Role of Transformation for Construction of Asymmetrical and Symmetrical Rotatable Designs

Abstract

In the thesis, the role of transformations in getting asymmetrical rotatable designs from the already existing symmetrical ones has been brought forth. The usefulness of transformations has been established beyond doubt since, apart from getting asymmetrical rotatable designs, it has been possible to obtain, through transformations, symmetrical rotatable designs which have the same number of levels as, or larger or smaller number of levels than in the original design. The method of getting such designs is very simple and consists in the multiplication of the design matrix with some suitable transformation matrix where the coefficients have to be chosen in accordance with two restrictions laid out. The resulting matrix gives the required transformed design and is symmetrical or asymmetrical – a fact which will depend upon the choice of transformation matrix. The number of levels that the factors may have in the transformed design can also be controlled to some extent, through proper choice of transformation. Application of such transformations has been extended to simple factorial experiments to get some interesting fractions of 3ndesign. Inter-relationship between the central composite designs and the rotatable design obtained through the incomplete block design has been shown in some of the cases and it is expected that for the cases of larger number of factors also, similar relationship exists.