Mixture discrepancy on symmetric balanced designs

Elsawah, A. M.; Qin, Hong

doi:10.1016/j.spl.2015.05.007

Cited by 20 publications

(5 citation statements)

References 5 publications

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“…As we know these results are new. On the other hand, as shown in Remarks 2 and 3, as two special cases of our main results Theorems 3 and 7, when t = 0, then the lower bounds in Corollaries 1 and 2 are the same as that in Elsawah and Qin (2015d) for two-level and threelevel balanced designs, respectively. Hence, our results are also useful complements to the lower bounds of the mixture discrepancy criterion for two-level and three-level balanced designs, which can be served as benchmarks for searching uniform designs in terms of the mixture discrepancy criterion.…”

Section: Discussionsupporting

confidence: 61%

“…The lower bound LB 2 (n; m) given in Corollary 1 is the same as the lower bound given in Elsawah and Qin (2015d).…”

Section: Corollary 1 For Any Two-level Balanced Designmentioning

confidence: 82%

“…then[MD(D)] 2 ≥ LB 3 (n; m) = max {LB 3:1 (n; m), LB 3:2 (n; m)} , The lower bounds LB 3:1 (n; m) and LB 3:2 (n; m) given in Corollary 2 are the same as the lower bounds given inElsawah and Qin (2015d).…”

mentioning

confidence: 80%

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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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Section: Discussionsupporting

confidence: 61%

“…The lower bound LB 2 (n; m) given in Corollary 1 is the same as the lower bound given in Elsawah and Qin (2015d).…”

Section: Corollary 1 For Any Two-level Balanced Designmentioning

confidence: 82%

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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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“…The lower bounds for balanced designs with a mixture of two and three levels in Corollary 3 are the same as those in Elsawah & Qin (). The lower bounds for symmetric two‐level and symmetric three‐level balanced designs in Corollaries 4 and 5, respectively are the same as those in Elsawah & Qin ().…”

Section: New and Efficient Lower Bounds On Scriptmd For Asymmetrical mentioning

confidence: 82%

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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“…对于可卷偏差, Fang 等 [22] 给出了二水平和三水平的正规和非正规设计的 WD 的一个下界, Fang 等 [23] 给出了三水平设计的 WD 的更紧的下界, Fang 等 [27] 对于任意 q 水平 U-型设计提出了 WD 的一个下界, Fang 等 [28] 从不同的角度出发得到任意 q 水平设计的更好的 WD 的下界, Chatterjee 等 [29] 研究了二、三混合水平设计的 WD 的下界, 后来 Zhou 和 Ning [30] 研究了任意不同混合水平设计的 WD 的下界. 对于混合偏差, Zhou 等 [16] 给出了两水平设计的 MD 的下界, Ke 等 [31] 给出了三水平设计的 MD 的下界, Elsawah 和 Qin [32] 给出二水平、三水平和四水平设计的 MD 的下界, Elsawah 和 Qin [33] 还给出二、三混合水平的 MD 的下界.…”

Section: 超矩形的均匀性度量unclassified

Theory and application of uniform designs

Ping¹,

GongJin

Liu³

et al. 2020

Sci. Sin.-Math.

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With the development of science and technology, the numbers of factors in experiments become larger and larger, and the relationships among factors become more and more complex, and then it is very important to organize the experiments scientifically. Orthogonal designs, uniform designs and optimal designs are the popular types of experimental designs. The main idea of uniform designs is to scatter the design points on the experimental domain uniformly. Uniform designs have many advantages such as choosing the numbers of runs flexibly, robustness for models, and suitability for different types of experimental domains. This paper reviews the theoretical development, current progress and application of uniform designs.

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Mixture discrepancy on symmetric balanced designs

Cited by 20 publications

References 5 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 powerful and efficient algorithm for breaking the links between aliased effects in asymmetric designs

Theory and application of uniform designs

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