近年來生命科學蓬勃發展，最令人興奮的莫過於人類基因序列的定序，這個跨時代的工程連帶的引起生物醫學上的快速發展，其中，cDNA 微陣列晶片由於可以大量分析每個基因受調控後，其表現量的變化，對於現今的分子生物學研究而言，是一種很有力的工具。cDNA微陣列實驗其過程很多環節都要用使統計方法，本論文主要針對實驗部份。本文以log Ratio來建模，並利用線性模型最佳性質φp-optimality來當作選擇設計的評斷標準，提供了二因子設計的最佳化理論上界，因此，對任一個設計我們都可以知道它是不是最佳設計(optimal design)或離最佳有多遠。另外，我們亦提供了一些建構高效設計的方法。

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