A new strategy is proposed for the optimum design of chemical plants whose uncertain parameters are expressed as bounded variables. The design is such that the plant specifications will be met for any feasible values of the parameters while optimizing a weighted cost function which reflects the costs over the expected range of operation. The strategy is formulated as a nonlinear programme, and an efficient method of solution is derived for constraints which are monotonic with the parameters, a case which arises frequently in practice. The designs of a pipeline with a pump, of a reactor-separator system, and of a heat exchanger network, all with uncertain technical parameters, illustrate the effectiveness of the strategy for rational overdesign of a chemical plant.