產品品質的監控是近年生產製程越來越重視的議題，如何更有效率地監控產品製程是很多學者在品質管制系統上共同努力的目標。在很多實際的製程中，製程的品質可以用一個或多個解釋變數與反應變數之間的某特定函數來界定，而這類的資料型態被稱為輪廓型資料。現今已有不少研究線性輪廓監控方法的文獻，但現有的線性輪廓監控方法僅適用於樣本數足以估計所有輪廓參數的情況，對於樣本數不足以估計所有輪廓參數的情形，尚未存在有效的方法來監控輪廓製程。
本文將針對多維度多重線性輪廓的製程監控，在樣本數不足的狀況下，提出一種利用部分最小平方法建構的管制圖。我們將使用這個管制圖來監控輪廓製程失控與否，並且將會利用統計模擬來評估其優劣。最後我們將利用一個實例來說明在實際情形下如何使用我們所提出的管制圖來執行輪廓製程的監控。

Quality control of the manufacturing process and how to monitor the process more effectively are important issues in the recent. In many practical manufacturing processes, the quality can be expressed by a function of one or more explanatory variables and response variables, and this kind of data is known as profile data. There are many literatures talking about the methods of linear profile monitoring today, but the current methods of linear profile monitoring apply only to the case that the number of observations is sufficient to estimate all regression parameters. For the case that the number of observations is not sufficient to estimate all parameters, there still have no effective methods to monitor the linear profile.
For the multivariate multiple linear profile monitoring in the case that the number of observations is not sufficient, this article would propose a control chart based on the partial least squares. We would also use the proposed control chart to perform linear profile monitoring, and then perform the statistical simulation to assess the efficiency. Finally, we would use an example to illustrate how to monitor the linear profile using the proposed control chart.

第一章 緒論 1
1.1 前言 1
1.2 輪廓監控的起源與發展 2
1.3 研究動機與目的 3
第二章 監控方法 5
2.1 PLS方法 5
2.1.1 起源與發展 5
2.1.2 基本概念 5
2.1.3 模型 6
2.1.4 運算法－SIMPLS 7
2.2 多維度多重線性模型 10
2.3 多維度多重線性輪廓之監測方法 11
2.3.1 監控PLS內部模型係數之管制圖 13
2.3.2 監控PLS內部模型誤差項共變異數矩陣之管制圖 13
2.3.3 監控PLS內部模型之聯合管制圖 14
第三章 統計模擬 16
3.1 模擬之模型 16
3.2 聯合管制圖的使用 17
3.2.1 潛在成份個數c的選取 18
3.2.2 第一階段－PLS內部模型參數估計 18
3.2.3 聯合管制圖之UCL 18
3.2.4 第二階段－監控多維度多重線性輪廓 19
3.3 EWMA與Shewhart聯合管制圖的效率比較 19
3.3.1 單一參數改變 20
3.3.2 兩個參數同時改變 21
3.3.3 效率比較結論 23
第四章 實例 24
4.1 資料背景 24
4.2 飛航校正模型 25
4.3 監控過程 27
第五章 結論與未來研究 29
附表 30
表一 不同潛在成分個數所能解釋的X變異與Y變異的比例 30
表二 EWMA和Shewhart聯合管制圖之UCL (模擬) 31
表三 改變為 時，聯合管制圖之 32
表四 改變為 時，聯合管制圖之 34
表五 改變為 時，聯合管制圖之 36
表六 、 改變為 且 改變為 時，聯合管制圖之 37
表七 、 改變為 且 改變為 時，聯合管制圖之 41
表八 、 改變為 且 改變為 時，聯合管制圖之 45
表九 EWMA和Shewhart聯合管制圖之UCL (實例) 49
參考文獻 50

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