2016-08-012024-05-17https://scholars.lib.ntu.edu.tw/handle/123456789/683350摘要：規劃區集為執行實驗時的一項重要技巧。當實驗單位俱有較大的變異時，研究者可將實驗單位劃分 成不同的區集，使得相同區集內的單位彼此差異小，不同區集間的單位彼此差異大。倘若區集效應 能夠有效地控制，研究者將可對實驗誤差做更精確的估計。另一個重要的實驗準則為執行重複。透 過執行重複，研究者可以得到實驗誤差的無偏估計量，並用以正確地分析資料。在研究初期，單一 重複二水準部分因子設計常被用來篩選對實驗結果有重要影響的因子，此類實驗因未執行重複，故 其資料分析結果通常較不可靠。倘若研究者將單一重複部分因子設計的處理組合進一步安排於不同 區集之中，實驗誤差的估計將受到區集效應影響，後續資料分析將變得更俱挑戰性。 本計畫擬探討部分重複二水準因子設計之區集規劃與資料分析。計畫第一年期間，我將分別討論在 固定型與隨機型區集效應假設之下，部分重複二水準因子實驗的最適區集規劃與建構方法，並製造 一系列實用的設計彙整成表格提供研究者執行實驗時參考使用。計畫第二年期間，我將專注於區集 結構存在時，部分重複二水準因子實驗之資料分析。當區集效應假設為隨機型效應時，擬採用廣義 檢定變數發展統計分析方法以檢定隨機型區集效應之顯著性，並進一步篩選重要的因子效應，除了 透過數值模擬評估其表現之外，本計畫所提出的分析方法亦將與現存於統計套裝軟體的標準分析流 程做比較，並給予研究者實際分析資料時一些建議。<br> Abstract: Blocking is a standard technique for experimentations. When the experimental units are drastically heterogeneous, the units are divided into several groups called blocks in such a way that the intra-block variation is smaller than the inter-block variation. If blocking is done well, the experimental error can therefore be estimated in a more precise manner than an unblocked design. Another fundamental principle for designing an efficient experiment is replication. Pure replicates can capture the unit-to-unit variation, and enable an investigator to unbiasedly estimate the error variance. At the preliminary stage of a multifactorial investigation, an unreplicated two-level factorial experiment is frequently conducted for screening active factorial effects. Based on my limited experience, however, it tends to produce ambiguous findings, especially when the effect sparsity assumption is not fully satisfied, primarily due to the lack of a replication-based estimate of the error variance. This phenomenon occurs in a blocked factorial experiment with single replicate as well. To my knowledge, construction methods and analysis strategy for blocked factorial designs with partial replication are still missing. This inspires me to develop systematic methods for addressing these practical issues. In this two-year project, design and analysis of blocked two-level factorial experiments with partial replication will be thoroughly investigated. In the first year, I plan to explore the design optimality and construction of blocked two-level designs with partial replication under the assumptions of fixed and random block effects. In addition, an algorithm will be developed for systematically generating the required designs, and a design catalogue will be produced for real-life applications. In the second year, analysis issues will be my main concern. Using the concepts of generalized test variables and generalized p-values, I am going to develop two replication-based testing procedures for identifying significant block variance component and active factorial effects. A series of Monte-Carlo simulations will be implemented for systematically evaluating the proposed methods. Furthermore, a comprehensive comparison of proposed analysis strategy and those standard methods, including maximum likelihood (ML), restricted maximum likelihood (REML) and generalized least squares estimation (GLSE), will be conducted through a series of numerical studies.廣義檢定變數混合效應模型最適設計平行板設計篩選實驗變異數成份。Generalized test variableMixed-effect modelOptimal designParallel-flats designScreening experimentVariance component.