An augmented approach to the desirability function

Abstract

The desirability function is widely used in the engineering field to tackle the problem of optimizing multiple responses simultaneously. This approach does not account for the variability in the predicted responses and minimizing this variability to have narrower prediction intervals is desirable. We propose to add this capability in the desirability function and also incorporate the relative importance of optimizing the multiple responses and minimizing the variances of the predicted responses at the same time. We show that the benefits of our augmented approach using two real data sets by comparing our solutions with those obtained from the desirability approach. In particular, it is shown that our approach offers greater flexibility and the solutions can reduce the variances of all the predicted responses resulting in narrower prediction intervals.

Keywords:

• desirability function
• optimization
• prediction
• regression
• response surface methodology

Acknowledgements

This work was supported by National Science Foundation DMS award 0806137 for Chen and Xu. The authors thank two referees for their comments.