Robustness of Augmented Third-order Response Surfaces Designs to Missing Observation

Missing observations are practical problems that occur frequently even in a well-planned experiment and can significantly impact the statistical accuracy of the experiment. This work introduces a new class of third-order designs called augmented orthogonal uniform composite minimax loss (AOUCM) designs, which are more robust to a single missing design point as a variation of the existing third-order augmented orthogonal uniform composite designs (AOUCDs). The AOUCM designs are constructed using the minimax loss criterion. The constructed AOUCM designs are evaluated and compared with AOUCDs based on the relative D- and G-efficiency criteria, generalized scaled deviation, and the fraction of design space plot. The AOUCM designs are shown to be robust and more efficient in estimating the parameters of the third-order model. Moreover, although the AOUCDs and AOUCM designs are stable and uniformly distributed throughout the design space, the AOUCM designs have the least scaled prediction variance.