Speaker
Description
An approach to the construction of Balanced Incomplete Block Designs (BIBD) is described. The exact pairwise balance of treatments within blocks (second-order balancing condition) is required by standard BIBD. This requirement is attainable when $\lambda = b \binom{k}{2} / \binom{t}{2}$ is an integer, where $t$ is the number of treatments, $b$ is the number of blocks and $k$ is the block size.
This work presents an algorithm for generating BIBD with particular attention to settings where a second blocking variable is taken into account (Youden squares) and the blocks are assigned to $s$ groups (sessions) where all treatments are equally represented inside each one.
Two real-world applications are presented. The first refers to an exploratory experiment with 8 two-level factors leading to $t$=20 trials, assessed by $k$=4 evaluators through $b$=20 blocks divided into $s$=4 balanced sessions. The second example refers to a robust design experiment based on a Central Composite Design involving 4 technological and 2 environmental factors leading to $t$=30 trials, evaluated in $k$=5 environmental conditions within $b$=30 blocks divided into $s$=5 balanced sessions. In these experimental settings, the second-order balancing condition is not attainable since $\lambda$ is not an integer.
The proposed algorithm has been designed to approximate this condition as closely as possible, maintaining the first-order balancing condition.
The implementation of the algorithm has been implemented in the R environment.
| Classification | Both methodology and application |
|---|---|
| Keywords | BIBD, Heuristic Optimization |