Construction of sub class of balanced asymmetrical factorial designs

Abstract

The main focus of this research is to construct balanced asymmetrical factorial designs in which main effects and higher order interactions are estimated with high efficiencies if not full efficiencies. The specific objectives in this work is to illustrate straight forward procedures for constructing balanced arrays/resolvable balanced incomplete block designs and hence balanced asymmetrical factorial designs. The available literature has given methods of calculating efficiencies for balanced asymmetrical factorial designs. These methods are not clear and have used the traditional approaches. Therefore in this work we have made a contribution in which we have given a direct method that uses Kronecker product of matrices to evaluate such efficiencies. Another major contribution is the use of Resolvable balanced incomplete block designs in construction of balanced asymmetrical factorial designs A notable contribution in this research work is in the construction of transitive arrays which are extensively used in the construction of balanced asymmetrical factorial designs by the use of Latin squares. In literature, such arrays have been constructed by using t − ply transitive groups An additional contribution in this work is in the construction of resolvable balanced incomplete block designs (BIBD’s) that have block size k = 3 More specifically we have used the geometry of chords constructed in a circle. We have used resolvable BIBD’s of block size k = 3 to construct many more balanced asymmetrical factorial designs This research work has come up with a noble method of constructing balanced arrays/resolvable BIBD’s which have been used to construct a wide range of balanced asymmetrical factorial designs. This research work is however based on the construction of balanced asymmetrical factorial designs that are connected, so the results that we have illustrated in this thesis are not valid in the disconnected case. This calls for suitable modifications of these results to make them applicable to the disconnected case. In this thesis we have restricted our considerations of balanced asymmetrical factorial designs to one way designs only. These concepts can also be extended to two way designs i.e. designs with rows and columns as blocks