OPTIMALITY AND ROBUSTNESS TO THE UNAVAILABILITY OF BLOCKS IN BLOCK-DESIGNS

This paper investigates the optimality of designs derived from binary, variance-balanced incomplete block designs (BIBDs) by removing t equal-sized blocks which are not necessarily disjoint. It is shown that the optimal design is derived by removing blocks which have disjoint sets of treatments, and the worst design is derived by removing identical blocks. For BIBDs and t = 2 all resulting designs are ordered. The implication for competing BIBDs which have the same parameters v, b and k but different support sizes (numbers of distinct blocks) is addressed. Optimality and robustness are measured through the non-zero eigenvalues of the C-matrix of the design missing observations using the iniversal optimality criteria of Bondar.