Construction Of Some Balanced Asymmetrical Factorial Designs

Abstract

Two distinct methods of obtaining high efficiency balanced asymmetrical factorial designs that are resolvable have been discussed. One of these methods uses pseudofactors and factors of asymmetry while the other method uses magnified arrays. The effect of confounded interactions of symmetrical factorial designs in context of correspondence between them and their corresponding asymmetrical factorial designs has been applied or used in one of these two methods of construction. A method of obtaining efficiency factors of main effects and interaction effects has also been discussed, this method uses Kronecker product matrices and it enables one to identify optimal designs in case of competing balanced asymmetrical factorial designs. The relationship between block size as a product of factor levels and the corresponding efficiencies of the relevant factors has also been explained. A general technique of collapsing of factor levels and replacement of factor levels when constructing multifactor balanced asymmetrical factorial designs from two factor balanced asymmetrical factorial designs has also been discussed.