Augmented Approach to Desirability Function Based on Principal Component Analysis

Abstract

The desirability function approach is commonly used in industry to tackle multiple response optimization problems.  The shortcoming of this approach is that the variability and correlated in each predicted response are ignored. It is now evident that the actual response may fall outside the acceptable region even though the predicted response at the optimal solution has a high overall desirability score. An augmented approach to the desirability function (AADF) and the Principal Component Analysis (PCA) is put forward to rectify this problem. This paper will discuss how the two methodologies have been used together where the goal is to determine the final optimal factor/level combination when several responses are to be optimized. Additionally, in this work optimization of multiple correlated responses was studied and AADF model was proposed based on PCA to optimize correlated multiple response problems. The proposed method is also demonstrated by numerical example from the literature to confirm the efficiencies.