Nonparametric time trends in optimal design of experiments

When performing an experiment, the observed responses are often influenced by a temporal trend due to aging of material, learning effects, equipment wear-out, warm-up effects, etc. The construction of run orders that are optimally balanced for time trend effects relies on the incorporation of a parametric representation of the time dependence in the response model. The parameters of the time trend are then treated as nuisance parameters. However, the price one has to pay for by purely parametric modeling is the biased results when the time trend is misspecified. This paper presents a design algorithm for the construction of optimal run orders when kernel smoothing is used to model the temporal trend nonparametrically. The benefits of modeling the time trend nonparametrically are outlined. Besides, the influence of the bandwidth and the kernel function on the performance of the optimal run orders is investigated. The presented design algorithm shows to be very useful when it is hard to model the time dependence parametrically or when the functional form of the time trend is unknown. An industrial example illustrates the practical utility of the proposed design algorithm.status: publishe