Robustness of General Efficiency Balanced Block Designs against Missing Observations

In the present communication, some results on robustness of generalized efficiency balanced (GEB) block designs with equal block sizes (binary and non-binary) are presented. The necessary & sufficient conditions are obtained for robustness as per criteria 1 (Ghosh, 1982) when the missing observations appear in the following patterns: (i) t (≥1) observations of a design pertaining to the same treatment are missing and (ii) all observations in a block are missing but the residual design still becomes connected. Sufficient conditions for robustness according to Criteria 1 are examined in each type of GEB designs. Another criterion (Criteria 2) for robustness of a block design is the small amount loss of efficiency values of the residual design after deletion of t (≥1) observations. The declining trend of efficiency values after deletion of treatments one by one are presented graphically for measuring the robustness of designs under study.