最優因析設計理論張潤楚 9787030776686 【台灣高等教育出版社】

Name: 最優因析設計理論 張潤楚 9787030776686 【台灣高等教育出版社】
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書名：最優因析設計理論
ISBN：9787030776686
出版社：科學
著編譯者：張潤楚
頁數：207
所在地：中國大陸 *此為代購商品
書號：1626614
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內容簡介

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最優設計準則、構造和分析的理論與方法。為適應現代試驗的需要，作者於2006年開始建立了一個新的最優因子分析設計理論，包括最優性準則、最優設計構造，以及他們在各種不同設計類中的推廣。本書首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。書中對由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（最大估計容量準則）得到的最優設計在只關心低階效應時是等價的。隨後的數章分別介紹了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。書中還給出了大量的最優設計表供實際應用。

「統計與數據科學叢書」序
Preface
1 Introduction
1 1 Factorial Designs and Factorial Effects
1 2 Fractional Factorial Designs
1 3 Optimality Criteria
1 3 1 Maximum Resolution Criterion
1 3 2 Minimum Aberration Criterion
1 3 3 Clear Effects Criterion
1 3 4 Maximum Estimation Capacity Criterion
1 4 Organization of the Book
2 General Minimum Lower-Order Confounding Criterion for 2n–m Designs
2 1 GMC Criterion
2 2 Relationship with MA Criterion
2 3 Relationship with CE Criterion
2 4 Relationship with MEC Criterion
Appendix A: GMC 2n–m Designs with m ？
Appendix B: GMC 2n–m Designs with 16， 32， and 64 Runs
3 General Minimum Lower-Order Confounding 2n–m Designs
3 1 Some Preparation
3 1 1 Several Useful Results
3 1 2 Structure of Resolution IV Design with N /4 + 1 ？ n ？ N /2
3 2 GMC 2n–m Designs with n ？ 5N /16 + 1
3 2 1 Main Results and Examples
3 2 2 Proof of Theorem 3 10
3 3 GMC 2n–m Designs with 9N /32 + 1 ？ n ？ 5N /16
3 3 1 Main Results and Example 46 3 3 2 Outline of the Proof of Theorem 3 16
3 4 GMC 2n–m Designs with N /4 + 1 ？ n ？ 9N
3 4 1 Some Properties of MaxC2 2n–m Designs with n = N /4 + 1
3 4 2 GMC 2n–m Designs with N /4 + 1 3 4 3 Outline of the Proof of Theorem 3 23
3 5 When Do the MA and GMC Designs Differ?
4 General Minimum Lower-Order Confounding Blocked Designs
4 1 Two Kinds of Blocking Problems
4 2 GMC Criteria for Blocked Designs
4 3 Construction of B-GMC Designs
4 3 1 B-GMC 2n–m : 2r Designs with 5N /16 + 1 ？ n ？ N /2
4 3 2 B-GMC 2n–m : 2r Designs with n > N /2
4 3 3 Weak B-GMC 2n–m : 2r Designs
4 4 Construction of B1-GMC Designs
4 4 1 B1-GMC 2n–m : 2r Designs with n ？ 5N /16 + 1
4 4 2 B1-GMC 2n–m : 2r Designs with 9N /32 + 1 ？ n ？ 5N /16
4 4 3 B1-GMC 2n–m : 2r Designs with N /4 + 1 ？ n ？ 9N /32
4 5 Construction of B2-GMC Designs
4 5 1 B2-GMC 2n–m : 2r Designs with n ？ 5N /16
4 5 2 B2-GMC 2n–m : 2r Designs with N /4 + 1 ？ n ？ 5N
5 Factor Aliased and Blocked Factor Aliased Effect-Number Patterns
5 1 Factor Aliased Effect-Number Pattern of GMC Designs
5 1 1 Factor Aliased Effect-Number Pattern
5 1 2 The F-AENP of GMC Designs
5 1 3 Application of the F-AENP
5 2 Blocked Factor Aliased Effect-Number Pattern of B1-GMC Designs
5 2 1 Blocked Factor Aliased Effect-Number Pattern
5 2 2 The B-F-AENP of B1-GMC Designs
5 2 3 Applications of the B-F-AENP 99 6 General Minimum Lower-Order Confounding Split-plot Designs
6 1 Introduction
6 2 GMC Criterion for Split-plot Designs
6 2 1 Comparison with MA-MSA-FFSP Criterion
6 2 2 Comparison with Clear Effects Criterion
6 3 WP-GMC Split-plot Designs
6 3 1 WP-GMC Criterion for Split-plot Designs
6 3 2 Construction of WP-GMC Split-plot Designs
7 Partial Aliased Effect-Number Pattern and Compromise Designs
7 1 Introduction
7 2 Partial Aliased Effect-Number Pattern
7 3 Some General Results of Compromise Designs
7 4 Class One Compromise Designs
7 4 1 Largest Class One Clear Compromise Designs and Their Construction
7 4 2 Supremum f ？(q， n) and Construction of Largest Class One CCDs
7 4 3 Supremum n？(q， f ) and Construction of Largest Class One CCDs
7 4 4 Largest Class One Strongly Clear Compromise Designs
7 4 5 Class One General Optimal Compromise Designs
7 5 Discussion
8 General Minimum Lower-Order Confounding Criteria for Robust Parameter Designs 147 8 1 Introduction
8 2 Selection of Optimal Regular Robust Parameter Designs
8 3 An Algorithm for Searching Optimal Arrays
9 General Minimum Lower-Order Confounding Criterion for sn–m Designs
9 1 Introduction to sn–m Designs
9 2 GMC Criterion and Relationship with Other Criteria
9 3 GMC sn–m Designs Using Complementary Desi
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