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系統識別號 U0026-2906201723142200
論文名稱(中文) 在製程微量變動下模糊指數加權移動平均管制圖之建構與研究
論文名稱(英文) Developing a New Fuzzy Exponentially Weight Moving Average Control Chart for Small Sustained Process Shifts
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 105
學期 2
出版年 106
研究生(中文) 李秀玲
研究生(英文) Xiu-Ling Lee
學號 R26031090
學位類別 碩士
語文別 中文
論文頁數 31頁
口試委員 指導教授-潘浙楠
口試委員-李俊毅
口試委員-鄭春生
中文關鍵字 模糊EWMA管制圖  平均連串長度  模糊平均連串長度 
英文關鍵字 fuzzy EWMA control chart  average run length  fuzzy average run length 
學科別分類
中文摘要 在現今工業界中,統計製程管制(statistical process control, SPC)是常用來及時監控及改善產品及製程品質的一種統計技術,其中又以管制圖(control chart)為統計製程管制技術中最廣泛被使用於監控製程品質之工具。然而在實際的應用中,往往因為操作人員、量測工具、製程環境等因素存在著不確定性,導致量測數據為不確定的模糊數而無法使用過去傳統的方式來建構管制圖。
近年來已有多位學者針對量測數據為模糊數提出了一系列的模糊管制圖,彼等運用解模糊化的方法建立明確管制界線並以其作為製程是否是管制狀態之依據。但此種方法並未考慮到數據的模糊性而失去部分訊息,因此考慮量測數據的模糊程度用以建立模糊管制界限確實有其必要性。
本研究利用Buckley(1985)所提出的模糊數相近關係測度來決定模糊統計量與模糊管制界線的大小關係並以其作為製程是否呈管制狀態之評判依據,接著我們根據模糊隸屬度的概念提出新的模糊ARL計算公式並透過其找尋在各種不同模糊程度下的修正管制界線的參數。實務工作者可透過修正管制界線參數在管制狀態內的ARL值( )決定其所能接受量測數據的模糊程度,再以此管制參數建構模糊EWMA管制圖。
最後本研究以Montgomery (2009, pp. 283)所提供的矽晶圓氧化層厚度量測資料說明模糊EWMA管制圖的使用步驟,可作為實務工作者的參考。
英文摘要 This research aims to develop a new fuzzy exponentially weighted moving average (EWMA) control chart for monitoring the process when the measurement data are fuzzy numbers. In this research, based on the fuzzy measures proposed by Buckley (1985), we construct a fuzzy control chart with different degrees of membership to monitor the manufacturing process. Then, a new fuzzy average run length (fuzzy ARL) is developed to evaluate the detecting performance of our purposed fuzzy control chart. It can be used as the basis for obtaining the parameters of adjusted control limits. Finally, a numerical example with fuzzy measurement data is used to demonstrate the usefulness of our purposed fuzzy control chart. Moreover, a standard operating procedures (SOP) is setup accordingly. Hopefully, it may serve as a useful guideline for quality practitioners when monitoring and control the process quality when the measurement data are indeterminate fuzzy numbers.
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 2
1.3 研究架構 2
第二章 文獻回顧與探討 4
2.1 EWMA管制圖 4
2.2 模糊集合理論 6
2.2.1 傳統集合論與模糊集合論 6
2.2.2 α-截集 8
2.2.3 模糊數運算 9
2.2.4 解模糊化方法 10
2.3 模糊管制圖之發展 10
第三章 模糊EWMA管制圖之建構 12
3.1 模糊EWMA管制界限之建構 12
3.2 模糊平均連串長度(Fuzzy Average Run Length) 14
3.3 修正管制界限參數的選取與平均連串長度計算 16
第四章 數值實例分析 23
第五章 結論與未來研究方向 29
5.1 結論 29
5.2 未來研究方向 29
參考文獻 30
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