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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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2024-12-01
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| Series: | Mathematics |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2227-7390/13/1/75 |
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| Summary: | 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. |
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| ISSN: | 2227-7390 |