Derivation and Assessment of Robustness Criteria for Vulnerability of Block Designs in the Event of Observation Loss

This presentation summarises the main content of my PhD, researching into
the robustness of incomplete block designs, which introduces a Vulnerability
Measure to determine the likelihood of a design becoming disconnected with
inestimable treatment contrasts, as a result of random observation loss. For
any general block design, formulae have been derived and a program has been
written to calculate and output the vulnerability measures.

Comparisons are made between the vulnerability and optimality of designs.
The vulnerability measures can aid in design construction, be used as a pilot
procedure to ensure the proposed design is sufficiently robust, or as a method
of design selection by ranking the vulnerability measures of a set of competing
designs in order to identify the least vulnerable design. In particular, this can
distinguish between non-isomorphic BIBDs. By observing combinatorial relationships
between concurrences and block intersections of designs, this ranking
method is compared with other approaches in literature that consider the
effects on the efficiency of BIBDs, by either the loss of two complete blocks, or
the loss of up to three random observations.

The loss of whole blocks of observations is also considered, presenting improvements
on bounded conditions for the maximal robustness of designs.
Special cases of design classes are considered, e.g. complement BIBDs and repeated
BIBDs, as well as non-balanced designs such as Regular Graph Designs
and Nearly Balanced Designs.