Strongly Coupled Designs for Computer Experiments with Both Qualitative and Quantitative Factors
Computer experiments often involve both qualitative and quantitative factors, posing challenges for efficient experimental designs. Strongly coupled designs (SCDs) are proposed in this paper to balance flexibility in run size and stratification properties between qualitative and quantitative factor...
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2024-12-01
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| author | Meng-Meng Liu Min-Qian Liu Jin-Yu Yang |
| author_facet | Meng-Meng Liu Min-Qian Liu Jin-Yu Yang |
| author_sort | Meng-Meng Liu |
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| description | Computer experiments often involve both qualitative and quantitative factors, posing challenges for efficient experimental designs. Strongly coupled designs (SCDs) are proposed in this paper to balance flexibility in run size and stratification properties between qualitative and quantitative factor columns. The existence and construction of SCDs are investigated. When <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>s</mi><mo>⩾</mo><mn>2</mn></mrow></semantics></math></inline-formula> is a prime or a prime power, the constructed SCDs of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>λ</mi><msup><mi>s</mi><mn>3</mn></msup></mrow></semantics></math></inline-formula> runs can accommodate <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>2</mn><mi>s</mi><mo>−</mo><mn>1</mn></mrow></semantics></math></inline-formula> qualitative factors and a substantial number of quantitative factors. Furthermore, a series of SCDs with <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi>s</mi><mi>u</mi></msup></semantics></math></inline-formula> rows and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mrow><mo>(</mo><mi>u</mi><mo>−</mo><mn>3</mn><mo>)</mo></mrow><msup><mi>s</mi><mn>3</mn></msup></mrow></semantics></math></inline-formula> columns of quantitative factors are constructed, where <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>u</mi><mo>⩾</mo><mn>4</mn></mrow></semantics></math></inline-formula>, with certain columns of quantitative factors achieving stratification in two or higher dimensions. The proposed SCDs achieve stratification between any two qualitative factors and all quantitative factors, which is superior to MCDs. With the number of levels of the qualitative factors given as <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi>s</mi><mn>2</mn></msup></semantics></math></inline-formula>, DCDs have <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>λ</mi><msup><mi>s</mi><mn>4</mn></msup></mrow></semantics></math></inline-formula> rows, while SCDs have only <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>λ</mi><msup><mi>s</mi><mn>3</mn></msup></mrow></semantics></math></inline-formula> rows, offering more flexibility. Furthermore, in the designs constructed in this paper with fewer than 100 rows, in 11 out of 17 cases, SCDs have a larger number and higher levels of qualitative factors than DCDs. |
| format | Article |
| id | doaj-art-6e1e372b2bd342ce868b751647d0c5db |
| institution | Kabale University |
| issn | 2227-7390 |
| language | English |
| publishDate | 2024-12-01 |
| publisher | MDPI AG |
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| series | Mathematics |
| spelling | doaj-art-6e1e372b2bd342ce868b751647d0c5db2025-01-10T13:18:11ZengMDPI AGMathematics2227-73902024-12-011317510.3390/math13010075Strongly Coupled Designs for Computer Experiments with Both Qualitative and Quantitative FactorsMeng-Meng Liu0Min-Qian Liu1Jin-Yu Yang2School of Science, Minzu University of China, Beijing 100081, ChinaNITFID, LPMC & KLMDASR, School of Statistics and Data Science, Nankai University, Tianjin 300071, ChinaNITFID, LPMC & KLMDASR, School of Statistics and Data Science, Nankai University, Tianjin 300071, ChinaComputer experiments often involve both qualitative and quantitative factors, posing challenges for efficient experimental designs. Strongly coupled designs (SCDs) are proposed in this paper to balance flexibility in run size and stratification properties between qualitative and quantitative factor columns. The existence and construction of SCDs are investigated. When <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>s</mi><mo>⩾</mo><mn>2</mn></mrow></semantics></math></inline-formula> is a prime or a prime power, the constructed SCDs of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>λ</mi><msup><mi>s</mi><mn>3</mn></msup></mrow></semantics></math></inline-formula> runs can accommodate <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>2</mn><mi>s</mi><mo>−</mo><mn>1</mn></mrow></semantics></math></inline-formula> qualitative factors and a substantial number of quantitative factors. Furthermore, a series of SCDs with <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi>s</mi><mi>u</mi></msup></semantics></math></inline-formula> rows and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mrow><mo>(</mo><mi>u</mi><mo>−</mo><mn>3</mn><mo>)</mo></mrow><msup><mi>s</mi><mn>3</mn></msup></mrow></semantics></math></inline-formula> columns of quantitative factors are constructed, where <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>u</mi><mo>⩾</mo><mn>4</mn></mrow></semantics></math></inline-formula>, with certain columns of quantitative factors achieving stratification in two or higher dimensions. The proposed SCDs achieve stratification between any two qualitative factors and all quantitative factors, which is superior to MCDs. With the number of levels of the qualitative factors given as <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi>s</mi><mn>2</mn></msup></semantics></math></inline-formula>, DCDs have <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>λ</mi><msup><mi>s</mi><mn>4</mn></msup></mrow></semantics></math></inline-formula> rows, while SCDs have only <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>λ</mi><msup><mi>s</mi><mn>3</mn></msup></mrow></semantics></math></inline-formula> rows, offering more flexibility. Furthermore, in the designs constructed in this paper with fewer than 100 rows, in 11 out of 17 cases, SCDs have a larger number and higher levels of qualitative factors than DCDs.https://www.mdpi.com/2227-7390/13/1/75computer experimentcompletely resolvable orthogonal arrayqualitative and quantitative factorregular designspace-filling design |
| spellingShingle | Meng-Meng Liu Min-Qian Liu Jin-Yu Yang Strongly Coupled Designs for Computer Experiments with Both Qualitative and Quantitative Factors Mathematics computer experiment completely resolvable orthogonal array qualitative and quantitative factor regular design space-filling design |
| title | Strongly Coupled Designs for Computer Experiments with Both Qualitative and Quantitative Factors |
| title_full | Strongly Coupled Designs for Computer Experiments with Both Qualitative and Quantitative Factors |
| title_fullStr | Strongly Coupled Designs for Computer Experiments with Both Qualitative and Quantitative Factors |
| title_full_unstemmed | Strongly Coupled Designs for Computer Experiments with Both Qualitative and Quantitative Factors |
| title_short | Strongly Coupled Designs for Computer Experiments with Both Qualitative and Quantitative Factors |
| title_sort | strongly coupled designs for computer experiments with both qualitative and quantitative factors |
| topic | computer experiment completely resolvable orthogonal array qualitative and quantitative factor regular design space-filling design |
| url | https://www.mdpi.com/2227-7390/13/1/75 |
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