Desirability Function Approach on the Optimization of Multiple Bernoulli-distributed Response

The multiple response optimization (MRO) problem is commonly found in industry and many other scientific areas. During the optimization stage, the desirability function method, first proposed by Harrington (1965), has been widely used for optimizing multiple responses simultaneously. However, the formulation of traditional desirability functions breaks down when the responses are Bernoulli-distributed. This paper proposes a simple solution to avoid this breakdown. Instead of the original binary responses, their probabilities of defined outcomes are considered in the logistic regression models and they are transformed into the desirability functions. An example is used for demonstration.