Computational Statistics

, Volume 33, Issue 2, pp 933–965 | Cite as

Choice of optimal second stage designs in two-stage experiments

  • A. M. Elsawah
Original Paper


In real-life projects, in order to obtain precious information about the process, we often partition the experiment into two stages with equal size. The main purpose of this article is to study how to choose the first stage experimental designs (FSED) and the second stage experimental designs (SSED) to construct uniform or at least good approximation to uniform (GATU) two-stage experimental designs (TSED) that involve a mixture of \(\omega _1\ge 1\) factors with \(\mu _1\ge 2\) levels and \(\omega _2\ge 1\) factors with \(\mu _2\ge 2\) levels whether regular or nonregular. Through theoretical justification, this paper proves that the SSED is uniform (GATU) if and only if the FSED is uniform (GATU), the TSED is uniform (GATU) if and only if its corresponding complementary TSED is uniform (GATU), and the TSED is uniform or at least GATU if and only if the FSED is uniform.


Second stage design Second stage map Two-stage design Uniform design Optimal design Complementary design 



The author greatly appreciate helpful suggestions of the two referees that significantly improved the paper. The author also thank Prof. Kai-Tai Fang for his guidance and support. This work was partially supported by the UIC Grants (Nos. R201409 and R201712) and the Zhuhai Premier Discipline Grant.


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2017

Authors and Affiliations

  1. 1.Department of Mathematics, Faculty of ScienceZagazig UniversityZagazigEgypt
  2. 2.Division of Science and TechnologyBNU-HKBU United International CollegeZhuhaiChina

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