Incorporating joint confidence regions into design under uncertainty

A new formulation is proposed to solve design problems under model uncertai nty. The proposed method combines well-known techniques for solving multipe riod design problems with the concept of joint confidence regions. One way to incorporate uncertainty into design problems is to discretize the uncert ain parameters into a number of finite values and solve a multiperiod desig n problem. Traditionally, the uncertain parameters are discretized to a low er and upper bound based upon their individual confidence intervals. Howeve r, a more accurate description of the model parameter uncertainty is availa ble through the use of joint confidence regions. In this work, we propose c hoosing the discrete values of uncertain model parameters based upon the pr incipal components of their joint confidence region. We demonstrate the pro posed method in several examples. The resulting optimal designs are more ac curate because they incorporate the actual model uncertainty using joint co nfidence regions. Moreover, faster convergence to an optimal solution is ob served using a two-stage algorithm because fewer discretization points may be needed in the multiperiod problem. (C) 1999 Elsevier Science Ltd. All ri ghts reserved.