試驗設計是近代科學發展的重要基礎理論之一。它研究不同條件下各種試驗的*優設計準則、構造和分析的理論與方法。為適應現代試驗的需要，作者于2006年開始建立了一個新的*優因子分析設計理論，包括*優性準則、*優設計構造，以及他們在各種不同設計類中的推廣。
《*優因析設計理論（英）》*先給出近代試驗設計，主要是多因子試驗設計的基本知識和數學基礎，接著從二水平對稱因子設計開始介紹了該理論的一些基本概念，包括AENP的提出、GMC準則的引進、GMC設計的構造等。《*優因析設計理論（英）》對由AENP建立的GMC準則得到的設計與由WLP建立的MA型準則得到的兩類設計的優良性進行了詳細比較。利用AENP理論，還證明了過去已有的兩個準則MA和MEC（*大估計容量準則）得到的*優設計在只關心低階效應時是等價的。隨后的數章分別介紹了GMC理論在各類設計中的推廣和應用，包括分區組因析設計、裂區設計、混合水平因析設計、非正規因析設計、多水平因析設計、折衷設計、穩健參數設計，建立了各種情形的GMC準則。《*優因析設計理論（英）》還給出了大量的*優設計表供實際應用。
Contents
“統計與數據科學叢書”序 i
Preface iii
1 Introduction 1
1.1 Factorial Designs and Factorial Effects 1
1.2 Fractional Factorial Designs 4
1.3 Optimality Criteria 9
1.3.1 Maximum Resolution Criterion 9
1.3.2 Minimum Aberration Criterion 10
1.3.3 Clear Effects Criterion 11
1.3.4 Maximum Estimation Capacity Criterion 12
1.4 Organization of the Book 13
2 General Minimum Lower-Order Confounding Criterion for 2n–m Designs 15
2.1 GMC Criterion 15
2.2 Relationship with MA Criterion 20
2.3 Relationship with CE Criterion 23
2.4 Relationship with MEC Criterion 25
Appendix A: GMC 2n–m Designs with m ？ 4 26
Appendix B: GMC 2n–m Designs with 16， 32， and 64 Runs 28
3 General Minimum Lower-Order Confounding 2n–m Designs 31
3.1 Some Preparation 31
3.1.1 Several Useful Results 31
3.1.2 Structure of Resolution IV Design with N /4 + 1 ？ n ？ N /2 34
3.2 GMC 2n–m Designs with n ？ 5N /16 + 1 39
3.2.1 Main Results and Examples 39
3.2.2 Proof of Theorem 3.10 40
3.3 GMC 2n–m Designs with 9N /32 + 1 ？ n ？ 5N /16 46
3.3.1 Main Results and Example 46 3.3.2 Outline of the Proof of Theorem 3.16 46
3.4 GMC 2n–m Designs with N /4 + 1 ？ n ？ 9N /32 47
3.4.1 Some Properties of MaxC2 2n–m Designs with n = N /4 + 1 47
3.4.2 GMC 2n–m Designs with N /4 + 1 < n ？ 9N /32 49
3.4.3 Outline of the Proof of Theorem 3.23 50
3.5 When Do the MA and GMC Designs Differ? 51
4 General Minimum Lower-Order Confounding Blocked Designs 53
4.1 Two Kinds of Blocking Problems 53
4.2 GMC Criteria for Blocked Designs 54
4.3 Construction of B-GMC Designs 57
4.3.1 B-GMC 2n–m : 2r Designs with 5N /16 + 1 ？ n ？ N /2 58
4.3.2 B-GMC 2n–m : 2r Designs with n > N /2 63
4.3.3 Weak B-GMC 2n–m : 2r Designs 67
4.4 Construction of B1-GMC Designs 69
4.4.1 B1-GMC 2n–m : 2r Designs with n ？ 5N /16 + 1 70
4.4.2 B1-GMC 2n–m : 2r Designs with 9N /32 + 1 ？ n ？ 5N /16 72
4.4.3 B1-GMC 2n–m : 2r Designs with N /4 + 1 ？ n ？ 9N /32 73
4.5 Construction of B2-GMC Designs 75
4.5.1 B2-GMC 2n–m : 2r Designs with n ？ 5N /16 + 1 76
4.5.2 B2-GMC 2n–m : 2r Designs with N /4 + 1 ？ n ？ 5N /16 78
5 Factor Aliased and Blocked Factor Aliased Effect-Number Patterns 80
5.1 Factor Aliased Effect-Number Pattern of GMC Designs 80
5.1.1 Factor Aliased Effect-Number Pattern 80
5.1.2 The F-AENP of GMC Designs 83
5.1.3 Application of the F-AENP 87
5.2 Blocked Factor Aliased Effect-Number Pattern of B1-GMC Designs 89
5.2.1 Blocked Factor Aliased Effect-Number Pattern 89
5.2.2 The B-F-AENP of B1-GMC Designs 92
5.2.3 Applications of the B-F-AENP 99 6 General Minimum Lower-Order Confounding Split-plot Designs 102
6.1 Introduction 102
6.2 GMC Criterion for Split-plot Designs 103
6.2.1 Comparison with MA-MSA-FFSP Criterion 105
6.2.2 Comparison with Clear Effects Criterion 110
6.3 WP-GMC Split-plot Designs 111
6.3.1 WP-GMC Criterion for Split-plot Designs 111
6.3.2 Construction of WP-GMC Split-plot Designs 114
7 Partial Aliased Effect-Number Pattern and Compromise Designs 119
7.1 Introduction 119
7.2 Partial Aliased Effect-Number Pattern 121
7.3 Some General Results of Compromise Designs 124
7.4 Class One Compromise Designs 126
7.4.1 Largest Class One Clear Compromise Designs and Their Construction 126
7.4.2 Supremum f ？(q， n) and Construction of Largest Class One CCDs 127
7.4.3 Supremum n？(q， f ) and Construction of Largest Class One CCDs 130
7.4.4 Largest Class One Strongly Clear Compromise Designs 133
7.4.5 Class One General Optimal Compromise Designs 137
7.5 Discussion 141
8 General Minimum Lower-Order Confounding Criteria for Robust Parameter Designs 147 8.1 Introduction 147
8.2 Selection of Optimal Regular Robust Parameter Designs 149
8.3 An Algorithm for Searching Optimal Arrays 155
9 General Minimum Lower-Order Confounding Criterion for sn–m Designs 162
9.1 Introduction to sn–m Designs 162
9.2 GMC Criterion and Relationship with Other Criteria 166
9.3 GMC sn–m Designs Using Complementary Designs 174
9.4 B-GMC Criterion for Blocked sn–m Designs 178
10 General Minimum Lower-Order Confounding Criterion for Orthogonal Arrays 182
10.1 Introduction 182
10.2 ANOVA Models and Confounding Between Effects 183
10.3 Generalized AENP and GMC Criterion 187
10.4 Relationship with Other Criteria 189
10.5 Some G-GMC Designs 193
References 196
Index 206
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