Robustness of group divisible (GD) designs is investigated, when one block is lost, in terms of efficiency of the residual design. The exact evaluation of the efficiency can be made for singular GD and semi-regular GD designs as ell as regular GD designs with λ1 = 0. In a regular GD design with λ1 > 0, the efficiency may depend upon the lost block and sharp upper and lower bounds on the efficiency are presented. The investigation shows that GD designs are fairly robust in terms of efficiency. As a special case, we can also show the robustness of balanced incomplete block design when one block is lost.

Robustness group divisible designs

This paper investigates locally resistant balanced incomplete block (LRBIB) designs of degree one. A new necessary condition for the existence of such an LRBIB design is presented. This condition yields a complete characterization of affine α-resolvable LRBIB designs of degree one. Furthermore, regarding construction methods of LRBIB designs of degree one, it is shown that Shah and Gujarathi's method (1977,Sankhya, B39, 406–408) yields the same parameters as Hedayat and John's method (1974,Ann. Statist.,2, 148–158), but their block structures are different and interesting.

Some characterization of locally resistant BIB designs of degree one

A general solution is derived to the problem of characterizing block designs that are simultaneously pairwise-balanced and variance-balanced. Applications of the characterizations obtained to some problems concerned with the local resistance of BIB designs are presented.

/pdf/pairwise-balanced-variance-balanced-and-resistant-incomplete-2gmk3pbp7j.pdf

Pairwise-balanced, variance-balanced and resistant incomplete block designs revisited

Robustness of some balanced block designs

Resistance of block designs

Hedayat and John (1974) opened up a new, elegant and practically useful area for research by introducing resistant and susceptible block designs. They have concluded their paper with many unsolved problems, which need to be attended. In this paper the author has made an attempt to answer some of those problems and in this process some related findings are also presented.

http://csa.sagepub.com/content/29/1-2/27.full.pdf

M.L. Chandak

Papers

On the Theory of Resistant Block Designs