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\noindent Statistica Sinica {\bf 15}(2005), 871-888

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\centerline{\large\bf TWO-STAGE GROUP SCREENING IN THE PRESENCE OF}
\vspace{2pt}
\centerline{\large\bf NOISE FACTORS AND UNEQUAL PROBABILITIES OF}
\vspace{2pt}
\centerline{\large\bf ACTIVE EFFECTS}
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\author{A. E. Vine$^1$, S. M. Lewis$^1$ and A. M. Dean$^2$}
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\centerline{\it $^1$University of Southampton and $^2$Ohio State University}
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\begin{quotation}
\noindent {\it Abstract:}
Group screening is a technique for
examining a large number of factors in order to discover the few
factors that have important influences on a measured response. In
two-stage group screening, factors are assigned to groups and new
``grouped factors'' are investigated in a first stage experiment
by varying all the factor values within a group simultaneously.
The factors within those groups identified as important are then
investigated individually in a second stage experiment. This paper
describes theory and software that allows investigation of group
screening in the presence of unequal-sized groups of factors in
the first stage experiment and different probabilities of the
various main effects and interactions being important (or active).
Examples are given to show how the results can be used in practice
to guide the choice of the
 number and sizes of the groups
and to investigate the advantages and disadvantages of different
group screening strategies.\par
\vspace{9pt}
\noindent {\it Key words and phrases:}
Design of experiments, fractional factorial
  experiment, interaction,  noise factor, screening, simulation.\par
\end{quotation}

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