部分重複之複因子設計用於篩選活潑分散效應與位置效應

Abstract

在一個生產或試驗的過程常常會存在許多的因子會影響生產或試驗的反應變數，當影響的因子的數量很大時往往會造成研究成本上升，因此如何找尋出有經濟效率的試驗設計一直是我們關心的課題。兩變級複因子設計為普遍被使用的設計，依照過去的研究，一個良好的試驗設計通常需要同時討論位置效應和分散效應，在過去的研究著重於位置效應，近年來對於分散效應的研究有深入探討，過去有不少的研究對於不重複與重複的試驗如何檢定分散效應皆提出不一樣的方法，Tasi,Liao & Chai(2015)提出對設計不一樣的想法，將不重複與重複的試驗取得一個平衡，簡而言之，對於部分處理組合進行重複試驗，該篇文章提出有效地重複二分之一處理組合的兩變級複因子設計，也提供了如何用Student’s t檢定位置效應以及應用廣義檢測變數（Generalized Test Variable)檢定分散效應，本文應用兩個方法做為檢測位置效應和分散效應的檢定方法，進一步延伸，將討論重複四分之一處理組合的設計，並提出如何重複四分之一處理組合兩變級複因子設計的方法且製作成表格提供參考。文中最後模擬在有分散效應的資料，並使用本文提供的設計是否能檢定出活潑效應，統計模擬的結果顯示我們提供的設計能良好判別分散效應。文中對於實例也有進行檢測，顯示使用該設計可以發現可能的活潑效應。

There might be several sources of variation that may impact the response during an experimental process. The two-level factorial design is often implemented in such a process. Those factors (effects) that affect the mean of the response are called as the active location factors (effects), also the factors (effects) that affect the variance of the response are called as the active dispersion factors (effects). Recently, Tasi & Liao & Chai (2015) proposed a class of partially replicated two-level factorial designs with repeated half (1/2) fractions. They also proposed a two-step procedure to identify both active location and dispersion effects. They first applied the concept of a generalized test variable (GTV) to develop a hypothesis test for identifying the active dispersion main effects. Then, use Student's t test to detect the active location effects. In this thesis, we adopt their testing procedure, but focus on the class of designs with repeated quarter (1/4) fractions. We present a series of the desired partially replicated designs with practical run sizes. In addition, some real data sets and simulation studies are given to evaluate the performance of the use of the proposed designs.