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Journals / Hacettepe Journal of Mathematics and Statistics / 2026 / Volume: 50 Issue: 4

Equivalence theorem of $D$-optimal equal allocation design for multiresponse mixture experiments

Xiaoyuan Zhu(Guangzhou University)0000-0003-0996-1775
Honghua Hao(Guangzhou University)0000-0002-2710-7209
Weixia Li(Guangzhou University)0000-0003-0453-3253
Chongqi Zhang(Guangzhou University)0000-0002-6177-200X
Pages
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Publication Date
2021-08-06
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

D-optimal designs for multiresponse are illustrated by two examples.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:The equivalence theorem is the most important theorem of experimental design.
📊
Key Findings & Data:For single response, the D-optimal equivalence theorem of the continuous design and equal allocation design already exist.
💡
Conclusion & Impact:D-optimal designs for multiresponse are illustrated by two examples.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:multiresponse · mixture experiment · D-optimal

Abstract

The equivalence theorem is the most important theorem of experimental design. For single response, the D-optimal equivalence theorem of the continuous design and equal allocation design already exist. However, the equivalence theorem of D-optimal equal allocation design for multiresponse mixture experiments has not been investigated. In this paper, we study this problem and find that the maximize of the variance function of the equivalence theorem equal to the number of response. D-optimal designs for multiresponse are illustrated by two examples.

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Cite This Article

Zhu, X., Hao, H., Li, W., Zhang, C. (2021). Equivalence theorem of $D$-optimal equal allocation design for multiresponse mixture experiments. Hacettepe Journal of Mathematics and Statistics, Volume: 50 Issue: 4. https://doi.org/10.15672/hujms.777430

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