本論文針對隨機誤差項可能不服從常態分配的非線性剖面製程提出一套使用B平滑曲線擬合剖面資料的監控方法，我們結合參數模型管制圖容易操作，與無母數管制圖對輸入變量的抽樣分配提供彈性選擇的優點，建議結合多變量符號指數加權平均管制圖與B平滑曲線剖面平均絕對差的雙管制圖，簡稱為MS_MAE管制圖，對非線性的剖面製程進行監控管制，模擬結果發現 MS_MAE管制圖有很好的效能監控製程的偏移，我們也使用一組刨花板的模擬資料示範 MS_MAE管制圖的操作。

In this study, we propose a monitoring method with using B-spline function for monitoring nonlinear profile data, in which the normality assumption of the error terms in a nonlinear profile model could not be true. Considering the merit of easily operation of parametric control chart and the flexibility on the sampling distribution assumptions of the input variables in a nonparametric control chart, a charting method that combining the multivariate sign exponentially weighted moving average control chart and the mean absolute error control chart, named MS_MAE control charts, is used for monitoring nonlinear profile data. Simulations show that the MS_MAE control charts have good ability for detecting process shifts. An example of vertical density profile data is used for illustrating the application of the proposed method.

目錄
論文提要I
AbstractII
目錄IV
圖目錄V
表目錄VI
第一章 緒論1
1.1研究主題概述與文獻回顧1
1.2研究動機與論文架構7
第二章 統計方法9
2.1統計模型9
2.2 Hotelling T^2 管制圖12
2.3 MSEWMA 管制圖13
2.4 雙管制圖監控方法17
第三章 模擬研究19
第四章 案例研討27
第五章 結論30
參考文獻32
附錄: Cox-de Boor recursion formulas35

圖目錄
圖3.1: 目標剖面與偏移後的剖面22
圖3.2: MS_MAE管制圖(實線)與T2_MAE管制圖(虛線)的ARL0值24
圖4.1: MS_MAE管制圖28

表目錄
表3.1: MS_MAE管制圖在σ=1,2 ,λ=0.5,1,3 六種組合下對各種偏移的ARL與SDRL值26

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