A highly efficient robust design under data contamination

• We propose various estimators in the robust design framework.
• We investigate the proposed methods thoroughly through Monte Carlo simulations.
• The proposed methods are outlier-resistant to contaminated observations.
• To evaluate the proposed methods, we provide two relative efficiency metrics.
• The proposed methods outperform existing methods when the data set is contaminated.

In robust design, the general assumption is that the experimental data are normally distributed without contamination. Under this assumption, the sample mean and variance are often used to estimate the process mean and the process variance at each design point. The process mean and variance response functions are then fitted based on the sample mean and variance obtained at each design point.However, the non-contamination component of the assumption may not hold in practice. If this assumption is violated in a serious manner, the optimal operating conditions of the control factors may not be estimated properly. Thus, an outlier-resistant approach to the robust design problem is clearly warranted.In this article, we estimate a dual quadratic response surface model for the expected value and logarithm-transformed variance of the target response. The response surface is estimated from a designed experiment with a common number of replications at each design point. Then, given the observed responses at each design point, the following outlier-resistant statistics are computed at each design point: (i) the median and Hodges Lehmann estimators of the mean response, and (ii) the natural logarithm of the squared normal-consistent MAD, IQR and Shamos estimators of the response standard deviation.Through extensive Monte Carlo simulations, we show that alternative estimators exist which are quite efficient when the data are normally distributed yet also outlier-resistant when the data are contaminated.