| Experimental designs play an more and more important role in industrial manu-facturing and production process. Especially at the early stage of developing new prod-ucts, we frequently use screening designs. Saturated design is a kind of design whoserun size equals to the number of parameters. This is economical and efcient way. It iswidely used for screening experiments. However, traditional saturated designs usuallycould not avoid confounding between main efects and two-factor interactions in thepresence of active two-factor interactions.Foldover design creates follow-up experiments by reversing the signs of someor all factors in an initial design. It can de-alias some confounding between mainefects and two-factor interactions. When we apply foldover designs to diferent knowndesigns, a problem is raised that the run size is doubled. In reality, the experimentalefciency is not high when the price is expensive.We combine saturated designs with foldover designs in this thesis. We proposenew construction methods for saturated designs and discuss their statistical properties.These designs have some properties of saturated designs and foldover designs. Besides,they have higher D-efciency. Our contributions are listed as follows.1. We propose SDRI designs for two-level factors’ first-order model. In SDRIdesigns, some factors’ main efects are orthogonal. It can de-alias some confoundingbetween main efects and two-factor interactions. That is, it is robust to two-factorinteractions.2. We propose DSC designs for three-level factors’ second-order model. In DSCdesigns, main efects are orthogonal to pure quadratic efects. Even though the realmodel contains two-factor interactions, it could not afect estimations of main efects. Itallows for separate estimation of the quadratic efects of each factor. When the numberof factors is even, the designs according to main efect model are orthogonal designs.Compared to traditional designs, DSC designs can avoid confounding between main efects and two-factor interactions.3. We propose the framework of FSSD designs for three-level factors’ fullsecond-order model. We investigate some possible construction methods. Especiallyfor one method among them, the correlations related to main efect and pure quadraticefect are very small. When k, the number of factor is greater than9, it has relative highD-efciency compared to traditional saturated designs. |
