Lee discrepancy on symmetric three-level combined designs

Elsawah, A. M.; Qin, Hong

doi:10.1016/j.spl.2014.09.027

Cited by 19 publications

(6 citation statements)

References 15 publications

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“…Now, from (3.1) and Lemma 2 after simple arrangements as in Elsawah and Qin (2015a), we have the following lower…”

Section: Theorem 2 For Any Two-level Combined Designmentioning

confidence: 98%

“…Cai (2014, 2015) obtained the optimal foldover plans of mixed two-and threelevel designs and three-level designs with minimum wrap-around L 2 -discrepancy criterion, respectively. Recently, Elsawah and Qin (2015a) studied the issue of the optimal foldover plans for three-level designs in view of the uniformity criterion measured by the Lee discrepancy criterion. Finally, Elsawah and Qin (2015c, in press) obtained a new look for optimal foldover two-level and three-level designs in terms of uniformity criteria measured by the commonly used discrepancies criteria in the literature with a comparison study, respectively.…”

Section: Introductionmentioning

confidence: 99%

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An efficient methodology for constructing optimal foldover designs in terms of mixture discrepancy

Elsawah

Qin

2016

Journal of the Korean Statistical Society

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Available online xxxx AMS 2000 subject classifications: 62K05 62K15 Keywords: Mixture discrepancy criterion Foldover plan Foldover design Combined design Balanced design Lower bound a b s t r a c t Mixture discrepancy criterion (Zhou et al., 2013) is more reasonable than other discrepancies criteria for measuring the uniformity of experimental designs. In this paper, we take the mixture discrepancy criterion as the optimality measure to assess optimal foldover plans, which serve as benchmarks for constructing optimal foldover and combined designs (see Definition 2). New analytical expressions as well as new lower bounds of the mixture discrepancy criterion for both symmetric two-level and three-level combined designs under general foldover plans are obtained. We also describe necessary conditions for the existence of optimal combined designs meeting these lower bounds. An algorithm for searching the optimal 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 algorithms for searching the optimal foldover and combined designs.

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“…Now, from (3.1) and Lemma 2 after simple arrangements as in Elsawah and Qin (2015a), we have the following lower…”

Section: Theorem 2 For Any Two-level Combined Designmentioning

confidence: 98%

Section: Introductionmentioning

confidence: 99%

An efficient methodology for constructing optimal foldover designs in terms of mixture discrepancy

Elsawah

Qin

2016

Journal of the Korean Statistical Society

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“…On the other hand, the above various discrepancies values on two-level combined designs can be expressed in one equation, denoted by [VD(d(γ ))] 2 , in terms of ζ ij , ζ γ ij and ζγ ij as in the following theorem, where the proof is similar to the proof of Theorem 1 in Elsawah and Qin (2015a).…”

Section: New Analytical Expressions Of the Uniformity Criteriamentioning

confidence: 99%

A new strategy for optimal foldover two-level designs

Elsawah

Qin

2015

Statistics & Probability Letters

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“…Fang, Lin & Qin () were the first to use the uniformity criterion measured by the

scriptCD

to search for optimal foldover plans. Elsawah & Qin () studied the issue of finding optimal foldover plans for symmetric three‐level designs in the context of the uniformity criterion measured by the Lee discrepancy (

scriptLD

) (Zhou, Ning & Song ). Subsequently, Elsawah & Qin (, ) discussed the construction of optimal symmetric two‐level and symmetric three‐level combined designs in the context of

WD, CD, LD

and

scriptMD

criteria, respectively, and included a comparison study.…”

Section: Introductionmentioning

confidence: 99%

A powerful and efficient algorithm for breaking the links between aliased effects in asymmetric designs

Elsawah

2017

Aus NZ J of Statistics

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SummaryFractional factorial (FF) designs are no doubt the most widely used designs in experimental investigations due to their efficient use of experimental runs. One price we pay for using FF designs is, clearly, our inability to obtain estimates of some important effects (main effects or second order interactions) that are separate from estimates of other effects (usually higher order interactions). When the estimate of an effect also includes the influence of one or more other effects the effects are said to be aliased. Folding over an FF design is a method for breaking the links between aliased effects in a design. The question is, how do we define the foldover structure for asymmetric FF designs, whether regular or nonregular? How do we choose the optimal foldover plan? How do we use optimal foldover plans to construct combined designs which have better capability of estimating lower order effects? The main objective of the present paper is to provide answers to these questions. Using the new results in this paper as benchmarks, we can implement a powerful and efficient algorithm for finding optimal foldover plans which can be used to break links between aliased effects.

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Lee discrepancy on symmetric three-level combined designs

Cited by 19 publications

References 15 publications

An efficient methodology for constructing optimal foldover designs in terms of mixture discrepancy

An efficient methodology for constructing optimal foldover designs in terms of mixture discrepancy

A new strategy for optimal foldover two-level designs

A powerful and efficient algorithm for breaking the links between aliased effects in asymmetric designs

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