Abstract
Some new construction methods of the optimum chemical balance weighing designs and pairwise efficiency and variance balanced designs are proposed, which are based on the incidence matrices of the known symmetric balanced incomplete block designs. Also the conditions under which the constructed chemical balance weighing designs become A-optimal are also been given.
Highlights
In that series we propose another new construction methods of obtaining optimum chemical balance weighing designs using the incidence matrices of symmetric balanced incomplete block designs and some more pairwise efficiency as well as variance balanced designs are proposed
If the SBIB design exists with parameters ν= b= N, r= k= ( N ± d ) 2, λ = ( N ± 2d +1) 4 ; the design matrix N∗1 so formed using above method is optimum chemical balance weighing design
If the SBIB design exists with block size r ≤ 6 and λ ≤ 5 ; the design matrix X so formed using above method II is optimum chemical balance weighing design
Summary
Awad et al [25] [26] gave the construction methods of obtaining optimum chemical balance weighing designs using the incidence matrices of symmetric balanced incomplete block designs and some pairwise balanced designs were been obtained which were efficiency as well as variance balanced. In that series we propose another new construction methods of obtaining optimum chemical balance weighing designs using the incidence matrices of symmetric balanced incomplete block designs and some more pairwise efficiency as well as variance balanced designs are proposed. In chemical balance weighing ( ) design, the elements of design matrix X = xij takes the values as +1 if the jth object is placed in the left pan in the ith weighing, −1 if the jth object is placed in the right pan in the ith weighing and 0 if the jth object is not weighted in the ith weighing.
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