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-le...

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Bibliographic Details
Published in:Acta mathematica Sinica. English series 2016-03, Vol.32 (3), p.286-296
Main Authors: Elsawah, A. M., Al-Awady, M. A., Abd Elgawad, M. A., Qin, Hong
Format: Article
Language:English
Subjects:
Algorithms
Design analysis
Factorial experiments
Factorials
Lower bounds
Mathematical analysis
Mathematical models
Mathematics
Mathematics and Statistics
Numerical analysis
Optimization
Searching
Studies
Theorems
函数
数学
数学理论
积分
算术
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Summary: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.
ISSN:1439-8516
1439-7617
DOI:10.1007/s10114-016-4749-3