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Some methods and applications of supersaturated designs
Abstract
This dissertation consists of three papers written on supersaturated split-plot designs (SSSPD) and a distribution-free analysis method for data from supersaturated designs. In the first paper, we developed construction methods for SSSPD using an E(S2)-optimal supersaturated design (SSD) as the whole plot design, and half fractions of a Plackett-Burman design (PBD) or a fractional factorial design as the sub plot design. Using half fractions of a PBD or a fractional factorial design in the sub plot resulted in orthogonal columns, which ensured that the sub plot factors were not aliased with each other. We showed that the resulting sub plot design was not E(S2)-optimal when the sub plot was constructed using E(S 2)-optimal SSD that were not half fractions of PBD. We also examined the alias patterns of supersaturated split-plot design, and proposed using the ANOVA method, the stepwise procedures and the SCAD method to analyze the sub plot of SSSPD. In the second paper, we proposed using the permutation test to analyze data from SSD. We showed that the unbiased minimum variance least squares estimators of the slopes for the factors could be obtained through the permutation test. The permutation test was compared to the stepwise procedures and the SCAD method in terms of their ability to correctly identify the true models, and the experimentwise error rates. We compared the three methods using data simulated from five different distributions and data that contained outliers. We found that none of the three methods outperformed the rest for all cases. In the third paper, we applied the methods developed previously to a real quasi-biodegradable packaging foams dataset. A small scale extrusion experiment was conducted to screen 8 extruder factors and 8 ingredient factors using as few experimental units as possible, because extrusion is a very time consuming process. A SSSPD was applied since the extruder factors were costly-to-change compared to the ingredient factors. The mean and [special characters omitted]i of the unit density and diameter of the foams were measured, and analyzed using the permutation test and the ANOVA. We found some significant extruder and ingredient factors, as well as some interactions between the extruder and ingredient factors.
Subject Area
Statistics
Recommended Citation
Koh, Woon Yuen, "Some methods and applications of supersaturated designs" (2009). ETD collection for University of Nebraska-Lincoln. AAI3365711.
https://digitalcommons.unl.edu/dissertations/AAI3365711