Supersaturated split-plot designs for robust parameter experiments

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The intention of robust parameter design (RPD) experiments is to identify the influence of control factors on the variation introduced by the uncontrollable noise factors. Split-plot designs can be effectively applied to decrease the cost in RPD experimentation when there are hard-to-change or hard-to-control factors. In the presence of many factors, either the traditional replicated split-plot designs or the Cartesian-product designs proposed by Taguchi are not of practical use since they require a large number of experimental units; thus, fractional factorial designs, such as supersaturated designs (SSDs) are needed. In this article, we propose a construction for supersaturated split-plot designs suitable for RPD experiments. We implemented the methodology of compound orthogonal arrays using orthogonal arrays of strength greater than 1, for the split-plot units and any relevant balanced SSD for the whole-plot units. The proposed methodology indicates that the experiments conducted in a split-plot point of view can be of tremendous value in RPD since they enable the estimation of the contrasts of interest in a considerably easier way than the designs proposed by Taguchi.