# 臺灣博碩士論文加值系統

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 多重實驗徑之一次一因子實驗是一個易於建構的設計，它不受限於實驗徑的限制，不管因子數是多是少都能輕鬆的建構。我們只需在修改的一次一因子實驗中額外加入基準實驗徑即可完成。本研究在主效果估計及交互作用估計兩個面向下進行模擬驗證，並說明多重實驗徑之一次一因子實驗的特性。相較於標準的一次一因子實驗，多重實驗徑之一次一因子實驗改善了實驗誤差無法估計的問題。而在與部分因子實驗比較部分，多重實驗徑之一次一因子實驗能在有二階交互作用的情況下，不會因為混淆關係而需要額外的實驗來釐清因子之間的關係。
 A one-factor-at-a-time experiment with multiple standard runs is not limited to the number of runs. It can be constructed easily by adding multiple standard runs in a modified one-factor-at-a-time experiment. In this work, we run a series of simulation studies to investigate the properties of one-factor-at-a-time experiments with multiple standard runs. In the simulation studies, we consider models with only main effects and models with both main effects and two-factor interactions. Compared to standard one-factor-at-a-time experiments, one-factor-at-a-time experiments with multiple standard runs provide degrees of freedom to estimate the experimental error. Besides, one-factor-at-a-time experiments with multiple standard runs can effectively identify important effects with the presence of two-factor interactions, which can be failed when using a fractional factorial design because of the aliasing relations.
 第一章 緒論 11.1研究背景 11.2研究目的 21.3論文架構 2第二章 文獻探討 22.1因子篩選實驗 32.1.1部分因子實驗 32.1.2一次一因子實驗 42.1.3修改的一次一因子實驗 52.2因子篩選方法 7第三章 多重實驗徑之一次一因子實驗 11第四章 模擬研究 134.1主效果估計 134.2交互作用估計 164.3 MBMM與多重實驗徑之一次一因子實驗 19第五章 結論與建議 21參考文獻 22
 張森傑 (2019)。因子篩選試驗的穩健性探討，東海大學碩士論文。Barton, R. R. (1999). Design-plots for factorial and fractional-factorial designs. In Graphical Methods for the Design of Experiments. Springer, New York, NY.Box, G. E. and Meyer, R. D. (1993). Finding the active factors in fractionated screening experiments. Journal of quality technology, 25, 94-105.Daniel, C. (1973) One-at-a-time plans. Journal of the American Statistical Association, 68, 353-360.Frey, D. D., Engelhardt, F., and Greitzer, E. M. (2003). A role for" one-factor-at-a-time" experimentation in parameter design. Research in Engineering Design, 14, 65-74.Hamada, M. (1993). Reliability improvement via Taguchi's robust design. Quality and reliability engineering international, 9, 7-13.Qu, X.G. and Wu, C.F.J (2005) One-factor-at-a-time designs of resolution V. Journal of Statistical Planning and Inference, 131, 407-416.Raftery, A. E., Madigan, D., and Hoeting, J. A. (1997). Bayesian model averaging for linear regression models. Journal of the American Statistical Association, 92, 179-191.Wu, C.F.J. and Hamada, M. (2009) Experiments: planning, analysis, and parameter design optimization 2nd ed. New York, NY, USA: John Wiley & Sons.Yu, I. T. (2013). A modification of the Box–Meyer method for finding the active factors in screening experiments. Journal of Applied Statistics, 40, 972-984.
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 1 因子篩選試驗的穩健性探討

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