Robust design under normal model departure

•We consider robust design when the normality assumption is not met.•Extensive Monte Carlo simulations are carried out to investigate the performance of the proposed methods.•The kurtosis of the underlying distribution is used as a measure of departure from normality.•Relative efficiency metrics are provided to compare the performance of the proposed methods.•Two potential future research areas are suggested.

The basic underlying assumption in robust design is that the experimental data have a normal distribution. However, in many practical cases, the experimental data may actually have an underlying distribution that is not normal. The existence of model departure can have a significant effect on the optimal operating condition estimates of the control factors obtained in the robust design framework.In this article, the effect of normal model departure on the optimal operating condition estimates is investigated and a methodology is constructed to deal with the effect of normal model departure. We provide simulation results which indicate that the sample mean and sample variance should not be used as estimators if one suspects that the underlying distribution of the sample is not normal. Extensive Monte Carlo simulations indicate that there exist attractive alternative estimators to the sample mean and sample variance. These estimators exhibit solid performance when the data are normally distributed and at the same time are quite insensitive to normal model departure.