Rotation designs for experiments in high-bias situations

Many experiments in the physical and engineering sciences study complex processes in which bias due to model inadequacy dominates random error. A noteworthy example of this situation is the use of computer experiments, in which scientists simulate the phenomenon being studied by a computer code. Computer experiments are deterministic: replicate observations from running the code with the same inputs will be identical. Such high-bias settings demand different techniques for design and prediction. This paper will focus on the experimental design problem introducing a new class of designs called rotation designs. Rotation designs are found by taking an orthogonal starting design D and rotating it to obtain a new design matrix D_R=DR, where R is any orthonormal matrix. The new design is still orthogonal for a first-order model. In this paper, we study some of the properties of rotation designs and we present a method to generate rotation designs that have some appealing symmetry properties.