A new formulation is proposed to solve design problems under model uncertainty. The proposed method combines well-known techniques for solving multiperiod design problems with the concept of joint confidence regions. One way to incorporate uncertainty into design problems is to discretize the uncertain parameters into a number of finite values and solve a multiperiod design problem. Traditionally, the uncertain parameters are discretized to a lower and upper bound based upon their individual confidence intervals. However, a more accurate description of the model parameter uncertainty is available through the use of joint confidence regions. In this work, we propose choosing the discrete values of uncertain model parameters based upon the principal components of their joint confidence region. We demonstrate the proposed method in several examples. The resulting optimal designs are more accurate because they incorporate the actual model uncertainty using joint confidence regions. Moreover, faster convergence to an optimal solution is observed using a two-stage algorithm because fewer discretization points may be needed in the multiperiod problem.