Robustness of Central Composite Design and Modified Central Composite Design to a Missing Observation for Non-Standard Models

Abstract

Missing observations in an experimental design may lead to ambiguity in decision making thereby bringing an experiment to disrepute. Robustness, therefore, enables a process, not to break down in the presence of missing observations. This work constructed a modified central composite design (MCCD) from a four-variable central composite design (CCD) augmented with four center points using the leverage of a hat-matrix. The robustness of the CCD and MCCD were assessed when a design point is missing at the factorial, axial, and center points of the experiment, for a non-standard model, using the loss criterion, D-optimality, D-efficiency, and relative D-efficiency. When the designs are complete the MCCD shows higher D-efficiency and D-optimality for the non-standard model when compared to the CCD. In the absence of an observation from any of the designs, the CCD is found to be a more robust and efficient design compared to the MCCD as it has overall lower loss values at all the factors levels.