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2m41 designs with minimum aberration or weak minimum aberration

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Abstract

For measuring the goodness of 2m41 designs, Wu and Zhang (1993) proposed the minimum aberration (MA) criterion. MA 2m41 designs have been constructed using the idea of complementary designs when the number of two-level factors, m, exceeds n/2, where n is the total number of runs. In this paper, the structures of MA 2m41 designs are obtained when m>5n/16. Based on these structures, some methods are developed for constructing MA 2m41 designs for 5n/16<m<n/2 as well as for n/2≤m<n. When m≤5n/16, there is no general method for constructing MA 2m41 designs. In this case, we obtain lower bounds for A 30 and A 31, where A 30 and A 31 are the numbers of type 0 and type 1 words with length three respectively. And a method for constructing weak minimum aberration (WMA) 2m41 designs (A 30 and A 31 achieving the lower bounds) is demonstrated. Some MA or WMA 2m41 designs with 32 or 64 runs are tabulated for practical use, which supplement the tables in Wu and Zhang (1993), Zhang and Shao (2001) and Mukerjee and Wu (2001).

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Authors and Affiliations

  1. Department of Statistics, School of Mathematical Sciences and LPMC, Nankai University, 300071, Tianjin, China

    Peng-Fei Li, Min-Qian Liu & Run-Chu Zhang

  2. Department of Statistics and Actuarial Science, University of Waterloo, N2L 3G1, Waterloo, Ontario, Canada

    Peng-Fei Li

Authors
  1. Peng-Fei Li
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  2. Min-Qian Liu
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  3. Run-Chu Zhang
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Correspondence to Min-Qian Liu.

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Li, PF., Liu, MQ. & Zhang, RC. 2m41 designs with minimum aberration or weak minimum aberration. Statistical Papers 48, 235–248 (2007). https://doi.org/10.1007/s00362-006-0328-5

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  • DOI: https://doi.org/10.1007/s00362-006-0328-5

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