Optimal Designs With Axial Values ( US 2018 203 )

[#1]

Level: Intermediate
Cameron Willden, Statistician, W. L. Gore & Associates
Willis Jensen, Global Statistics Team Leader, W. L. Gore & Associates

Optimal designs have become increasingly popular due to their flexibility and broad applicability, especially with robust implementations in software tools such as Custom Design in JMP. However, traditional optimal response surface designs tend to have lower power for quadratic terms due to high collinearity. Central composite designs (CCD) with off-face axial values tend to have significantly less collinearity among quadratic effects, and result in higher power for quadratic terms, better D-efficiency, and lower average prediction variance (i.e., I-optimality) relative to their corresponding equal-sized optimal designs. We propose a new optimal design algorithm and provide an accompanying JMP application to generate designs that combine the relative advantages of CCD and optimal designs into a single design. This modification to the coordinate-exchange algorithm for generating optimal experimental designs incorporates off-face axial runs, and we call the resulting designs “optimal designs with axials” or ODA designs. These ODA designs generally outperform both CCDs and current optimal designs for quadratic response surface models evaluated over cuboidal experimental regions. We show examples of how to easily generate ODA designs using our JMP application and compare them to other competing designs to show their advantages.

All presentation materials are attached as a .zip file.  The JMP journal file acts as a central hub for all of these presentation materials.  A paper based on this work has been accepted to the Journal of Quality Technology, and is expected to appear in print sometime in 2019.  The accepted manuscript can be downloaded here.

The Optimal Design with Axials (ODA) Add-in can also be downloaded from the File Exchange.  This add-in contains the custom application used to generate ODA designs and a user guide.