Modified Desirability Functions for Multiple Response Optimization

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Abstract
Desirability functions have been used extensively to simultaneously optimize several responses. Since the original formulation of these functions contains non-differentiable points, only search methods can be used to optimize the overall desirability response. Furthermore, all responses are treated as equally important. We present modified desirability functions that are everywhere differentiable so that more efficient gradient-based optimization methods can be used instead. The proposed functions have the extra flexibility of allowing the analyst to assign different priorities among the responses. The methodology is applied to a wire bonding process that occurs in semiconductor manufacturing, an industrial process where multiple responses are common.