Outlier robust orthogonal uniform composite designs for third-order models

Outliers are outrageous values that occur in an experiment and can almost be inevitable. The presence of outliers in an experiment can affect the results of a response surface design due to disruption in the design's structure. In this paper, a new class of orthogonal uniform composite designs (OUCD4) for fitting third-order response surface model are constructed using the minimax outlying effect criterion that minimizes the maximum outlying effect. These constructed designs referred to as orthogonal uniform composite minimax outlying (OUCO4) designs are robust to a single outlier. The OUCO4 designs are shown to be more efficient in terms of relative efficiency compared to the OUCD4.