Sankhya: The Indian Journal of Statistics

2006, Volume 68, Pt. 4, 554--568

Reverse Foldovers for $2^{m-k}$ Fractional Factorial Designs

Mike Jacroux, Washington State University, USA

SUMMARY. Two-level regular fractional factorial designs are often used in industry as screening designs to help identify early in an experimental process those experimental or system variables which have significant effects on the process being studied. In a recent paper, Li and Lin (2003) suggested a strategy for constructing optimal follow up designs using the well known foldover technique and the minimum aberration criterion. In this paper, we consider the reverse foldover problem. In particular, given a $2^{m-k}$ combined design $D$, we derive simple sufficient conditions which can be used to determine if there exists a $2^{m-(k+1)}$ initial design $d$ which yields $D$ as a foldover combined design, as well as show how to generate all such $d$. Such information is useful in developing an overall experimental strategy in situations where a follow up design is anticipated and the experimenter is looking for an overall ``good" design possessing desirable properties.

AMS (2000) subject classification. Primary 62K15.

Key words and phrases. Foldover design, minimum aberration criterion, optimal foldover, combined design, word length pattern.

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