The Use of Hodges-Lehmann Estimator in Multiple Response Optimization with Replication

Abstract

The development of an approximation model for the true response surface is needed in Response Surface Methodology. In multiple response optimization (with replication), the sample mean is widely used to calculate the mean value at each design point of every quality characteristic before the model fitting. However, the existence of outliers may have certain effects on the sample mean. Thus, the Hodges-Lehmann estimator, a robust estimator, is proposed in place of the sample mean in this paper. A summary of the properties and advantages of the Hodges-Lehmann estimator will be given together with an example from the literature to illustrate the computation of this proposal. Keywords: Response surface methodology; Hodges-Lehmann estimator; Optimization; Generalized reduced gradient.