Design parameters are subject to variations of manufactures, environments, and applications, which result in output deviations and constraint uncertainties. Quality products must perform to specifications despite these variations. Conventional constrained optimum may not be statistically feasible due to design variations. This paper addresses design variation characteristics and proposes a design procedure to ensure feasibility robustness in design optimization. Product life cycles often affect design variables with characteristic patterns. The Design Variation Hyper Sphere (DVHS) is presented using the concept of statistical joint confidence regions and decoupling techniques to characterize the coupled variations of design variables. The pattern represents the possible design dispersions at a specified probability, which is a hyper sphere for normal variables. The radius of the hyper sphere is determined by the feasibility requirement. The proposed robust optimization algorithm, SROP, introduces DVHS to the sequential quadratic programming, and modifies the feasible region to accommodate the activity uncertainty. The procedure ensures the design feasibility without over sacrificing the performance optimality. The design of a helical spring serves as an illustrative example of the proposed procedure.

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