臺灣博碩士論文加值系統

在完成一個實驗之後，實驗者會去分析觀察結果，然後在為了估計更多效能而去選擇一個最佳的後續實驗。目前有眾多可以建構出後續實驗的方法，其中較常使用的一種，我們稱它為折疊設計。我們將某些因子的性質倒轉，這種方法就稱為折疊設計。我們可藉由結合兩個部份因子設計，有效地將我們感興趣的因子給隔離出來。但是它有時卻很浪費實驗點個數，間接造成浪費實驗成本。因此我們將考慮另一種方法，我們稱之為半折疊設計。在某些情況下，對部份因子設計來說，半折疊設計所能估計出來的效能和折疊設計一樣多，而且半折疊設計比折疊設計所需要的實驗點足足少了四分之一。所以本文將針對這些特殊情況來作討論，並且在三十二個實驗點的部份因子設計中，利用自訂的標準來尋找最佳的半折疊設計，然後製作成表格，以供實驗者運用。

After finishing an experiment, the experimenter will analyze the result, and choose the follow-up experiment in order to estimate more clear effects. One of the methods which construct the follow-up experiment is called foldover. It can systematically isolate effects of potential interest by combining fractional factorial designs in which certain signs are switched. Sometimes it is wasteful if the experimenter concerns the experimental run numbers. Hence, we can consider another method named semifolding, a quarter replicate of the original design. In some conditions, the method of semifolding of 2^{k-p} fractional factorial design can estimate the same effects as the foldover design does. We will dicuss these situations, and then search the optimal semifolding designs produced by exhausting all possible semifolding designs of the fractional factorial designs, and tabulate the results of the 16-run and 32-run case for practical use in this article.

1. Introduction
2. The Relationships between Foldover and Semifolding Designs
3. Optimal Semifolding Designs
4. Conclusion
References

[1] Barnett, J., Czitrom, V., John, P. W. M., and Leon, R. V. (1997), "Using Fewer Wafers to Resolve Confounding in Screening Experiments," in Statistical Case Studies for Industrial Process Improvement, eds. V. Czitrom and P. D. Spagon, Philadelphia: SIAM, pp.235-250.
[2] John, P. W. M. (2000), "Breaking Alias Chains in Fractional Factorials," Communications in Statistics-Theory and Methods, 29, pp.2143-2155.
[3] Chen, J., Sun, D. X., and Wu, C. F. J. (1993), "A Catalogue of Two-Level and Three-Level Fractional Factorial Designs With Small Runs", International Statistical Review, 61, 131-145.
[4] Li, W. and Lin, D. K. J. (2003), "Optimal Foldover Plans for Two-Level Fractional Factorial Designs", Technometrics, 45, 142-149.
[5] Mee, R. W., and Peralta, M. (2000), "Semifolding 2^{k-p} Designs", Technometrics, 42, 122-134.
[6] Montgomery, D. C. (2001), Design And Analysis of Experiments, 6th ed., John Wiley & Sons, New York, NY.
[7] Wu, C. F. J., and Hamada, M. (2000), Experiments:Planning, Analysis, and Parameter Design Optimization, John Wiley & Sons, New York, NY.
[8] Lee, Chien-Te (2003), "Optimal Semifolding 2^{k-p} Designs".