Improved conditions for the robustness of binary block designs against the loss of whole blocks

A Link Between theE-Value and the Robustness of Block Designs

“…Proof: (i) This is proved in Lemma 1 of Godolphin and Warren (2011) for the case p = r [υ] − 1 and the general result is obtained in the same way.…”

“…Designs with t * = r [υ] are described as being maximally robust with regards to loss of individual observations and loss of entire blocks. Baksalary and Tabis (1987), Sathe and Satam (1992) and Godolphin and Warren (2011) derive conditions for a binary incomplete block design to be maximally robust. However, the concept of maximal robustness has the limitation that the size of r [υ] sets the bar at which a design has the status of being maximally robust.…”

“…Dey et al (2001) focus on the loss of a single observation or a single block from diallel cross designs. Design properties associated with Criterion 1 robustness in the event of the loss of complete blocks from any binary incomplete block design are derived by Baksalary and Tabis (1987), Sathe and Satam (1992) and Godolphin and Warren (2011). Notz et al (1994) investigate the loss of n observations or t blocks according to Criterion 1, Lal et al (2001) give a condition for a block design to be robust against the loss of any n observations and Godolphin and Warren (2014) provide an algorithm for determining robustness of any binary design with all blocks of size k with respect to loss of individual observations.…”

A note on the robustness of PBIBD(2)s against breakdown in the event of observation loss

“…Ghosh () established that all BIBDs have t * = r . For binary incomplete block designs, not necessarily with equal treatment replication, robustness against the loss of whole blocks was investigated by Baksalary & Tabis (), Sathe & Satam (), Godolphin & Warren () and Godolphin (). Bailey, Schiffl & Hilgers () and Tsai & Liao () focussed attention on robustness of designs with blocks of size two.…”

The robustness of resolvable block designs against the loss of whole blocks or replicates

“…For example: batches of raw material can be found to be contaminated; areas of agricultural land can be flooded; harvests occasionally fail; trials are ended prematurely due to lack of resources. Baksalary and Tabis (1987), Sathe and Satam (1992) and Godolphin and Warren (2011) considered the robustness of an arbitrary binary block design against the loss of whole blocks. Results obtained by these authors provide lower bounds for λ * , the minimal treatment concurrence of the design, i.e.…”