由於以基因微陣列(microarray)實驗去檢測基因的表現量在生物醫學上已有廣泛的應用，因此，我們有必要針對微陣列實驗的反應值(response)來建模分析，而於建模的同時，我們知道實驗中有許多變異的來源是必需考慮的，因此，在實驗前的設計中，很重要的一件事就是必需先確定所建構的設計必須能確保我們所關心的參數效應不能與其他實驗因素的效應混淆(confounded)在一起而造成這些參數在估計時的偏誤(bias)；而另一件重要的事就是怎樣安排實驗種類(variety)的樣本在每一片晶片(array)上而使得在估計我們所關心的參數或參數組合時擁有最佳的精確度(precision)。
在kerr et al.(2000)的研究中以ANOVA model來建模去探討維陣列設計與不完全區集設計(incomplete block design)間的關係，並利用一些廣義的不完全區集的性質推導A-optimality當作篩選設計的法則，而於本文中則是由log Ratio model的角度來建模去探討維陣列設計與線性模型間關係，並利用一些廣義的線性模型最佳化理論的性質推導D-optimality來當作選擇設計的評斷法則，且提供了最佳化理論的上界，也就是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，我們亦提供了用電腦所搜尋出來的一些常用的最佳化設計，並由一些好的實驗設計原則及D-optimality建議了建構有效設計(efficient design)的方法，而事實上我們與kerr et al.(2000)在尋找最佳設計時，所用的觀點及切入的角度雖不盡相同，但其結果卻具一致性。

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