Split-Plot Central Composite Designs Robust to a Pair of Missing Observations

Abstract

This study constructs robust split-plot central composite designs against missing pairs of observations. Split-plot central composite designs (CCD) consist of factorial (f), whole-plot axial (α), subplot axial (β), and center (c) points. A loss function in terms of determinant (D) criterion was formulated based on two different configurations of the factorial and axial parts; losses due to missing pairs of observations of these different categories of points were investigated. Robust split-plot central composite designs against missing pairs of observations were then developed under each of the two configurations. It was observed that the losses, L_ff, L_ββ, and L_fβ, due respectively, to missing pairs of observations of the factorial, subplot axial, and, factorial and subplot axial points, were higher than the losses due to missing pairs of observations of the whole-plot axial and center points given by L_αα and L_cc respectively. Thus the factorial (f) and the subplot axial (β) points were found to be the most influential points in these designs while the whole-plot axial (α) and the center (c) points were less influential. This work has therefore identified and properly classified the losses due to missing design points in the split-plot CCD portions. In this way, the practitioner can avoid the experimental points having less influence from the full CCD experiments and this could lead to a possible increase in design efficiency.

Keywords: Robustness, Split-plot Central Composite Designs, Missing observations, loss function