Central composite designs with three missing observations

Abstract

In an experiment, there are many situations when some observations are missed, ignored or unavailable due to some accidents or high cost experiments. A missing observation can make the results of a response surface model quite misleading. This work therefore investigates the impact of a three missing observation of them various design points: factorial, axial and center points, on the estimation and predictive capability of the central composite design (CCD). Therefore minimaxloss CCD is formulated under a minimaxloss criterion. The minimaxloss CCD is considered to be robust to three missing observation and the investigation has been made in this article. The general formulas for the efficiency of the design when missing three observations, are presented in closed form as a function of α, where α is the value used in the CCDs' axial part. For the first time in this paper, these are calculated explicitly for CCDs from $k=2$ to $k=7$ factors and displayed in tables for practitioners to use. The corresponding graphs for the efficiencies are presented and suggestions are made for the values of α to maximize the robustness and estimability of the design for all cases.