Abstract
ABSTRACTThe purpose of this paper is to find and construct optimal designs for estimating the standardized linear and quadratic contrasts in fractional factorials with k factors, each at 3 levels, when the number of runs or assemblies is N. The case N=3m is examined, the notion of Balanced Arrays or for short, is introduced and the optimal is specified. It is shown that for N=9m the orthogonal array or for short, is the φ-optimal design. If N=9m+3 and N=9m+6 the optimal designs are which are specified for every value of N and k. In the case N=9m+3 and k=3 the optimal are constructed by augmenting by three rows which are specified. If the does not exist, algorithms are developed to construct the optimal . For N=9m+6 and k=3 the optimal are constructed by augmenting by six rows, which are specified, otherwise algorithms are developed. Under optimal , the estimators of linear and quadratic contrasts are uncorrelated. The cases N=12,15,21,24,30,33 are examined in detail and optimal are presented for different values of the number k of factors.
Published Version
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