试验设计是近代科学发展的重要基础理论之一。它研究不同条件下各种试验的*优设计准则、构造和分析的理论与方法。为适应现代试验的需要，作者于2006年开始建立了一个新的*优因子分析设计理论，包括*优性准则、*优设计构造，以及他们在各种不同设计类中的推广。
《*优因析设计理论（英）》*先给出近代试验设计，主要是多因子试验设计的基本知识和数学基础，接着从二水平对称因子设计开始介绍了该理论的一些基本概念，包括AENP的提出、GMC准则的引进、GMC设计的构造等。《*优因析设计理论（英）》对由AENP建立的GMC准则得到的设计与由WLP建立的MA型准则得到的两类设计的优良性进行了详细比较。利用AENP理论，还证明了过去已有的两个准则MA和MEC（*大估计容量准则）得到的*优设计在只关心低阶效应时是等价的。随后的数章分别介绍了GMC理论在各类设计中的推广和应用，包括分区组因析设计、裂区设计、混合水平因析设计、非正规因析设计、多水平因析设计、折衷设计、稳健参数设计，建立了各种情形的GMC准则。《*优因析设计理论（英）》还给出了大量的*优设计表供实际应用。
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Contents
“统计与数据科学丛书”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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