**Sankhya:
The Indian Journal of Statistics**

2004, Volume 66, Pt. 2, 327--342

**Designing Two-level Fractional
Factorial Experiments in Blocks of Size
Two**

P.C. Wang , National Central University, Chung Li, Taiwan

SUMMARY. We need extra runs to design two-level factorial experiments in blocks of size two to estimate all the available effects, as is possible in experiments without blocking. The number of runs suggested is $(n-p)2^{n-p}$ for $2^{n-p}$ fractional factorial experiments. In designing such an experiment, two issues need to be considered. First, the precision of estimates is usually different because different numbers of observations are used for estimation in the analysis of the resulting data. It is important to have more precise estimates of the effects with which we are most concerned. Second, the trade-off between run-size reduction and the possibly negligible effects is of significance, especially when the number of factors is large. To deal with these two issues, several assignment rules are suggested for designing good experiments.

*AMS (1991) subject classification. 62K05, 62K15.*

*Key words and phrases. *Precision, blocking, factorial designs,
orthogonal arrays.