2006-08-012024-05-16https://scholars.lib.ntu.edu.tw/handle/123456789/669315摘要：工業產品研發初期或其它科學實驗，當實驗變因很多時，2-變級複因子設計（two-level factorial designs），被廣泛用於估計實驗中重要的位置效應（location effects）。在同質變異數(homogeneity of variance)前題下，最適2n-k部分複因子設計(fractional factorial designs)的研究已相當完善(參見Wu and Hamada, 2001) 。但是當實驗的反應變數（response）的變異(variation)程度，會因某些因子的變級（levels）的改變而改變時，即分散效應(dispersion effects)存在條件下，如何決定最適設計(optimal designs)是一個在文獻上少見的研究議題，值得深入探討。 　　本研究將從最簡單的模式:僅有一個實驗因子會影響分散效應，開始探討。基於最小偏差準則(minimum aberration criterion)，希望能建構最適設計。 可預期的，最適設計的決定會受分散效應的影響，因此defining words (defining contrasts) <br> Abstract: During the initial stages of experimentation, two-level fractional factorial designs (FFDs) are commonly used to screen out the important factorial effects. The issue regarding the optimal regular FFDs based on the aberration criterion has been studied extensively. However, almost all the optimality criteria (the minimum aberration or maximum estimation capacity) are basically derived from the ANOVA models assuming the homogeneity of variance. In some practical applications, the variation of response may change from a run to next, meaning that there are some factors which may be responsible for the dispersion of the response. Hence, the assumption of variance homogeneity may be violated and the BLUEs of factorial effects need to be obtained from the generalized least square estimation. Clearly, the estimation depends upon the existing dispersion effects. In this research project, we shall investigate the optimality of regular FFDs under the assumption that there are some specific factors responsible for the dispersion effects. The choice of optimal designs may be related to the prior information on the dispersion effects. We hope to clarify the confounding relationships between location effects and the existing dispersion effects and develop a new criterion to determine the optimal designs. Specific attention will first be given to the simplest situation that there is exactly single one factor responsible for the dispersion. After a thorough investigation on this, we hope to extend the results to the situations involving multiple dispersion factors.最小偏差準則部分複因子設計最適設計篩選實驗分散因子線型模式minimum aberration criterionfractional factorial designoptimal design