A Note on Optimal Foldover Four-level Factorials

The foldover is a quick and useful technique in construction of fractional factorial designs, which typically releases aliased factors or interactions. The issue of employing the uniformity criterion measured by the centered L2-discrepancy to assess the optimal foldover plans was studied for four-level design. A new analytical expression and a new lower bound of the centered L2-discrepancy for fourlevel combined design under a general foldover plan are respectively obtained. A necessary condition for the existence of an optimal foldover plan meeting this lower bound was described. An algorithm for searching the optimal four-level foldover plans is also developed. Illustrative examples are provided, where numerical studies lend further support to our theoretical results. These results may help to provide some powerful and efficient Mgorithms for searching the optimal four-level foldover plans.

Optimal foldover plans of three-level designs with minimum wrap-around L-_2 discrepancy

Abstract The objective of this paper is to study the issue of employing the uniformity criterion measured by the wrap-around L2-discrepancy to assess the optimal foldover plans for three-level designs.For three-level fractional factorials as the original designs,the general foldover plan and combined design under a foldover plan are defined,some theoretical properties of the defined foldover plans are obtained,a tight lower bound of the wrap-around L2-discrepancy of combined designs under a general foldover plan is also obtained,which can be used as a benchmark for searching optimal foldover plans.For illustration of the usage of our theoretical results,a catalog of optimal foldover plans for uniform initial designs with s three-level factors is tabulated,where 2≤ s ≤11.

A Note on Lower Bound of Centered L_2 -discrepancy on Combined Designs

This note provides a theoretical justification of optimal foldover plans in terms of uniformity. A new lower bound of the centered Lu-discrepancy values of combined designs is obtained, which can be used as a benchmark for searching optimal foldover plans. Our numerical results show that this lower bound is sharper than existing results when more factors reverse the signs in the initial design. Keywords Centered L2-discrepancy, optimal foldover plan, uniformity, uniformity pattern

Effective Lower Bounds of Wrap-Around L_2-Discrepancy on Three-Level Combined Designs

How to obtain an effective design is a major concern of scientific research. This topic always involves high-dimensional inputs with limited resources. The foldover is a quick and useful technique in construction of fractional designs, which typically releases aliased factors or interactions.This paper takes the wrap-around L_2-discrepancy as the optimality measure to assess the optimal three-level combined designs. New and efficient analytical expressions and lower bounds of the wraparound L_2-discrepancy for three-level combined designs are obtained. The new lower bound is useful and sharper than the existing lower bound. Using the new analytical expression and lower bound as the benchmarks, the authors may implement an effective algorithm for constructing optimal three-level combined designs.

A Note on Supersaturated Design

Supersaturated designs are common choice for screening experiments.This paper studies the properties of supersaturated designs.We give new lower bounds of E(s^(2))-criterion and E(f_(NOD))-criterion.Some linkages between the combined/double design and its original design are firstly provided,and the lower bounds of E(s^(2)) and E(f_(NOD)) for the combined/double design are also given.Furthermore,the close relationship between the minimum Lee-moment aberration criterion and the criteria for optimal supersaturated designs is revealed.These theoretical results can be used to construct or search for optimal supersaturated designs in practice.Numerical results are also provided,which lend further support to our theoretical findings.