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| Title: | 分散效應存在下位置主效應之最適部份因子設計
Optimal Two-Level Fractional Factorial Designs for Location Main Effects with Dispersion Effects |
| Authors: | 張富凱
Chang, Fu-Kai |
| Contributors: | 丁兆平
Ting, Chao-Ping
張富凱
Chang, Fu-Kai |
| Keywords: | 同名關係
分散效應
位置效應
defining relation
dispersion effect
location effect
defining contrast |
| Date: | 2005 |
| Issue Date: | 2009-09-17 18:46:53 (UTC+8) |
| Abstract: | 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. |
| Reference: | Bergman, B. and Hyn n, A., (1997). Dispersion effects from unreplicated designs in the series. Technometrics 39, 191-198.
Box, G. E. P. and Meyer, R. D., (1986). Dispersion effects from fractional designs. Technometrics 28, 19-27.
Jiahua Chen, D. X. Sun and C. F. J. Wu, (1993). A catalogue of two-level and three-level fractional factorial designs with small runs. International Statistical Review 61, 131-145.
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Liao, C. T. and Iyer, H. K., (2000). Optimal fractional factorial designs for dispersion effects under a location-dispersion model. Commun.Statistics. – Theory Methods 29, 823-835.
Liao, C. T., (2005). Two-level factorial designs for searching dispersion factors and estimating location main effects. Journal of Statistical Planning and Inference ( in press).
Lin, M. Y., 2005. D-optimal regular fractional factorial designs for location effects with single dispersion factor. Unpublished master’s thesis, Department of Agronomy, National Taiwan University. Taipei.
McGrath, R. N. and Lin, D. K. J., (2001a). Testing multiple dispersion effects in unreplicated fractional factorial designs. Technometrics 43, 406-414.
McGrath, R. N. and Lin, D. K. J., (2001b). Confounding of location and dispersion effects in unreplicated fractional factorials designs. Journal of Quality Technology 33, 129-139.
Montgomery, D. C., (1990). Using fractional factorial designs for robust process development. Quality Eng. 3, 193-205.
Pan, G., (1999). The impact of unidentified location effects on dispersion effects identification from unreplicated factorial designs. Technometrics 41, 313-326.
Wang, P. C., (1989). Tests for dispersion effects from orthogonal arrays. Comput. Statist. Data Anal. 8, 109-117. |
| Description: | 碩士
國立政治大學
統計研究所
93354022
94 |
| Source URI: | http://thesis.lib.nccu.edu.tw/record/#G0093354022 |
| Data Type: | thesis |
| Appears in Collections: | [統計學系] 學位論文
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