Robustness of orthogonal uniform composite designs against missing data

Abstract

Missing data can hardly be prevented in most experiments due to setbacks that occur during the data entry process, and may grossly affect the estimation of the regression coefficients. The effects of missing data may be extremely significant if the design is almost saturated, saturated or fully saturated. It is of practical significance to identify designs that are least affected by missing data. In this paper, new orthogonal uniform minimax loss (OUCM) designs are constructed. These designs are more robust to one missing design point than the original orthogonal uniform composite designs (OUCDs) of Zhang, Liu, and Zhou (2020). The proposed designs are compared with central composite design (CCDs), small composite designs (SCDs), orthogonal array composite designs (OACDs), orthogonal array composite minimax loss designs (OACMs), and orthogonal uniform composite designs (OUCDs) based on the D-efficiency, A-efficiency and T-efficiency for estimating the parameters of the second-order model and under the generalized scaled standard deviations. These designs perform better in term of losses and also have higher D-efficiency, A-efficiency and T-efficiency.