Semiparametric Exact Optimal Run Orders

Abstract

When performing an experiment, the observed responses are often influenced by a temporal trend possibly due to aging of material, learning effects, equipment wear-out, or warm-up effects. The construction of run orders that are optimally balanced for time trend effects usually relies on the incorporation of a parametric representation of the time dependence. Using a parametric approach works very well as long as the unknown time dependence is properly specified or overspecified. However, for complicated temporal trends of unknown periodicity, or when the design size is small compared to the complexity of the response model, a parametric approach may lead to underspecification of the true time trend. Serious problems of bias can result. In this paper we show that, contrary to a fully parametric approach with an underfitted time trend, modeling the time trend nonparametrically is very attractive in terms of both bias and precision of the parameter estimators. An algorithm is presented for the construction of optimal run orders when kernel smoothing is used to model the temporal trend. An industrial example illustrates the practical utility of the proposed design methodology.

• Design of Experiments
• Optimal Design
• Simulated Annealing
• Trends