臺灣博碩士論文加值系統

一個區集的實驗設，若有趨勢存在，則我們可以考慮每個區集內的趨勢是否相同 ，且為何種趨勢，如 : 倒數趨勢、線性趨勢，…，等等。為了去除趨勢所造成處理比較的影響，我們可以選擇共變異數分析，來探討處理比較的變異數問題。另外，在不改變處理-區集的發生矩陣 N ，適當地安排處理給區集內的實驗單元，則可以找到最佳的趨勢區集設計，使得趨勢對估計的影響最低。

當一個完全的區集設計，假設有線性(p=1)趨勢存在且考慮每個區集內的趨勢皆相同時，除了已知可以使其轉成對稱的去線性趨勢設計外，我們探討使其轉成非對稱的去線性趨勢設計，並且解決了，k是奇數且b=3時，可以找到區集實驗單元位置的組合效果為0的情況，再利用系統相異元素代表系統(systems of distinct representatives)來指派處理給區集內的實驗單元，而得到非對稱的去線性趨勢的完全區集設計。

第一章 緒論…1
1.1 背景介紹…1
1.2 區集設、去趨勢和去線性趨勢的區集設計…3
1.3 實例分析…8
1.4 最佳的趨勢區集設計…16
第二章 去趨勢區集設計的文獻回顧…19
2.1 去線性趨勢區集設計的文獻探討…19
2.2 可轉成去線性趨勢的特殊區集設計…22
2.3 去趨勢區集設計的最近發展…23
第三章 一些非對稱的去線性趨勢的完全區集設計…25
3.1 對稱與非對稱的去線性趨勢區集設計…25
3.2 k 為奇數時，存在非對稱的去線性趨勢區集設計的必要條件…29
3.3 k 為奇數且 b=3 時，非對稱的去線性趨勢的完全區集設計…31
第四章 結論與尚待解決的問題…38

參考文獻…39

附錄: 一些非對稱的去線性趨勢的完全區集設計…42

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