Algorithms to obtain generalized neighbor designs in minimal circular blocks

Noreen, Khadija; Rashid, Muhammad Sajid; Shehzad, Farrukh; Hassan, Mahmood Ul; Noreen, Zahra; Omer, Talha; Ahmed, Rashid

doi:10.1080/03610918.2022.2098330

Cited by 3 publications

(20 citation statements)

References 18 publications

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“…Here, some generators are developed under the logic of Rule I to obtain sets of shifts for MCWBNDs-II in blocks of three different sizes for m (mod 4) ≡ 0. [7,8,10,15], [16,17,18,19], [11,12,13], [19,22] 0.786…”

Section: Sizes For M (Mod 4) ≡mentioning

confidence: 99%

“…See Table 6. [7,8,9,11,12], [16,18,25,26], [19,20,21,23], 0.821 [13,14,22] 50 5 4 3 i (mod 4) ≡ 3 [3,4,16,26], [20,21,22,23], [7,9,13,15], [8,18,19], [11,12,17], 0.781 [23,25] • k 1 = 4l + 2, i even.…”

Section: Example 2 Mcwbnds-ii Obtained Through Generator 1 See Tablementioning

confidence: 99%

“…See Table 19. [3,4,5,6,7,15], [9,10,11,13,12,21], [16,17,18,19], [19,22] 0.834 Generator 17. MCWBNDs-II for v = 2ik 1 + 2k 2 + 2k 3 -2 with k 2 = k 1 -2, k 3 = 4 can be obtained if:…”

Section: For Kmentioning

confidence: 99%

“…Generators for these designs have not been developed for m (mod 4) ≡ 0 & 3. Noreen et al (2022) [17] developed an R-coded algorithm based on Rule I to generate MCPBRMDs. Shabbir et al (2023) [24] developed an R-coded algorithm based on Rule I to generate GN2-designs.…”

Section: Introductionmentioning

confidence: 99%

“…Fardos et al (2023) [5] presented catalogues of some important classes of MCBNDs. Noreen et al (2023 a, b) [16,18] constructed MCNSBNDs and MCWBNDs, respectively.…”

Section: Introductionmentioning

confidence: 99%

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Efficient Neighbor Designs Weakly Balanced in Circular Blocks of Three Different Sizes

Sajid Hussain,

Jamshaid ul Hassan,

Abid Khan

et al. 2023

VFAST trans. math.

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Minimal circular weakly balanced neighbor designs (MCWBNDs) are efficient to controlneighbor effects for v even. MCWBNDs-II are designs where3v/2 unordered pairs of different treatments occur twice but remaining pairs occur once as neighbors, are not available for m (mod 4) ≡ 0& 3 in blocks of three different sizes with m = (v-2)/2 and v even. Here, some new generators are presented to develop cyclic shifts to get MCWBNDs-II in blocks of three different sizes.

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Section: Sizes For M (Mod 4) ≡mentioning

confidence: 99%

Section: Example 2 Mcwbnds-ii Obtained Through Generator 1 See Tablementioning

confidence: 99%

“…See Table 19. [3,4,5,6,7,15], [9,10,11,13,12,21], [16,17,18,19], [19,22] 0.834 Generator 17. MCWBNDs-II for v = 2ik 1 + 2k 2 + 2k 3 -2 with k 2 = k 1 -2, k 3 = 4 can be obtained if:…”

Section: For Kmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

“…Fardos et al (2023) [5] presented catalogues of some important classes of MCBNDs. Noreen et al (2023 a, b) [16,18] constructed MCNSBNDs and MCWBNDs, respectively.…”

Section: Introductionmentioning

confidence: 99%

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Efficient Neighbor Designs Weakly Balanced in Circular Blocks of Three Different Sizes

Sajid Hussain,

Jamshaid ul Hassan,

Abid Khan

et al. 2023

VFAST trans. math.

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Algorithm to generate efficient circular designs robust to neighbor effects

Fardos,

Hassan,

Jamal

et al. 2024

Kuwait Journal of Science

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An Algorithm Coded with R to Generate GN2 -designs in Circular Blocks

Shabbir,

Hassan,

Hassan

et al. 2023

VFAST trans. math.

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Minimal neighbor balanced designs are economical, therefore, these are preferred by the experimenters to minimize the bias due to neighbor effects. Minimal circular balanced neighbor designs cannot be constructed for almost every case of v even, where v is number of the treatments to be compared. For v even, the circular GN2-designs in which each treatment appears exactly once as neighbors with all other treatments except the one with which it appears twice, are considered the better alternate to the minimal balanced neighbor designs. In this article, an algorithm is developed to generate the circular GN2-designs for v even which can be converted directly into minimal circular balanced and strongly balanced neighbor designs. This algorithm is also coded with R.

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Algorithms to obtain generalized neighbor designs in minimal circular blocks

Cited by 3 publications

References 18 publications

Efficient Neighbor Designs Weakly Balanced in Circular Blocks of Three Different Sizes

Efficient Neighbor Designs Weakly Balanced in Circular Blocks of Three Different Sizes

Algorithm to generate efficient circular designs robust to neighbor effects

An Algorithm Coded with R to Generate GN2 -designs in Circular Blocks

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