在科技日新月異的現代，產品不僅講求高品質，也需要有良好的穩定性。當製程的變異增大時，不穩定的產品品質將會增加製程的不良率，而當製程的變異減少時，則代表需要重新設定管制圖的管制界限以維持較高的製程監控效率，並希望找出變異減少的原因以利製造成本的降低。此外，當製程含有多個品質特徵時，同時監控這些品質特徵並考慮特徵間的相關性也是不可或缺的課題。在本文中，我們提出用於監控多個品質特徵的共變異數矩陣，並且結合指數加權移動平均機制的改變點偵測管制圖。我們模擬數種共變異數矩陣的異常情境，並觀察當製程發生改變時，改變點偵測管制圖的監控效率以及改變點估計的準確度。最後，我們以一筆血壓資料來說明所提出的改變點偵測管制圖的實際應用。

With the rapid development of science and technology, products not only require high quality but also need to have good stability. As the process variability increases, the unstable product quality will increase the defect rate of the process. On the other hand, as the process variability decreases, this implies process improvement, and we have to reset the control limits of control charts to maintain high monitoring efficiency. Also, the decreasing process variability is an opportunity to capture the reason for causing variability to facilitate the reduction of manufacturing costs.
In addition, monitoring multiple quality characteristics at once and considering the correlation between them are also essential issues. In this thesis, We develop a change-point detection control chart that combines the exponential weighted moving average mechanism to monitor process covariance matrices in this article. We simulate several out-of-control scenarios of covariance matrices to evaluate the monitoring efficiency and the accuracy of the change-point estimation of the proposed chart. Lastly, we demonstrate the use of the proposed change-point detection control chart with a set of blood pressure data from a diabetic patient.

目錄
1 緒論1
1.1 前言. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 管制圖簡介. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.3 共變異數矩陣管制圖的相關文獻. . . . . . . . . . . . . . . . . . . . . . 2
1.4 研究目的與動機. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
2 監控共變異數矩陣管制圖5
2.1 自啟式指數加權移動平均管制圖. . . . . . . . . . . . . . . . . . . . . . 5
2.2 改變點偵測管制圖. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
2.2.1 改變點模型與概似比檢定. . . . . . . . . . . . . . . . . . . . . . 9
2.2.2 對不同改變點的檢定統計量使用Bartlett 修正與標準化. . . . . 12
2.2.3 結合指數加權移動平均的CPD 管制圖. . . . . . . . . . . . . . . 13
3 模擬分析研究16
3.1 管制圖的管制界限. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
3.2 共變異數矩陣的OC 情境. . . . . . . . . . . . . . . . . . . . . . . . . . 19
3.3 監控效率比較. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
3.4 改變點估計表現. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
4 實例26
4.1 資料介紹. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
4.2 分析結果. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
5 結論28
iv
參考文獻29
附錄32
附表35
附圖77

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