Algorithm to generate efficient circular designs robust to neighbor effects

Fardos, Akbar; Hassan, Mahmood Ul; Jamal, Farrukh; Ali, Hurria; Noreen, Khadija; Ahmed, Rashid

doi:10.1016/j.kjs.2023.10.003

Cited by 1 publication

(7 citation statements)

References 17 publications

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“…2 appears twice with v even then these sets will produce MCSBGND-I, where [1,6,7] and S 2 = [3,4,5] produce MCSBGND-I for v = 14 and k = 4.…”

Section: Methods Of Constructionmentioning

confidence: 99%

“…Proof. S * = [1, 6, 7, 0, 3,4,5,12,13,8,7,11,10,9,2], Here each of 0, 1, 2, • • • , 13 appears once except 7 which appear twice. Hence S 1 = [1,6,7] and S 2 = [3,4,5] produce MCSBGND-I for v = 14, k = 4.…”

Section: Methods Of Constructionmentioning

confidence: 99%

“…Proof. S * = [3,4,6,8,21,2,9,11,0,7,10,17,19,18,16,14,1,20,13,11,15,12,5], Here each of 0, 1, 2, • • • , 21 appears once except 11 which appear twice. Hence S 1 = [3,4,6,8], S 2 = [2,9,11], S 3 = [7,10] produce MCSBGNDs-I for v = 22, k 1 = 5, k 2 = 4 and k 3 = 3.…”

Section: Methods Of Constructionmentioning

confidence: 99%

“…MCSBGNDs-I for v = 2ik 1 + 4k 2 + 2k 3 -2 with m (mod 4) ≡ 2. See Table 11 6.4 MCSBGNDs-I can be constructed in Three Different Block Sizes for v = 2ik 1 + 4k 2 + 2k 3 -2 when m (mod 4) ≡ 3 with [6,13,14,22,27,46,47,48,52,53]+ [17,19,23,24,25,30,37,40] + [4,5,21,30,37,39,40,43]+ [20,21,23,28] (v)…”

Section: Mcsbgnds-i Can Be Constructed In Three Differentmentioning

confidence: 99%

“…Hassan et al (2023) [8] constructed efficient MCWBNDs in blocks of three different sizes. Fardos et al (2024) [5] developed an algorithm to construct MCBNDs and its efficient classes. Munir et al (2023) [15] developed the following constructors for MCSBGNDs-I.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Some New Generators to Produce Minimal Circular Strongly Balanced Generalized Neighbor Designs of Class-I

Abdul Salam,

Hurria Ali,

Zubia Batool Shamshi

et al. 2024

VFAST trans. math.

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Minimal circular strongly balanced neighbor designs control the neighbor effects economically but these designs can only be constructed for v odd. For v even, their alternates are minimal circular strongly balanced generalized neighbor designs of class-I (MCSBGNDs-I) which are the designs in which (i) each treatment appears exactly once with itself as neighbors, (ii) v/2 unordered pairs appear twice as neighbors while the remaining ones appear once. On the basis of constructors developed by Munir et al. (2023), some new generators are developed in this article to generate cyclic shifts for efficient MCSBGNDs-I in blocks of (i) equal sizes, (ii) two different sizes, and (iii) three different sizes for m (mod 4) ≡ 2 & 3 with v even and k = 4l, k = 4l+2, k (odd) > 3, k (mod) ≡ 1 & k (mod) ≡ 3. Efficiency of neighbor effects and of Separability show that our proposed generators produce designs which control the neighbor effects efficiently as well as estimate the direct effects and neighbor effects independently.

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“…2 appears twice with v even then these sets will produce MCSBGND-I, where [1,6,7] and S 2 = [3,4,5] produce MCSBGND-I for v = 14 and k = 4.…”

Section: Methods Of Constructionmentioning

confidence: 99%