Chen, Hegang; Hedayat, A. S. \(2^{n-l}\) designs with weak minimum aberration. (English) Zbl 0867.62066 Ann. Stat. 24, No. 6, 2536-2548 (1996). Summary: Since not all \(2^{n-l}\) fractional factorial designs with maximum resolution are equally good, A. Fries and W. G. Hunter [Technometrics 22, 601-608 (1980; Zbl 0453.62063)] introduced the minimum aberration criterion for selecting good \(2^{n-l}\) fractional factorial designs with the same resolution. We modify the concept of minimum aberration and define weak minimum aberration and show the usefulness of this new design concept. Using some techniques from finite geometry, we construct \(2^{n-l}\) fractional factorial designs of resolution III with weak minimum aberration. Further, several families of \(2^{n-l}\) fractional factorial designs of resolution III and IV with minimum aberration are obtained. Cited in 1 ReviewCited in 52 Documents MSC: 62K15 Factorial statistical designs 62K05 Optimal statistical designs 05B25 Combinatorial aspects of finite geometries Keywords:regular fraction; wordlength pattern; fractional factorial designs; maximum resolution; minimum aberration criterion; weak minimum aberration Citations:Zbl 0453.62063 × Cite Format Result Cite Review PDF Full Text: DOI References: [1] Bose, R. C. (1947). Mathematical theory of the sy mmetrical factorial design. Sankhy\?a Ser. A 8 107-166. · Zbl 0038.09601 [2] Chen, H. (1993). Contributions to experimental designs. Ph.D. dissertation, Univ. Illinois, Chicago. [3] Chen, J. (1992). Some results on 2n-k fractional factorial designs and search for minimum aberration designs. Ann. Statist. 20 2124-2141. · Zbl 0770.62063 · doi:10.1214/aos/1176348907 [4] Chen, J. and Wu, C. F. J. (1991). Some results on sn-k fractional factorial designs with minimum aberration or optimal moments. Ann. Statist. 19 1028-1041. · Zbl 0725.62068 · doi:10.1214/aos/1176348135 [5] Franklin, M. F. (1984). Constructing tables of minimum aberration pn-m designs. Technometrics 26 225-232. JSTOR: · doi:10.2307/1267548 [6] Fries, A. and Hunter, W. G. (1980). Minimum aberration 2k-p designs. Technometrics 22 601- 608. JSTOR: · Zbl 0453.62063 · doi:10.2307/1268198 [7] Heday at, A. S. and Pesotan, H. (1992). Two-level factorial designs for main effects. Statist. Sinica 2 453-464. · Zbl 0820.62068 [8] Heday at, A. S. and Pesotan, H. (1997). Designs for two-level factorial experiments with linear models containing main effects and selected two-factor interactions. J. Statist. Plann. Inference. · Zbl 0904.62091 · doi:10.1016/S0378-3758(96)00209-1 [9] Pu, K. (1989). Contributions to fractional factorial designs. Ph.D. dissertation, Univ. Illinois, Chicago. [10] Raktoe, B. L., Heday at, A. S. and Federer, W. T. (1981). Factorial Designs. Wiley, New York. · Zbl 0593.62074 [11] Wu, C. F. J. and Chen, Y. (1992). A graph-aided method for planning two-level experiments when certain interactions are important. Technometrics 34 162-175. This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.