Some results on blocked regular 2-level fractional factorial designs with clear effects.

*(English)*Zbl 1099.62082Summary: Blocking is commonly used in design of experiments to reduce systematic variation and increase precision of effect estimation. In this article, the clear effect concept is discussed for blocked fractional factorial designs. First, some theoretical results on the existence of clear main effects and two-factor interactions (2fi’s) in regular \(2^{m-p}:2^{l}\) designs with resolution III, IV\(^{-}\) and IV are obtained, where a \(2^{m-p}:2^{l}\) design means a \(2^{m-p}\) design in \(2^{l}\) blocks. Then, the blocked designs containing clear 2fi’s are mainly considered and the upper and lower bounds on the maximum number of clear 2fi’s in \(2^{m-p}:2^{l}\) designs with resolution III and IV\(^{-}\) are derived. The lower bounds are achieved by constructing specific designs. Some tables are also given for comparing the bounds with true values, which show that many designs constructed by our methods have the maximum number of clear 2fi’s.

##### MSC:

62K15 | Factorial statistical designs |

##### Keywords:

blocked fractional factorial design; clear; main effect; minimum aberration; resolution; two-factor interaction
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\textit{B.-J. Chen} et al., J. Stat. Plann. Inference 136, No. 12, 4436--4449 (2006; Zbl 1099.62082)

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