在因子設計的研究中，同構設計的完整分類，是一個重要卻又不容易的問題。本文考慮二水準因子實驗，旨在建立不同構二水準正規設計的完整分類表。然而此問題與因子效應的定義方式有密不可分的關係。大多數的時候，因子效應是以一組兩兩直交的對比定義，稱之為直交參數化。但在某些實驗情境下，基線參數化是一種更為適當的因子效應定義方式。在直交參數化下，正規設計的完整分類可從現有的文獻中查詢，但在基線參數化下的完整分類則付之闕如。本文中，我們指出了前者的完整分類有助於後者完整分類，並以此為基礎發展了一種演算法來找出基線參數化底下的所有不同構正規設計。其中，正規設計的結構和設計矩陣的重量分佈扮演了相當關鍵的角色。我們計算出試驗次數N=8和N=16的分類結果，並整理成表格供讀者使用。

In the study of factorial designs, building a complete catalog of non-isomorphic designs is an important but challenging task. In fact, this problem is closely related to the definition of factorial effects, since it affects how we define two designs are isomorphic. In this paper, we consider the two-level factorial designs, where the factorial effects are a set of mutually orthogonal contrasts, usually referred to as the orthogonal parameterization (OP). In some experimental situations, however, the baseline parameterization (BP) is a more appropriate alternative to the OP. The objective of this study is to build a complete catalog for regular designs, which has been done under the OP in an existing work, but remains unsolved under the BP. We point out that the catalog under the OP is useful in building a catalog under the BP. Based on this, an algorithm is developed to find all non-isomorphic regular designs under the BP. The structure of the regular designs and the weight distribution play a key role. Results for designs of small run sizes are summarized in tables.

目錄
第一章 緒論-----------------------------------------1
1.1 研究背景----------------------------------------1
1.2 研究目的與方法----------------------------------2
1.3 導讀--------------------------------------------3
第二章 正規設計和預備知識---------------------------4
2.1 正規設計----------------------------------------4
2.2 直交和基線參數化--------------------------------7
2.3 同構設計和相關性質------------------------------8
第三章 演算法及結果--------------------------------10
3.1 目標與預處理-----------------------------------10
3.2 BP同構分類演算法-------------------------------11
3.3 針對重量分佈相同的設計矩陣之BP同構檢驗法-------13
3.4 演算結果---------------------------------------14
第四章 結論----------------------------------------17
參考文獻-------------------------------------------18
附錄-----------------------------------------------19

1.Chen, J., Sun, D., and Wu, C. (1993). A catalogue of two-level and three-level fractional factorial designs with small runs. International Statistical Review/Revue Internationale de Statistique, pages 131–145.
2.Mukerjee, R. and Tang, B. (2012). Optimal fractions of two-level factorials under a baseline parameterization. Biometrika, 99(1):71–84.