A new optimization scheme for robust design modeling with unbalanced data

The Lin and Tu (LT) optimization scheme which is based on mean squared error (MSE) objective function is the commonly used optimization scheme for estimating the optimal mean response in robust dual response surface optimization. The ordinary least squares (OLS) method is often used to estimate the parameters of the process location and process scale models of the responses. However, the OLS is not efficient for the unbalanced design data since this kind of data make the errors of a model become heteroscedastic, which produces large standard errors of the estimates. To remedy this problem, a weighted least squares (WLS) method is put forward. Since the LT optimization scheme produces a large difference between the estimates of the mean response and the experimenter actual target value, we propose a new optimization scheme. The OLS and the WLS are integrated in the proposed scheme to determine the optimal solution of the estimated responses. The results of the simulation study and real example indicate that the WLS is superior when compared with the OLS method irrespective of the optimization scheme used. However, the combination of WLS and the proposed optimization scheme (PFO) signify more efficient results when compared to the WLS combined with the LT optimization scheme.

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