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

Authors

DOI:

https://doi.org/10.21015/vtm.v12i1.1716

Keywords:

Direct Effects;Economical neighbor designs;Efficiency of Separability; Neighbor effects

Abstract

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.

References

Ahmed, R. and Akhtar, M. (2008). "Neighbor Balanced Block Designs Construction." Journal of Statistical Theory and Practice, 2(4), 551–558.

Ahmed, R. and Akhtar, M. (2011). "Circular Blocks of Size Six: Balanced Designs for Neighbor Effects." Journal of Statistical Planning and Inference, 141, 687–691.

Ali, H., Nasir, M., Rashid, M. S., Noreen, K., Ahmed, R., & Ulhassan, M. (2023). "Generalized Circular Designs Strongly Balanced for Neighbor Effects." Journal of Statistics Application and Probability, 12(1), 11–17.

Divecha, J. and Gondaliya, J. (2014). "Minimal Balanced Cross Over Designs Construction with Good Separability Efficiency." Electronic Journal of Statistics, 8, 2923–2936.

Fardos, A., Ul Hassan, M., Jamal, F., Ali, H., Noreen, K., & Ahmed, R. (2024). "Efficient Circular Designs Robust to Neighbor Effects: An Algorithmic Approach." Kuwait Journal of Science, 51(1), 100135.

Hamad, N. (2014). "Partially Neighbor Balanced Designs for Circular Blocks." American Journal of Theoretical and Applied Statistics, 3, 125–129.

Hamad, N. and Hanif, M. (2016). "Non-binary Partially Neighbor Balanced Designs for Circular Blocks." Communication in Statistics - Theory and Methods, 45, 5961–5965.

Hassan, J., Khan, A., Hussain, S., Ali, H., Safdar, A., & Salam, A. (2023). "Weakly Balanced Efficient Neighbor Designs in Circular Blocks of Three Different Sizes." VFAST Transactions on Mathematics, 11(2), 155–173.

Hwang, F. K. (1973). "Neighbor Designs Constructions for Various Classes." Annals of Statistics, 1(4), 786–790.

Iqbal, I. (1991). "Experimental Design Construction using Cyclic Shifts." Ph.D. Thesis, University of Kent at Canterbury, U.K.

James, A. T. and Wilkinson, G. N. (1971). "Residual Operator Factorization and Non-orthogonal Factor Canonical Decomposition in Analysis of Variance." Biometrika, 58, 258–294.

Mehmood, Q., Arshad, H. M., Noreen, K., Munir, I., Salam, A., & Ahmed, R. (2023). "Minimal Circular Partially Balanced Neighbor Designs: New Constructors." Journal of Statistics Application and Probability, 12(1), 93–99.

Mehmood, Q., Nadeem, M., Noreen, K., & Ahmed, R. (2022). "Generalized Neighbor Designs Construction in Circular Blocks of Two Different Sizes." The Nucleus, 59(1-4), 16–25.

Mettei, K. K. S. (1996). "Incomplete Block Neighbour Designs Series." Sankhya Series B, 58(1), 145–147.

Munir, I., Ali, H., Rashid, M. S., Noreen, K., Ahmed, R., & Ulhassan, M. (2023). "New Constructors of Circular Strongly Generalized Neighbor Designs." Journal of Statistics Application and Probability, 12(1), 71–74.

Nadeem, M., Ahmed, R., Mehmood, Q., & Berihan, R. A. (2022). "Minimal Circular Partially Balanced Neighbor Designs: New Constructions." Journal of Statistics Applications and Probability, 11(3), 835–843.

Nadeem, M., Noreen, K., Rasheed, H. M. K., Ahmed, R., & Ul Hassan, M. (2023). "New Generators for Minimal Circular Generalized Neighbor Designs in Blocks of Two Different Sizes." Statistics in Transition New Series, 24(2), 85–92.

Nadeem, M., Rasheed, M., Tahir, M. H., Noreen, K., Hussain, S., & Ahmed, R. (2022). "Generalized Neighbor Designs Construction in Minimal Circular Blocks." Kuwait Journal of Science, 49(4), 1–11.

Nadeem, M., Tahir, M. H., Ismail, M., Ahmed, R., & Iqbal, U. (2021). "Economical Classes of Minimal Circular Generalized Neighbor Designs." International Journal of Innovation, Creativity and Change, 15(8), 243–255.

Noreen, K., Rasheed, M., Rasheed, H. M. K., Jamal, F., Ahmed, R., & Onyango, R. (2022). "New Dimensions for Economical Circular Weakly Balanced Neighbor Robust Designs Construction." Mathematical Problems in Engineering, 2022, Article ID 8473332, 10 pages.

Pearce, S. C., Calinski, T., & Marshall, T. F. C. (1974). "Basic Contrasts of Experimental Design with Special Reference to Data Analysis." Biometrika, 61, 449–460.

Rasheed, M., Noreen, K., Ahmed, R., Tahir, M. H., & Jamal, F. (2022). "Useful Classes of Minimal Weakly Balanced Neighbor Designs in Circular Blocks of Two Different Sizes." Communications in Statistics - Theory and Methods, 21(24), 8822–8839.

Rees, D. H. (1967). "Designs Use in Serology." Biometrics, 23, 779–791.

Salam, A., Ahmed, R., Daniyal, M., & Berihan, R. A. (2022). "Nearly Strongly-Balanced Minimal Circular Neighbor Designs with Equal Left and Right Neighbor Effects." Journal of Statistics Applications and Probability, 11(3), 883–891.

Salam, A., Ahmed, R., Daniyal, M., Ismail, M., & Rehman, H. (2021). "New Constructions of Minimal Neighbor Designs in Circular Blocks." International Journal of Innovation, Creativity and Change, 15(8), 435–456.

Shabbir, J., Hassan, J., Ul Hassan, M., Noreen, K., Hussain, S., & Ahmed, R. (2023). "R-Encoded Algorithm for GN2-Designs Generation in Circular Blocks." VFAST Transaction on Mathematics, 11(2), 16–27.

Sharif, S., Ahmed, R., Mehmood, Q. and Shahid, M. R. [2022], ‘The construction of some new quasi rees

neighbor designs using cyclic shifts’, Pakistan Journal of Statistics and Operations Research 18(3), 643–

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Published

2024-03-23

How to Cite

Abdul Salam, Hurria Ali, Zubia Batool Shamshi, Jamshaid ul Hassan, Abid Khan, & Sajid Hussain. (2024). Some New Generators to Produce Minimal Circular Strongly Balanced Generalized Neighbor Designs of Class-I. VFAST Transactions on Mathematics, 12(1), 71–91. https://doi.org/10.21015/vtm.v12i1.1716