A general approach to studying fractional factorial designs with multiple groups of factors is proposed. A structure function is generated by the defining contrasts among different groups of factors and the
remaining columns. The structure function satisfies a first-order partial differential equation. By solving this equation, general results about the structures and properties of the designs are obtained. As an important application, practical rules for the selection of "optimal" single arrays for robust parameter design experiments are derived.
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WEST LAFAy ETTE, INDIANA 47907 E-MAIL: yuzhu@stat.purdue.edu
