在尋找實驗之最佳化反應值中，反應曲面法為一很有用的統計方法。在這篇論文中，討論在因子實驗下，當中心點僅有少數重複觀測值之實驗時，提出一個新的檢定統計量，以用來檢測反應曲面是否有曲率效應，並藉由模擬結果來探討這個新的統計量之表現。在第二部份，則討論當反應變數為比例類型的資料，即實驗取值範圍介於0 到1 之間時，應如何建立模型進行分析較適當。我們將以實驗範圍裡之預測變異數作為依據，進而來比較一些分析方法。

The response surface methodology is a useful method to find the optimum response in an experiment. In this work, a new test statistic with only few replicates at the center point for curvature detection is discussed. The performance of the new
statistic is investigated through simulation. In the second part of this work, when
the response variable is of the proportional type taking only values between 0 and 1,
some analysis methods are compared based on the predicted variances on the design
region.

Contents
Abstract iv
1 Introduction 1
2 Test statistic 2
2.1 Inferences with known noncentral parameter . . . . . . . . . . . . . . . . . 5
2.2 Inferences with known variance . . . . . . . . . . . . . . . . . . . . . . . . 7
2.3 Inferences with unknown noncentral parameter and variance . . . . . . . . 9
2.4 Inferences with repeated center points . . . . . . . . . . . . . . . . . . . . . 10
2.5 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
3 The response surface method for proportional data 11
3.1 Model selection for the mean estimate . . . . . . . . . . . . . . . . . . . . 13
3.2 First-order model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
3.3 An example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
3.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
References 21

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