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\footnotesize \noindent Statistica Sinica {\bf 21} (2011), 1001-1021

\vspace{3pc} \normalsize \centerline{\large\bf MULTISTRATUM
FRACTIONAL FACTORIAL DESIGNS} \vspace{.25cm}
\author{Ching-Shui Cheng and Pi-Wen Tsai}
\vspace{.4cm} \centerline{\it University of California, Berkeley and
National Taiwan Normal University} \vspace{.55cm} 
\begin{quotation}
\noindent {\it Abstract:} Recent work on multistratum fractional
factorial designs is set in a general and unified framework, and a
criterion for selecting multistratum fractional factorial designs
that takes stratum variances into account is proposed. Application
of the general theory is illustrated on designs of experiments with
multiple processing stages, including split-lot designs, blocked
strip-plot designs, and post-fractionated strip-block designs. In
particular, this helps elucidate the relationship between the three
different design settings studied by Miller (1997), Bingham et al
(2008), and Vivacqua and Bisgaard (2009). The construction and
selection of two-stage designs in these settings are shown to be
equivalent. Good designs based on our criterion are found and
compared with those tabulated in Vivacqua and Bisgaard (2009).\par
 \vspace{9pt} \noindent {\it Key words and phrases:}
Block structure, information capacity, minimum aberration,
orthogonal design, post-fractionated strip-block design, split-lot
design, split-plot design, strip-plot design. \par
\end{quotation}

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