A0488
Title: Theory and construction of complex experimental designs
Authors: Chunyan Wang - Renmin University (China) [presenting]
Abstract: Fractional factorial designs are important designs for experiments. They can be divided into regular designs and nonregular designs. As a special kind of nonregular design, the parallel flats design has received more and more attention. Parallel flat designs (PFDs) consisting of three parallel flats (3-PFDs) are the most frequently utilized PFDs due to their simple structure. Generalizing to f-PFD with $f>3$ is more challenging. A method for obtaining the confounding frequency vectors is proposed for all nonequivalent f-PFDs to find the least G-aberration f-PFD from any single flat. PFDs are particularly useful for constructing nonregular fractions, split plots, or randomized block designs. The quaternary code design series is also characterized as PFDs. Finally, it shows how designs constructed by concatenating regular fractions from different families may also have a parallel flat structure. Moreover, a different approach is pursued, applying coordinate exchange optimization to the structure of the parallel flat and employing an efficient computation for the confounding frequency vector. Beginning with any single flat design, the proposed algorithm can construct an efficient f-PFD in terms of G-aberration. A user-friendly software function called GMAPFDace has also been developed in MATLAB and GUN Octave to implement this algorithm, which allows one to obtain low G-aberration PFDs with the required sizes easily and quickly.
