簡易期望容量的最佳因子設計

Factorial Designs with Optimal Simplified Estimation Capacity

李碧瑜(Bih-Yu Li)

指導教授 ： 王丕承

國立中央大學/管理學院/工業管理研究所/碩士(2006年)

摘要

當問題產生時，要試著找出問題的癥結，才能有效的解決。若自己或他人缺乏經驗，且資料不齊全時，無法取得適當的解決方式，需藉助實驗的方式來尋找答案。實驗設計就是在有限的資源下，選擇少數適當的方案，以實驗的方式去蒐集資料後，加以分析去得經驗，並找到最佳方式來處理問題。

選擇少數適當的方案，如同選擇最佳的設計，一般用來判斷設計優劣的標準是利用Fries & Hunter（1980）提出的最小偏誤設計（minimum aber- ration），目的要讓因子與交互作用或交互作用間混淆的情況越少越好，減少效應值混淆不清的情況，是一個用來判定部份因子設計優劣的熱門準則。除了上述混淆的觀點外，亦可利用設計涵蓋範圍的觀點來加以探討，希望選擇的設計可用來估計的資訊越多越好，Sun（1993）基於這個觀點，提出期望容量設計（estimation capacity）來判斷設計的優劣，從二階交互作用的個數為一開始，到可分配給交互作用的最大自由度下，逐一比較兩設計的期望容量，雖然後續很多學者探討這方面找出最佳設計的研究，但此法過於繁雜不符合成本效益。

本研究提出簡易期望容量設計，探討當交互作用的個數為一時，就可利用期望容量來比較出優劣，若兩設計的期望容量相等時，則繼續往下比較交互作用的個數為二時的期望容量，直至比較出優劣為止，此法較簡易
且結果一致，提供計畫實驗者選擇設計時的另一個比較基準。

關鍵字

最小偏誤設計 ； 期望容量設計 ； 簡易期望容量設計 ； 二水準部分因子設計

並列摘要

We should find the key points to solve the problems. When lacking of experience or information, we can’t find the proper way, so have to get solutions by use of experiments. Design of Experiment could help us to find the best way when the resources are limited.

Choosing the proper plans is the same to choose the best design. Fries & Hunter（1990）proposed minimum aberration to judge designs and in order to reduce aliases between main effect or interaction. It’s a popular criterion now. Except minimum aberration, we also could judge designs in terms of the coverage of design. So Sun（1993）proposed estimation capacity by comparing the estimation capacity between two designs one by one from the number of interaction is one to extreme degree of freedom which could allocate to interactions. Although many researchers have research to find out the best design on this topic, but the criteria is too complicated and costly.

We propose simplified estimation capacity in this paper to research that few comparisons of estimation capacity could come out the better design. This criterion is simplified and the result is the same, so could provide experimenter another criterion when choosing design.

並列關鍵字

estimation capacity ； simplified estimation capacity ； minimum aberration ； 2-level fractional factorial design

參考文獻

Box, G. E. P. and Hunter, J. S. (1961), “The 2n-p Fractional Factorial Designs Part I,” Technometrics, 3, 311-352.

Chen, H. and Cheng, C. S. (2004), “Aberration, Estimation Capacity and Estiamtion Index,” Statistica Sinica, 14, 203-215.

Chen, H. and Hedayat, A. S. (1996),”2n-m Fractional Factorial Designs with Weak Minimum Aberration,” Annals of Statistics, 24, 2536-2548.

Chen, J. (1992), “Some Results on 2n-k Fractional Factorial Designs and Search for Minimum Aberration Designs,” Annals of Statistics, 20, 2124-2141.

Chen, J. and Wu, C. F. J. (1991), “Some Results on sn-k Fractional Factorial Designs with Minimum Aberration or Optimal Moments,” Annals of Statistics, 19, 1028-1041.