An Induction on Semi-Regular Group Divisible Design
K.K. Singh Meitei
A Group Divisible design (v, b, r, k, , ; m, n) is said to be Semi-Regular when r- > 0 and rk – v = 0. In this paper it is proposed that starting from Semi-Regular Group Divisible (SRGD) design with k = m, = 0, many series of Group Divisible (GD) designs are constructed without disturbing its Semi-Regular property. Such design are useful in the formation of different plats of same size reinforced Cement concrete, by having choice of different iron bars of different gauges by civil engineers.
Semi-Regular Group Divisible design, Balanced Incomplete Block design
 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.
 Vartak, M. N (1955), “ On application of Kronecker product of matrices to Statistical designs.” Ann. Math. Statist., 26, pp. 420-438.
 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.
 Kumar, K. S. (1992-93), “A Note on construction of two associate GD Designs from a given BIBD.” Aligarh J. Statistics, Vol-12 &13, pp. 31-32.
[K.K. Singh Meitei (2016), An Induction on Semi-Regular Group Divisible Design, International Journal of Innovative Research in Computer Science & Technology (IJIRCST), Vol-4, Issue-5, Page No-156-158], (ISSN 2347 - 5552). www.ijircst.org
K.K. Singh Meitei
Department of Statistics, Manipur University, Canchipur, Imphal 795003, India