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系統識別號 U0026-1507202021403800
論文名稱(中文) 利用Tweedie過程模型建構具輪廓內相關之輪廓管制圖
論文名稱(英文) Control Charts for Linear Profile Monitoring with Within-Profile Correlation Using Tweedie Process Model
校院名稱 成功大學
系所名稱(中) 統計學系
系所名稱(英) Department of Statistics
學年度 108
學期 2
出版年 109
研究生(中文) 蔡孟容
研究生(英文) Meng-Rong Tsai
學號 R26071032
學位類別 碩士
語文別 中文
論文頁數 50頁
口試委員 口試委員-鄭春生
口試委員-潘浙楠
指導教授-李俊毅
中文關鍵字 線性輪廓監控  Tweedie指數分散過程  MEWMA管制圖  階段Ⅱ研究 
英文關鍵字 Linear profile monitoring  Tweedie exponential dispersion process  MEWMA control chart  Phase Ⅱ study 
學科別分類
中文摘要 就某些產品或製程而言,其品質特性可藉由反應變數與一個以上解釋變數間的函數關係來描述,這種函數關係稱之為輪廓(profile)。而透過管制圖來觀察此函數關係是否隨著時間改變而發生變化的過程稱為輪廓監控(profile monitoring)。本研究係針對具輪廓內相關之資料建構參數模型,並估計每一時間點的輪廓資料參數,進而監控這些參數是否隨著時間而改變。過去針對輪廓資料的研究中常假設輪廓內觀察值彼此之間互相獨立,但由於製造或資料收集過程等因素導致某些輪廓資料無法滿足此一假設。故本研究先以Tweedie 指數分散隨機過程描述此輪廓內相關(within-profile correlation),接著在階段Ⅱ利用多變量指數加權移動平均管制圖(multivariate exponentially weighted moving average; MEWMA)建構輪廓管制圖以監控模型主要參數,並藉此判斷製程是否呈穩定狀態。
在利用Tweedie 指數分散過程模型配適線性輪廓資料的模擬分析中,我們考慮不同冪參數、斜率參數及分散參數組合下,比較MEWMA管制圖和Zhang et al. (2014)提出T2與MMR管制圖的表現能力,由統計模擬結果發現本研究所提出之MEWMA管制圖在不同參數組合下的表現能力優於T2與MMR管制圖。最後我們以蘋果生長直徑及吸收度之校準線兩筆資料為例,針對MEWMA管制圖在監控具輪廓內相關之輪廓資料上的適用性做進一步的驗證與說明。
英文摘要 For some manufacturing processes, the quality of a product can be characterized by a functional relationship between the response variable and explanatory variables, which has been referred to as a profile. Recently, profile monitoring is used to maintain the stability of the product quality over time by various industries. In this research, we focus on the single-variate linear profile monitoring. Firstly, the Tweedie exponential dispersion process (Tweedie ED) model is used to describe the correlated relationship among within-profile data. Then, a multivariate exponentially weighted moving average (MEWMA) control chart is constructed to detect the process change in Phase Ⅱ study.

In the simulation studies, different combinations of slope and dispersion parameters are considered in our Tweedie ED model. Moreover, the in-control and out-of-control average run lengths (ARLs) are used as a criteria to evaluation the performance of MEWMA and T^2, MMR control charts. Based on the simulation results, we find that our proposed MEWMA control chart has a better detecting performance than the T^2 and the MMR control charts in Phase Ⅱ study since the Tweedie ED model is more suitable to fit linear profile data if the within-profile data are correlated.

Finally, two numerical examples are given to demonstrate the usefulness of our proposed control charts in practical applications.
論文目次 第一章 緒論1
1.1研究背景與動機 1
1.2研究目的 3
1.3研究架構 3
第二章 文獻回顧 4
2.1管制圖 4
2.1.1 EWMA管制圖 4
2.1.2EWMA-μ與EWMA-ν管制圖5
2.1.3平均連串長度 6
2.2輪廓監控管制圖 7
2.3隨機效果 9
2.4隨機過程 11
2.4.1高斯隨機過程11
2.4.2 Tweedie指數分散過程13
第三章 研究方法 16
3.1指數分散過程模型16
3.2輪廓內相關結構 17
3.3管制圖之制定 19
3.3.1多變量管制圖19
3.3.2斜率參數管制圖與平均連串長度22
3.3.3分散參數管制圖與平均連串長度24
3.4製程呈穩定狀態內之參數估計26
第四章 模擬與實例分析28
4.1 模擬比較28
4.1.1製程穩定下管制圖之表現29
4.1.2製程脫離穩定下管制圖之表現31
4.2 數值實例分析35
4.2.1 蘋果生長之直徑資料36
4.2.2.吸收度之校準線資料38
第五章 總結43
5.1 結論43
5.2 未來研究方向44
參考文獻 45
附錄一48
附錄二49
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