Five-level Non-Sequential Third-Order Response Surface Designs and their Efficiencies

Abstract

New non-sequential third-order response surface designs are proposed with good optical properties. They are suitable as one-stage experimental designs for use in modeling third-order effects. The new designs are presented for cuboidal region in k dimensions and the technique employed in the construction of the non-sequential designs on the cuboidal region is flexible for use in regions that may be non-cuboidal. The new non-sequential designs lay importance on the use of axial points and two or three other blocks of points selected from a discrete design region such that the design is non-singular. For a continuous design region, uniform grids are formed over the entire design region. Five grid levels are utilized in this work thus resulting in 5^k grid points from which blocks of points are selected to form the desired non-sequential designs. The goodness of the designs is assessed via optimality and efficiency criteria and the new designs possess good optimality properties and are very high by G-efficiency.