Efficient Asymmetrical Extended Designs Under Wrap-Around L_2-Discrepancy

The purpose of the present article is to introduce a class of mixed two-and three-level extended designs obtained by adding some new runs to an existing mixed two-and three-level design.A formulation of wrap-around L_2-discrepancy for the extended designs is developed. As a benchmark of obtaining(nearly) uniform asymmetrical extended designs, a lower bound to the wrap-around L_2-discrepancy for our proposed designs is established. Thorough numerical results are displayed, which provide further corroboration to the derived theoretical results.     

Uniformity Pattern of Asymmetric Fractional Factorials

The objective of this paper is to discuss the issue of the projection uniformity of asymmetric fractional factorials. On the basis of Lee discrepancy, the authors define the projection Lee discrepancy to measure the uniformity for low-dimensional projection designs. Moreover, the concepts of uniformity pattern and minimum projection uniformity criterion are proposed, which can be used to assess and compare two and three mixed levels factorials. Statistical justification of uniformity pattern is also investigated.     

Efficient Asymmetrical Extended Designs Under Wrap-Around <Emphasis Type="Italic">L</Emphasis><Subscript>2</Subscript>-Discrepancy

The purpose of the present article is to introduce a class of mixed two- and three-level extended designs obtained by adding some new runs to an existing mixed two-and three-level design. A formulation of wrap-around L₂-discrepancy for the extended designs is developed. As a benchmark of obtaining (nearly) uniform asymmetrical extended designs, a lower bound to the wrap-around L₂-discrepancy for our proposed designs is established. Thorough numerical results are displayed, which provide further corroboration to the derived theoretical results.