Optimally designing experiments under non-standard experimental situations

Abstract

There are numerous situations in which experiments need to be optimally designed since classic experimental design techniques are no longer effective. The experimental design space may be constrained, or already-performed experiments may have to be included. The experiment may involve qualitative factors with more than two levels, mixture and process factors in the same design, or a specific set of design points. In addition, the situation may call for reducing the number of experimental runs or using a reduced regression model in fitting the data. Finally, the region where the model is to be fitted may not be the same as where the measurements are to be made, or the model errors may have a known correlation matrix. Unfortunately, researchers in the experimental design community have paid full attention to only a few popular optimal designs; however, there are a number of other optimal designs which may be useful under different experimental situations. The main objective of this paper is the collective documentation of a broad spectrum of optimal design families, application areas, and key mathematical properties.