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In two-level fractional factorial designs, homogeneous variance is a commonly made assumption in analysis of variance. When the variance of the response variable changes when a factor changes from one level to another, we called the factor dispersion factor. Formerly, many researches have discussed about how to define the dispersion effects, but the problem of finding optimal designs when dispersion effects present is relatively unexplored. However, a good design not only save the experiment cost but also let the estimation more efficiency. In this research, we focus on finding optimal designs for the estimation of location main effects when there are one or two dispersion factors, in the class of regular unreplicated two-level fractional factorial designs of resolution Ⅲ and higher. We show that by an appropriate choice of the defining contrasts, A-optimal and D-optimal designs can be identified. Efficiencies of an arbitrary design are also investigated.

京都大学 / 0048 / 新制・課程博士 / 博士(人間健康科学) / 甲第19970号 / 人健博第38号 / 新制||人健||3(附属図書館) / 33066 / 京都大学大学院医学研究科人間健康科学系専攻 / (主査)教授 杉本 直三, 教授 精山 明敏, 教授 黒田 知宏 / 学位規則第4条第1項該当 / Doctor of Human Health Sciences / Kyoto University / DFAM