Construction of Three Associate Class PBIB Designs with Three Replicates Using Pairing in Triplets System

Abstract

A Series of three associate class Partially Balanced Incomplete Block (PBIB) designs with three replicates is introduced in this paper. The method of construction of new designs is based on method of pairing in symbols of triplets system. In the construction of three associate class PBIB designs, we take nine blocks with three replicates. We then paired the iterative values of triplets with its initial values under different conditions to get blocks of new designs. Association scheme of new series of designs is also based on occurrence of treatment pairs. Efficiency factors of three kinds of comparisons E1, E2, E3 and overall efficiency factor E along with illustration have also been given in the paper.