近年來，有些產品品質的好壞或製程是否穩定不再只是利用產品或製程的品質特徵是否滿足某個品質特徵的分配來判斷，而是藉由資料是否滿足某個函數關係來判斷，這種類型的資料稱為輪廓資料，而監控此種資料的過程則稱為輪廓監控。在過去的文獻中，通常假設製程的觀察值在不同時間之下具有相同且彼此獨立的常態分配，但是許多設備或系統的連續性製程會使得模型的隨機誤差項具有相關性。因此在本文中，考慮在第二階段一般線性輪廓模型，且輪廓間具有一階自我相關時，我們提出新的監控方法並與舊有的方法做比較。由模擬的結果可以得到，本文提出的 MEWMA (multivariate exponentially weighted moving average) 監控方法比舊有的方法好。最後會透過一個例子來說明如何實際應用本文所提出的監控方法。

Recently, for some applications, the quality of a process or product cannot be represented by a distribution of a quality characteristic but better characterized and summarized by a functional relationship. This kind of data is called a profile. Profile monitoring is to check the stability of this relationship over time. In the
literature, it is often assumed that the error terms of models are independent and identically normally distributed. However, in some applications, there is an autocorrelation between the error terms due to continuous processes. Thus, general linear profiles with a first 
 order autocorrelation between profiles in Phase II are considered in this study. We propose new monitor schemes for this profile data and compare with existing monitor schemes. By the simulation results, our proposed MEWMA (multivariate exponentially weighted moving average) scheme has better performance than the existing monitor schemes. Finally, an example is used to illustrate the applicability of the proposed scheme.

第一章 緒論 1 
 1.1 前言 1 
 1.2 文獻探討  2 
 1.3 研究動機與目的 6 
第二章 現有的輪廓監控方法  . 8 
 2.1 T 2管制方法 9 
 2.2 VEWMA*管制方法 10 
 2.3 T 2 U管制方法 12 
第三章 新的輪廓監控方法 14 
 3.1 MEWMA管制方法 15 
 3.2 FMEWMA管制方法  15 
 3.3 MEWMAE1管制方法 16 
 3.4 MEWMAE2管制方法 17 
第四章 模擬的結果與分析 18 
 4.1 管制圖的比較準則 18 
 4.2 一階自我相關簡單線性模型的模擬設定 18 
 4.2.1 單一參數的改變 19 
 4.2.2 兩個參數的改變 21 
 4.3 一階自我相關二次式模型 22 
 4.3.1 單一參數的改變23 
第五章 實例 25 
第六章 結論與未來研究 27 
附錄 28 
 附錄 A 28 
 附錄 B 31 
參考文獻 34

表目錄
表 1 在一階自我相關簡單線性模型下，當整體ARL 0 ≈ 200時，所有方法所使用的管制界線或係數值 (其中括號內為標準差) 3
表 2 在一階自我相關簡單線性模型下， A 0 → A 0 + λσ各管制方法的ARL 1 值 44 
表 3 在一階自我相關簡單線性模型下， A 1 → A 1 + βσ各管制方法的ARL 1值 45 
表 4 在一階自我相關簡單線性模型下，σ → γσ 各管制方法的ARL 1值 . . . . . . 46 
表 5.1 在一階自我相關簡單線性模型下，當 φ = 0.1時，B 0 → B 0 + λσ , B 1 → B 1 + βσ各管制方法的ARL 1值 47 
表 5.1 (續) 48 
表 5.2在一階自我相關簡單線性模型下，當 φ = 0.5時，B 0 → B 0 + λσ , B 1 → B 1 + βσ各管制方法的ARL 1值49 
表 5.2 (續) 50 
表 5.3在一階自我相關簡單線性模型下，當 φ = 0.9時，B 0 → B 0 + λσ , B 1 → B 1 + βσ各管制方法的ARL 1值51 
表 5.3 (續) 52 
表 6.1在一階自我相關簡單線性模型下，當 φ = 0.1時， B 0 → B 0 + λσ , σ → γσ 各管制方法的ARL 1值53 
表 6.1 (續) 54 
表 6.2 在一階自我相關簡單線性模型下，當 φ = 0.5時， B 0 → B 0 + λσ , σ → γσ 各管制方法的ARL 1值 55 
表 6.2 (續) 56 
表 6.3 在一階自我相關簡單線性模型下，當 φ = 0.9時， B 0 → B 0 + λσ , σ → γσ 各管制方法的ARL 1值 57 
表 6.3 (續) 58 
表 7.1在一階自我相關簡單線性模型下，當 φ = 0.1時， B 1 → B 1 + βσ , σ → γσ 各管制方法的ARL 1值 59 
表 7.1 (續) 60 
表 7.2在一階自我相關簡單線性模型下，當 φ = 0.1時， B 1 → B 1 + βσ , σ → γσ 各管制方法的ARL 1值 61 
表 7.2 (續) 62 
表 7.3 在一階自我相關簡單線性模型下，當 φ = 0.1時， B 1 → B 1 + βσ , σ → γσ 各管制方法的ARL 1值 63 
表 7.3 (續) 64 
表 8 在一階自我相關二次式模型下，當整體ARL 0 ≈ 200時，所有方法所使用的管制界線或係數值 (其中括號內為標準差) 65 
表 9 在一階自我相關二次式模型下，A 0 → A 0 + λσ各管制方法的ARL 1 值65 
表 10 在一階自我相關二次式模型下，A 1 → A 1 + βσ各管制方法的ARL 1值66 
表 11 在一階自我相關二次式模型下，A 2 → A 2 + δσ各管制方法的ARL 1值66 
表 12 在一階自我相關二次式模型下，σ → γσ 各管制方法的ARL 1值 67 
表 13 十四種水泥化合物與每週產生的累積熱能 67 
表 14 例子所使用的資料與監控統計量 68 

圖 1 在一階自我相關簡單線性模型且分別在 φ = 0.1, 0.5, 0.9之下，A 0 → A 0 + λσ各管制方法的ARL 1 值 69 
圖 2 在一階自我相關簡單線性模型且分別在 φ = 0.1, 0.5, 0.9之下，A 1 → A 1 + βσ各管制方法的ARL 1值 70 
圖 3 在一階自我相關簡單線性模型且分別在 φ = 0.1, 0.5, 0.9之下，σ → γσ 各管制方法的ARL 1值 1 
圖 4 監控A 0、A 1、A 2、A 3、A 4以及標準差的 MEWMA 管制方法 72

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