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Optimality Of Chemical Balance Weighing Designs., Joseph Costantino. Masaro
Optimality Of Chemical Balance Weighing Designs., Joseph Costantino. Masaro
Electronic Theses and Dissertations
Net N and n be positive integers with N (GREATERTHEQ) n and let D(N,n) denote the set of all N x n matrices X = (x(,ij)) with x(,ij) = -1,0 or 1. Let D'(N,n) be the set of all matrices in D(N,n) with entries -1,1. Each such matrix in D(N,n) or D'(N,n) will be called a weighing design matrix. If X(,0) minimizes (PHI)(X('T)X) over D(N,n) for some real valued function (PHI), then X(,0) is said to be (PHI)-optimum over D(N,n). The characterization of such X(,0) arises from the statistical problems of weighing designs, certain block designs and 2('n) fractional factorial …