On the Construction of VB Designs

This paper gives complete analytical study of suitability and non-availability of I-associate and II-associate designs of a given 2-class partially balanced incomplete block (2-PBIB) design in the construction of a variance balance (VB) design using the given 2-PBIB design.

Construction of Variance Balanced Designs through Triangular PBIB Designs

Several authors have obtained variance balanced (VB) and ternary variance balanced ( V B) designs using balanced incomplete block (BIB) designs and group divisible (GD) designs. In the present investigation, another systematic methods have been developed for the construction of VB designs using A Triangular PBIB design and an incomplete block design where the blocks of the incomplete block design are formed by taking the second associate treatments of the given triangular PBIB design. Two Triangular PBIB designs. The methods of construction of VB designs are further illustrated by examples.

On the block structure of PBIB designs

Let{θ,θ1,…,θn1}denote the set having any treatmentθand itsn1first associates in a PBIB design withm(≥2)associate classes. A theorem on distribution of the elements of this set among the blocks of the block design is proved and results related to certain well known association schemes of three associate classes are obtained.

On the Evaluation of Some Expressions Concerning the PBIB Designs

Consider a two associate class partially balanced incomplete block (PBIB) design [2] with parameters of the first kind t, b, r, λ,1 λ,2 n1, n2, and parameters of the second kind . Let the letters m, p, l, s represent treatments and define associates of treatment m, λmps = number of times the treatments m, p and s all occur together in the same block, λmpls = number of times the treatments m, p, l and s all occur together in the same block.