Investigation On Fractional Factorial Designs

Abstract

The problem of constructing fractional replicates of the

2m, 3n, and 2m x 3n designs which permit estimation of main effects and two-factor interactions, assuming higher factor interactions to be absent is not new in literature. Extensive work in this field has been done by Rao (22), Chakravarti (10), Bose and Connor (8), Connor (11), Dykstra, (14), Sydney Addelman (1), (2), (3), (4), Sydney Addelman and Kempthorne (5), Patel (16), (17), (18), and Srivestera, (23) •

This is yet another attempt on the subject and follows more

or less the line of approach of Connor (11), Patel (16), (17), and Sydney Addelman (2). Much work still remains to be done particularly in the field of mixed fractional factorial designs.

Chapter II deals with orthogonal main effects plans for 2m, 3n, and 2m x 3n designs with and without blocks. In this, one more method has been developed, whi ch generates orthogonal arrays of strength,-. ---;f2or factors each at 2 levels 0, 1 and of size N=4A (A! positive integer), earlier given by Plackett and Burman (21), Patel and Gupta (19).

Chapter III deals with the construction of orthogonal main effects and two-factor interactions pl~lS for 2m and 3n design. The method of writing linear forms which could generate orthogonal arrays of strength 2 for factors each at 3 levels 0, 1, and 2, is given and used to construct fractional plans for 3n designs.

In Chapter IV, some useful

~ irrgular

designs of type m

are given, aslo, some attempt has been made to obtain

-5-

n economic main effects plans for 3 design. In the

end, using non-homogeneous quadric surfaces In E G (n,3), some mixed designs of the type 2m x 3n are also obtained.