Some results on constructing three-level blocked designs with general minimum lower-order confounding
Blocked designs are widely used in experimental situations when the experimental units are not homogeneous. This article introduces the blocked general minimum lower-order confounding (B 1 -GMC) criterion for selecting optimal three-level blocked designs. Some properties of three-level B 1 -GMC desi...
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| Vydané v: | Communications in statistics. Theory and methods Ročník 54; číslo 22; s. 7105 - 7122 |
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| Jazyk: | English |
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Taylor & Francis
17.11.2025
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| Abstract | Blocked designs are widely used in experimental situations when the experimental units are not homogeneous. This article introduces the blocked general minimum lower-order confounding (B
1
-GMC) criterion for selecting optimal three-level blocked designs. Some properties of three-level B
1
-GMC designs are provided in terms of their complementary sets. We obtain a systematic theory on constructing three-level B
1
-GMC designs. Several efficient algorithms for finding three-level B
1
-GMC designs are provided and implemented by Python. For application, B
1
-GMC designs with 27-, 81- and 243-run, respectively, are tabulated. |
|---|---|
| AbstractList | Blocked designs are widely used in experimental situations when the experimental units are not homogeneous. This article introduces the blocked general minimum lower-order confounding (B
1
-GMC) criterion for selecting optimal three-level blocked designs. Some properties of three-level B
1
-GMC designs are provided in terms of their complementary sets. We obtain a systematic theory on constructing three-level B
1
-GMC designs. Several efficient algorithms for finding three-level B
1
-GMC designs are provided and implemented by Python. For application, B
1
-GMC designs with 27-, 81- and 243-run, respectively, are tabulated. Blocked designs are widely used in experimental situations when the experimental units are not homogeneous. This article introduces the blocked general minimum lower-order confounding (B1-GMC) criterion for selecting optimal three-level blocked designs. Some properties of three-level B1-GMC designs are provided in terms of their complementary sets. We obtain a systematic theory on constructing three-level B1-GMC designs. Several efficient algorithms for finding three-level B1-GMC designs are provided and implemented by Python. For application, B1-GMC designs with 27-, 81- and 243-run, respectively, are tabulated. |
| Author | Li, Zhi Tian, Rui Li, Zhiming Li, Zhengqi |
| Author_xml | – sequence: 1 givenname: Zhi surname: Li fullname: Li, Zhi organization: College of Mathematics and System Science, Xinjiang University – sequence: 2 givenname: Zhiming surname: Li fullname: Li, Zhiming organization: College of Mathematics and System Science, Xinjiang University – sequence: 3 givenname: Rui surname: Tian fullname: Tian, Rui organization: College of Mathematics and System Science, Xinjiang University – sequence: 4 givenname: Zhengqi surname: Li fullname: Li, Zhengqi organization: College of Mathematics and System Science, Xinjiang University |
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| Title | Some results on constructing three-level blocked designs with general minimum lower-order confounding |
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