A Weighted Mean-Squared Error Optimization Model with both Controllable and Noise Input Variables for a Cuboidal Design Region

A central composite design is a good choice for a spherical design region while providing high-quality predictions over the entire spherical design region. However, this design requires design variable settings outside the range of the design variables in the factorial part. On the other hand, a face-centered design provides high-quality prediction over the entire cuboidal design region and does not require using design points outside the factorial ranges. Therefore, a face-centered design is preferred over other designs. In the literature, controllable input variables have been addressed. However, both controllable and noise input variables have been paid little attention. The aim is to build regression models for both the process mean and variance. The next task is to obtain an optimal operating condition for both controllable and noise input variables. A weighted mean-squared error optimization model is proposed. Comparison studies are conducted while considering different weights for each component of the objective function. Finally, the proposed methodology is an effective technique to obtain optimal settings for a cuboidal design region.