Enumeration and Multicriteria Selection of Orthogonal Minimally Aliased Response Surface Designs

Abstract

Response surface designs (RSDs) are a core component of the response surface methodology, which is widely used in the context of product and process optimization. In this contribution, we consider three-level RSDs, which can be viewed as matrices with entries equal to $\left\{-1,0,1\right\}$. Each column of an RSD corresponds to a factor and each row to an experimental test. We define a new family of orthogonal RSDs, for which there is no aliasing between the main effects and the second-order effects (two-factor interactions and quadratic effects). Using integer programming techniques, we construct a database of 55,531 such RSDs for 3–7 factors. We name these designs orthogonal minimally aliased RSDs (or OMARS designs). Each design in the catalog is extensively characterized in terms of efficiency, power, fourth-order correlations, fraction of design space plots, projection capabilities, etc. We identify interesting designs and investigate trade-offs between different quality criteria. Finally, we present a multiattribute decision algorithm to select designs from the catalog. An important result of our study is that we discovered some novel and interesting designs that challenge standard RSDs.

Keywords:

• Design efficiency
• Integer programming
• Multiattribute decision algorithm