本文針對一般線性輪廓製程，提出一個結合EWMA機制的新改變點偵測管制圖。此管制圖可以在管制狀態參數未知，且只有少數的管制狀態資料下對一般線性輪廓製程進行監控。此外，新管制圖不只可以同時偵測多個線性輪廓參數的改變，並且能夠在管制圖發出失控警訊的同時估計製程參數開始發生改變的時間點，還可以確認所有發生改變的參數以及參數改變的方向。透過統計模擬，我們所提出的新改變點偵測管制圖有良好的監控效率，並且在改變點的估計以及判斷改變參數和參數改變方向的診斷上有出色的準確度。此外，新管制圖和文獻中既有的監控線性輪廓製程的管制圖的監控效力相比毫不遜色，且在大多數參數改變的情況下都有較好的表現。最後，我們以一例子說明如何將新管制圖應用在監控線性輪廓製程的資料上。

A new control chart based on the change-point model and combined with the EWMA mechanism is proposed to monitor general linear profiles. This new control chart can monitor general linear profiles when the true in-control parameters are unknown and only a few historical data are available. In addition, the new change-point detection chart can not only detect multiple shifts in the parameters but also estimate the location of the change point and identify which of the parameters have changed and the change directions when an out-of-control signal triggers. Using statistical simulations, we show that the proposed control chart is efficient and has good diagnostic performance. Furthermore, the simulation results show that the proposed control chart has better efficiency than the existing control charts in most of the out-of-control scenarios. Finally, we use an example to illustrate how to implement the new change-point detection chart.

目錄
第一章 緒論 1
1.1 管制圖簡介 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 監控線性輪廓 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.3 研究目的與動機 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
第二章 改變點偵測管制圖 5
2.1 線性輪廓的參數估計 . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2.2 利用概似比檢定建構改變點偵測管制圖 . . . . . . . . . . . . . . . . . 7
2.3 利用不同監控統計量建構改變點偵測管制圖 . . . . . . . . . . . . . . 10
2.3.1 新的改變點偵測 . . . . . . . . . . . . . . . . . . . . . . . . . 11
2.3.2 診斷方法 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
第三章 統計模擬 18
3.1 改變點偵測管制圖的管制界限 . . . . . . . . . . . . . . . . . . . . . . 19
3.2 管制圖效力的比較 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
3.2.1 ARL 的比較 . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
3.2.2 改變點估計的比較 . . . . . . . . . . . . . . . . . . . . . . . . 26
3.2.3 確認改變參數準確度的比較 . . . . . . . . . . . . . . . . . . . 27
3.3 例子 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
第四章 結論 31
參考文獻 32
附表 35
附圖 68

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