Fractional resolution and minimum aberration in blocked \(2^{n-k}\) designs.

*(English)*Zbl 0913.62073Summary: Systematic sources of variation can be reduced in fractional factorial experiments by grouping the runs into blocks. This is accomplished through the use of blocking factors. The concepts of resolution and minimum aberration, design optimization criteria ordinarily used to rank unblocked fractional factorial designs, are extended to such blocked fractional factorial designs by treating the treatment and blocking factors differently in terms of their contribution to word length in the defining contrast subgroup. Some limited theoretical results are derived, and tables of minimum-aberration blocked two-level fractional factorial designs are presented and considered. The relationship between clear effects (effects that are estimable when higher-order effects are assumed negligible) and minimum aberration in the presence of blocking is discussed.

##### MSC:

62K15 | Factorial statistical designs |