectors. Numerical examples are calculated for analyzing the sensitivity of optimal investment policies.