In this work we develop a method to perform simultaneous design and tolerance allocation for engineering problems with multiple objectives. Most studies in existing literature focus on either optimal design with constant tolerances or the optimal tolerance allocation for a given design setup. Simultaneously performing both design and tolerance allocation with multiple objectives for hierarchical systems increases problem dimensions and raises additional computational challenges. A design framework is proposed to obtain optimal design alternatives and to rank their performances when variations are present. An optimality influence range is developed to aid design alternatives selections with an influence signal-to-noise ratio that indicates the accordance of objective variations to the Pareto set and an influence area that quantifies the variations of a design. An additional tolerance design scheme is implemented to ensure that design alternatives meet the target tolerance regions. The proposed method is also extended to decomposed multi-level systems by integrating traditional sensitivity analysis for uncertainty propagation with analytical target cascading. This work enables decision-makers to select their best design alternatives on the Pareto set using three measures with different purposes. Examples demonstrate the effectiveness of the method on both single- and multi-level systems.

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