Split-plot designs for robotic serial dilution assays

This article explores effective implementation of split-plot designs in serial dilution bioassay using robots. We show that the shortest path for a robot to fill plate wells for a split-plot design is equivalent to the shortest common supersequence problem in combinatorics. We develop an algorithm for finding the shortest common supersequence, provide an R implementation, and explore the distribution of the number of steps required to implement split-plot designs for bioassay through simulation. We also show how to construct collections of split plots that can be filled in a minimal number of steps, thereby demonstrating that split-plot designs can be implemented with nearly the same effort as strip-plot designs. Finally, we provide guidelines for modeling data that result from these designs.