title: Split-plot designs for robotic serial dilution assays.
abstract: 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.
authors.affiliation: Department of Mathematics and Statistics, University of Vermont, Burlington, Vermont 05401, USA. buzas@cems.uvm.edu
authors.forename: Jeffrey S
authors.initials: JS
authors.lastname: Buzas
authors.forename: Carrie G
authors.initials: CG
authors.lastname: Wager
authors.forename: David M
authors.initials: DM
authors.lastname: Lansky
mesh_terms: D000465:Algorithms; D001681:Biological Assay / Q000379:methods*; D003198:Computer Simulation; D007201:Indicator Dilution Techniques; D015233:Models, Statistical; D012371:Robotics / Q000379:methods*