Robust design modeling and optimization with unbalanced data

The usual assumption behind robust design is that the number of replicates at each design point during an experimental stage is equal. In practice, however, it is often the case that this assumption is not met due to physical limitations and/or cost constraints. In this situation, using the usual method of ordinary least squares (OLS) to obtain fitted response functions for the mean and variance of the quality characteristic of interest may not be an effective tool. In this paper, we first show simulation results, indicating that an alternative method, called the method of weighted least squares (WLS), outperforms the OLS method in terms of mean squared error. We then lay out the WLS-based robust design modeling and optimization. A case study is presented for numerical purposes.