| Summary: | 碩士 === 國立臺灣大學 === 農藝學研究所 === 95 === During the initial stages of experimentation, two-level regular fractional factorial designs (FFDs) are commonly used to identify important factors which may significantly affect the response(s) of the experiment. The homogeneity of variance is a basic assumption in the ANOVA for location effects. The design issue of optimal 2n-p regular FFDs based on the homogenous variance assumption has been studied extensively. However, when the variance of the response variable changes as some specific factors change from one setting to another, these factors affecting the variation of the response are called dispersion factors in this study. Interestingly, to the best of our knowledge, the issue addressing the minimum aberration designs for location effects in the presence of dispersion factors has not been found in the literature.
In this study, we shall investigate the minimum aberration 2n-p regular FFDs under the assumption that there are some specific factors responsible for the dispersion of the response. The dispersion effects may violate the usual assumption of variance homogeneity in ANOVA. Therefore, the aberration criterion needs to be modified in order to discuss this issue. It is anticipated that the choice of minimum aberration designs may depend upon the prior information on the dispersion effects. Specific attention will first be given to the simplest situation that there is exactly one factor responsible for the dispersion effects. After a thorough investigation on this, we extend the results to the situation that two factors involve the dispersion effects.
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