Statistica Sinica 18(2008), 493-513

FACTORIAL DESIGNS WITH MULTIPLE LEVELS

OF RANDOMIZATION

Derek Bingham$^1$, Randy Sitter$^1$, Elizabeth Kelly$^{2}$, Leslie Moore$^{2}$

and J. David Olivas$^{2}$

$^1$Simon Fraser University and $^{2}$Los Alamos National Labs

Abstract: Design and analysis of factorial experiments with randomization restrictions has received considerable attention in recent years; motivated by studies of multi-stage processes or systems. This has given rise to seemingly unrelated methods of design construction, specific to the layout (e.g., split-plot, split-lot, strip-plot designs). We develop a general approach to this problem that includes most approaches in the literature as special cases, and is easily adaptable to designs which are combinations of different layouts.

Key words and phrases: Blocking, orthogonal array, split-lot, split-plot, strip-plot.