A new strategy for optimal foldover two-level designs

Elsawah, A. M.; Qin, Hong

doi:10.1016/j.spl.2015.04.020

Cited by 32 publications

(4 citation statements)

References 10 publications

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“…For instance, choose the design in Example 2 of [6] as the initial design d 0 , and assume n 1 = 4, r = 1; then both of the lower bounds in Theorem 1 and Theorem 2 are 53.5134, because m = 14 is even. However, consider the design in Example 1 of [6] as the initial design d 0 , and let n 1 = 2, r = 1, then the lower bounds in Theorem 1 and Theorem 2 are 3.4094 and 3.4307, respectively, since m = 7 is odd. Theorem 3 Given an initial design d 0 ∈ U(n; 3 m ), the lower bound of WD-value of column augmented designs D 3 ∈ C 3 (n + n 1 ; 3 m • 3 r ) is…”

Section: Propositionmentioning

confidence: 99%

“…However, if m is odd, the lower bound in Theorem 2 is more tight. For instance, choose the design in Example 2 of [6] as the initial design d 0 , and assume n 1 = 4, r = 1; then both of the lower bounds in Theorem 1 and Theorem 2 are 53.5134, because m = 14 is even. However, consider the design in Example 1 of [6] as the initial design d 0 , and let n 1 = 2, r = 1, then the lower bounds in Theorem 1 and Theorem 2 are 3.4094 and 3.4307, respectively, since m = 7 is odd.…”

Section: Column Augmented Uniform Designs With Additional Three-level...mentioning

confidence: 99%

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Mixed-level column augmented uniform designs

Yang

Zhou

Zhang

2019

Journal of Complexity

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Follow-up experimental designs are popularly used in industry. In many follow-up designs, some additional factors with two or three levels may be added in the follow-up stage since they are quite important but may be neglected in the first stage. Such follow-up designs are called mixed-level column augmented designs. In this paper, based on the initial designs, mixed-level column augmented uniform designs are proposed by using the uniformity criterion, wrap-around L 2 -discrepancy (WD). The multi-stage augmented procedure which adds the additional design points stage by stage is also investigated. We present the analytical expressions and the corresponding lower bounds of the WD of the column augmented designs. It is shown that the column augmented uniform designs are also the optimal designs under the non-orthogonality criterion, E( f NOD ). Furthermore, a construction algorithm for the column augmented uniform design is provided. Some examples show that the lower bounds are tight and the construction algorithm is effective.

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Section: Propositionmentioning

confidence: 99%

Section: Column Augmented Uniform Designs With Additional Three-level...mentioning

confidence: 99%

Mixed-level column augmented uniform designs

Yang

Zhou

Zhang

2019

Journal of Complexity

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“…Lemma 2 (Elsawah & Qin, 2015c). Suppose  n i=1 β i = c and β i 's are nonnegative, then for any positive λ, we have…”

Section: Theorem 2 For Any Two-level Combined Designmentioning

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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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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“…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. Recently, Elsawah & Qin () studied optimal foldover plans in terms of the

scriptMD

criterion for both symmetric two‐level and symmetric three‐level designs.…”

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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A new strategy for optimal foldover two-level designs

Cited by 32 publications

References 10 publications

Mixed-level column augmented uniform designs

Mixed-level column augmented uniform designs

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

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