On the Construction of Multi-Stratum Factorial Designs

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李協諭(XIE-YU LI) 查詢紙本館藏

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統計研究所

論文名稱

(On the Construction of Multi-Stratum Factorial Designs)

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摘要(中)

對於無結構實驗單位的因子設計，Fries 與Hunter（1980）提出的最
小像差準則被廣泛運用在決定正規部分因子設計上。之後，許多相關研
究都集中在擁有多個誤差項的多層因子設計上，這些誤差項來自於複雜
的實驗單元結構。Chang 與Cheng (2018) 提出一種貝氏決策準則，它是
一個廣義版本的最小像差準則，並且可以運用在最佳化多層因子設計的
問題上。對於處理最佳化問題，粒子群優化演算法(PSO) 已是非常流行
並被廣泛應用於各種議題。在本篇論文中我們將提出了一個新版本的粒
子群優化演算法，來解決正規與非正規多層因子設計的最佳化問題。在
正規因子設計下，我們將定義字詞視為粒子群優化演算法中的粒子並將
粒子群優化演算法與設計鍵矩陣結合在一起。而在非正規的多層因子設
計下，則以處理組合做為演算法中的粒子。

摘要(英)

For unstructured experimental units, minimum aberration in Fries and Hunter (1980) is a popular criterion for choosing regular fractional factorial designs. Following which, many related studies focused on multistratum
factorial designs with multiple error terms that arise from the complicated structures of experimental units. Chang and Cheng (2018) proposed a Bayesian criterion, which can be considered as a generalized version of the minimum aberration for selecting optimal multi-stratum factorial designs. Particle Swarm Optimization (PSO) algorithm is a popular optimization method that has been widely used in various applications. In this thesis, a new version of PSO is proposed to select regular and nonregular multi-stratum designs. We treat defining words as particles in PSO and link PSO with Design key matrix for selecting regular ones. For nonregular multi-stratum designs, we treat treatment combinations as particles in PSO.

關鍵字(中)

★ 最小像差
★ 最佳化設計
★ 粒子群優化演算法
★ 設計鍵矩陣

關鍵字(英)

★ Minimum Aberration
★ Optimal Design
★ PSO
★ Design Key matrix

論文目次

1 Introduction p.1
2 Literature Review p.3
2.1 Multi-stratum p.3
2.2 Tool p.11
3 Algorithm p.17
3.1 Regular factorial design p.17
3.2 Nonregular case p.23
4 Application p.25
4.1 Regular case p.25
4.2 Nonregular case p.32
5 Optimal designs with random effects p.35
6 Conclusion p.38
Bibliography p.39

參考文獻

[1] Chang, M.-C. and Cheng, C.-S. (2018). A bayesian approach to the selection of
twolevel multi-stratum factorial designs. The Annals of Statistics, 46, No. 4, 1779-
1806.
[2] Cheng, C.-S. and Tsai, P.-W. (2011). Multistratum fractional factorial designs. Statistica
Sinica 21, 1001-1021.
[3] Cheng, C.-S. and Tsai, P.-W. (2013). Templates for design key construction. Statistica
Sinica 23, 85-93.
[4] Phoa, F. K. H. (2016) A swarm intelligence based (SIB) method for optimization in
designs of experiments. Nat Comput DOI 10.1007/s11047-016-9555-4.
[5] Fries, A. and Hunter, W. G. (1980). Minimum aberration 2k−p designs. Technometrics
22, 601-608.
[6] Cheng, C.-S. and Tsai, P.-W. (2009). Optimal two-level regular fractional factorial
block and split-plot designs. Biometrika 96, 83-93.
[7] Cheng, C.-S., Steinberg, D. M. and Sun, D. X. (1999). Minimum aberration and
model robustness for two-level fractional factorial designs. J. R. Stat. Soc. Ser. B.
Stat. Methodol. 61, 85-93.
[8] Chen, H. and Cheng, C.-S. (1999). Theory of optimal blocking of 2n−m designs. The
Annals of Statistics 27, 1948-73.
[9] Cheng, S. W. and Wu, C. F. J. (2002). Choice of optimal blocking schemes in twolevel
and three-level designs. Technometrics 44, 269-77.
[10] Cheng, C. S. (2014). Theory of Factorial Design: Single- and Multi-Stratum Experiments.
CRC Press, Boca Raton, FL.
[11] Kennedy, J. and Eberhart, R. (1995). Particle swarm optimization. In: Proceedings
of IEEE international conference on neural networks 4:1942-1948.
[12] Phoa, F.K.H. and Xu, H. (2009) Quarter-fraction factorial designs constructed via
Quaternary codes. The Annals of Statistics, 37, 2561-2581.

指導教授

張明中(Ming-Chung Chang)

審核日期

2019-7-12

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