Semi-Regular Group Divisible Designs For Smaller Block Size
Keywords:
Semi-Regular Group Divisible design, Balanced Incomplete Block design,, orthogonal arrayAbstract
A group divisible (GD) design is said to be Singular (S) if ; Semi regular (SR) if and rk – v = 0; Regular (R) if
and . In the paper, a new procedure of constructing SRGD design with and , is proposed from a parent SRGD after reducing number of treatment and same number of blocks without disturbing its Semi-Regularity property. It privileges the experimenters to decrease the number of treatment without affecting the number of blocks. Such designs are useful in civil engineers, Agricultural experiments and others.
AMS Subject Classification: 05 B05
Downloads
References
K. K. Singh Meitei (2016). “An Induction on Semi Regular Group Divisible Design” IJIRCST, pp.156- 158, ISSN: 2347-5552, Volume-4, Issue-5, September 2016.
Bagchi, S. (2004). “Construction of group divisible designs and rectangular designs from resolvable and almost resolvable balanced incomplete block de signs”. JSPI, 119, 401-410.
Plackett, R. L and Burman, J. P. (1943-44), “The design of optimum multifactorial experiments,” Biometrika, Vol. 33, pp. 305-325.
Bose, R.C and Connor, W. S (1952), “Combinatorial properties of group divisible incomplete block designs.” Ann. Math. Statist., 23, pp. 367-383.
Bose, R. C., ShriKhande, S. S and Bhattacharya, K. N. (1953), “On the construction of group divisible incomplete block designs.” Ann. Math. Statist., 24, pp. 167-195.
Clathworthy, W. H. (1973), “Tables of Two associate Partially Balanced Designs.” National Bureau of Standards, Applied Maths. Series No. 63. Washington D.C..
Raghava Rao, D.(1970), “Construction and combinatorial problems in Design of Experiments.” John Wiley and Sons Inc., New York.
Clathworthy, W. H. (1973), “Tables of Two associate Partially Balanced Designs.” National Bureau of Standards, Applied Maths. Series No. 63. Washington D.C.
Kageyama, S. and Tsuji, T. (1977), “Characterization of certain incomplete block designs.” J. Statist. Plann. Inf., 1, pp. 151-161.
Dey, A. and Nigam, A. K. (1985), “Construction of Group Divisible designs.” J. Indian Soc. Agril. Statist., 37(2), pp. 163-166.
Kageyama, S. (1985), “A Construction of Group Divisible Designs.” J. Statist. Plan. Inf., 12, pp. 123- 125.
Banerjee, S. and Kageyama, S. (1986), “ A method of constructing Regular Block Design.” J. Statist. Plan. Inf. 13, pp. 399-401.
Sastry, D. V. S. (1990), “On a method of construction of Group Divisible Designs.” Cal. Statist. Asson. Bull. Vol-39, Sept. and Dec., pp. 227- 230.