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This paper develops a flexible Physical Programming (PP) based Robust Design Optimization (RDO) method. RDO yields a system that performs with minimal variability in the face of input variations or uncertainties. RDO methods generally seek to minimize the variation of an Aggregate Objective Function (AOF), thereby also minimizing the effect of input variations on the physical system --- it is hoped. RDO seeks to maintain design feasibility under input variations. The optimization outcome depends on (i) the acceptable level of variation in performance, and (ii) the level of input variations. For RDO to be flexible, it is desirable to allow designers to express preference with respect to specific design metric values, and variation levels thereof. Similarly, RDO would ideally allow the designer either to prescribe parameter tolerance levels, or to maximize their allowable levels to minimize manufacturing cost. This paper's approach possesses the above desirable features, and provides numerical examples. This paper also discusses the benefits of formulating RDO in terms of physically meaningful design performance degradation levels, rather than in terms of the variation of an AOF.