An Analysis of Partially Replicated Two-Level Main-Effect Plans

在單一重複設計下增加部份重複數，主要原因為對誤差變異有實質的估計，通常對於找出明顯影響試驗結果的因子有較佳的表現，然而大多數在正交單一重複設計下增加部分重複數後，將導致設計不再具有正交性，根據Tsai and Liao(2010)提出的延伸最小偏差(extended minimum aberration) (EMA)準則，可用以評估當不可忽略的二階交感效應或更高階的交感效應存在下，非正交的部份重複2-變級主效應設計的穩健性，本文則針對部份重複2-變級主效應設計，探討具EMA性質之設計與其他設計在篩選重要因子能力上的差異。 此外，在違反效應貧乏準則(effect sparsity principle)下，我們已知部份重複設計相較於單一重複設計在選出真實的顯著因子上具有較好的效果，然而應增加多少重複數可以以較少的實驗次數達到實驗目的是我們感興趣的，本研究將說明如何決定適當重複數，並以檢定力曲線圖呈現，提供試驗者參考使用。Partially replicated designs usually have better performance on screening experiments than unreplicated designs, due mainly to that they provide error variance estimates based on pure replicates. However, when additional repeated runs augmented to an orthogonal design, the resulting partially replicated design usually turns to be non-orthogonal. According to the extended minimum aberration (EMA) criterion proposed by Tsai and Liao (2010), we assess the robustness of non-orthogonal partially replicated two-level main-effect designs against non-negligible two-factor or higher order interactions. This study first investigates type I error rate control and power of EMA partially replicated two-level main-effect plans in significance test for active factors. Then, expected length and coverage probability for the confidence interval estimation for main effects, and determination for the number of repeated runs are also discussed