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Designing Optimal Large Four-Level Experiments:A New TechniqueWithout Recourse to Optimization Softwares

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Communications in mathematics and Statistics 2022年第4期10卷 623-652页

作者： A.m.elsawah Division of Science and Technology Beijing Normal University-Hong Kong Baptist University United International CollegeZhuhai 519085China Department of mathematics Faculty of ScienceZagazig UniversityZagazig 44519Egypt

Experimental design is an effective statistical tool that is extensively applied in modern industry,engineering,and *** is proved that experimental design is a powerful and efficient means to screen the relationships between input factors and their responses,and to distinguish significant and unimportant factor *** many practical situations,experimenters are faced with large experiments having four-level *** though there are several techniques provided to design such experiments,the challenge faced by the experimenters is still *** practice has demonstrated that the existing techniques are highly time-consuming optimization procedures,satisfactory outcomes are not guaranteed,and non-mathematicians face a significant challenge in dealing with them.A new technique that can overcome these defects of the existing techniques is presented in this *** results demonstrated that the proposed technique outperformed the current techniques in terms of construction simplicity,computational efficiency and achieving satisfactory results *** non-mathematician experimenters,the new technique is much easier and simpler than the current techniques,as it allows them to design optimal large experiments without the recourse to optimization *** optimality is discussed from four basic perspectives:maximizing the dissimilarity among experimental runs,maximizing the number of independent factors,minimizing the confounding among factors,and filling the experimental domain uniformly with as few gaps as possible.

关键词： multiple quadrupling technique TA algorithm Augmented design technique Level permutation technique Confounding Hamming distance Space-filling

Cross-Entropy Loss for Recommending Efficient Fold-Over Technique

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维普期刊数据库

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Journal of Systems Science & Complexity 2021年第1期34卷 402-439页

作者： WENG Lin-Chen elsawah a m FANG Kai-Tai Division of Science and Technology Beijing Normal University-Hong Kong Baptist University United International CollegeZhuhai 519085China Department of mathematics Faculty of ScienceZagazig UniversityZagazig 44519Egypt The Key Lab of Random Complex Structures and Data Analysis Chinese Academy of SciencesBeijing 100190China

Due to the limited resources and budgets in many real-life projects, it is unaffordable to use full factorial experimental designs and thus fractional factorial(FF) designs are used instead. The aliasing of factorial effects is the price we pay for using FF designs and thus some significant effects cannot be estimated. Therefore, some additional observations(runs) are needed to break the linages among the factorial effects. Folding over the initial FF designs is one of the significant approaches for selecting the additional runs. This paper gives an in-depth look at fold-over techniques via the following four significant contributions. The first contribution is on discussing the adjusted switching levels foldover technique to overcome the limitation of the classical one. The second contribution is on presenting a comparison study among the widely used fold-over techniques to help experimenters to recommend a suitable fold-over technique for their experiments by answering the following two fundamental questions:Do these techniques dramatically lessen the confounding of the initial designs, and do the resulting combined designs(combining initial design with its fold-over) via these techniques have considerable difference from the optimality point of view considering the markedly different searching domains in each technique? The optimality criteria are the aberration, confounding, Hamming distance and uniformity. many of these criteria are given in sequences(patterns) form, which are inconvenient and costly to represent and compare, especially when the designs have many factors. The third innovation is on developing a new criterion(dictionary cross-entropy loss) to simplify the existing criteria fromsequence to scalar. The new criterion leads to a more straightforward and easy comparison study. The final contribution is on establishing a general framework for the connections between initial designs and combined designs based on any fold-over technique.

关键词： Aberration confounding cross-entropy dictionary ordering fold-over Hamming distance loss function uniformity

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

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Journal of Systems Science & Complexity 2017年第6期30卷 1459-1469页

作者： elsawah A.m. HU Jianwei QIN Hong Faculty of mathematics and Statistics Central China Normal University Division of Science and Technology BNU-HKBU United International College Department ofmathematics Faculty of Science Zagazig University

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 *** 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.

关键词： Combined design Foldover plan L2-discrepancy lower bound optimal combined design wrap-around

An Adjusted Gray map Technique for Constructing Large Four-Level Uniform Designs

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Journal of Systems Science & Complexity 2023年第1期36卷 433-456页

作者： elsawah a m VISHWAKARmA G K mOHAmED H S FANG Kai-Tai Department of Statistics and Data Science Faculty of Science and TechnologyBeijing Normal University-Hong Kong Baptist University United International CollegeZhuhai 519087China Guangdong Provincial Key Laboratory of Interdisciplinary Research and Application for Data Science BNU-HKBU United International CollegeZhuhai 519087China Department of mathematics Faculty of ScienceZagazig UniversityZagazig 44519Egypt Department of mathematics&Computing Indian Institute of Technology DhanbadDhanbad 826004India College of Transportation and Civil Engineering Fujian Agriculture and Forestry UniversityFuzhou 350002China The Key Lab of Random Complex Structures and Data Analysis The Chinese Academy of SciencesBeijing 100190China

A uniform experimental design(UED)is an extremely used powerful and efficient methodology for designing experiments with high-dimensional inputs,limited resources and unknown underlying models.A UED enjoys the following two significant advantages:(i)It is a robust design,since it does not require to specify a model before experimenters conduct their experiments;and(ii)it provides uniformly scatter design points in the experimental domain,thus it gives a good representation of this domain with fewer experimental trials(runs).many real-life experiments involve hundreds or thousands of active factors and thus large UEDs are *** large UEDs using the existing techniques is an NP-hard problem,an extremely time-consuming heuristic search process and a satisfactory result is not *** paper presents a new effective and easy technique,adjusted Gray map technique(AGmT),for constructing(nearly)UEDs with large numbers of four-level factors and runs by converting designs with s two-level factors and n runs to(nearly)UEDs with 2^(t−1)s four-level factors and 2tn runs for any t≥0 using two simple transformation *** justifications for the uniformity of the resulting four-level designs are given,which provide some necessary and/or sufficient conditions for obtaining(nearly)uniform four-level *** results show that the AGmT is much easier and better than the existing widely used techniques and it can be effectively used to simply generate new recommended large(nearly)UEDs with four-level factors.

关键词： Aberration adjusted Gray map technique Gray map technique Hamming distance moment aberration threshold accepting algorithm uniform design

A Note on Optimal Foldover Four-level Factorials

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Acta mathematica Sinica,English Series 2016年第3期32卷 286-296页

作者： A.m.elsawah m.A.AL-AWADY m.A.ABD ELGAWAD Hong QIN Department of mathematics Faculty of ScienceZagazig UniversityZagazig 44519Egypt Faculty of mathematics and Statistics Central China Normal UniversityWuhan 430079P.R.China Department of mathematics Faculty of ScienceBenha UniversityBenha 13518Egypt

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.

关键词： Centered L2-discrepancy foldover plan optimal foldover plan combined design lower bounds