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研究生: 黃昱昇
Huang, Yu-Sheng
論文名稱: 模糊理論應用於管制圖之建立
Applying fuzzy set theory in the development of quality control charts
指導教授: 潘南飛
Pan, Nang-Fei
學位類別: 碩士
Master
系所名稱: 工學院 - 土木工程學系
Department of Civil Engineering
論文出版年: 2015
畢業學年度: 103
語文別: 中文
論文頁數: 107
中文關鍵詞: 模糊管制圖工程管理模糊統計模糊集合理論
外文關鍵詞: Fuzzy control chart, Engineering management, Fuzzy statistics, Fuzzy set theory
相關次數: 點閱:139下載:4
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  • 統計製程管制在國際上公認可提升品質的技術,也已被廣泛地應用於包括營建業等諸多的工業界。品質管制圖為統計製程管制中主要用於監控制造或施工過程,進而判定造成製成變異的原因,用以採用可確保品質穩定之有效改善方案。傳統管制圖的主要應用的技術為X ̅R(平均數-全距)、X ̅S(平均數-變異數)及不合格率(P),其包括管制中線、管制上限即下限。管制圖之管制界限係基於樣本的平均數即變異數所建立而成,而由試驗的樣本落於管制界限的位置,可用於判定製程是處於管制中或非管制的狀態。
      然而,對許多問題而言,當樣本為語意評量的結果、模糊數值,或來自於檢測者、量測工具與製程環境存有不確定性時,管制界限則不能或無法精確地訂出。當樣本不是明確的數值時,模糊理論為處理其不確定性的良好工具。利用隸屬函數與模糊運算可用以建立較傳統管制圖更合理與彈性的模糊管制界限。本研究提出的模糊管制圖,根據模糊直方圖來判斷模糊樣本的分配情形,進而配適可能性分佈函數,並根據選用的可能性分佈函數,依照其特徵值,訂定管制限制繪製管制圖,最後並以實際的營建施工的案例來說明分析的結果,所提出的方法的有效性,以及顯示其在處理模糊資料的潛在應用。
      而本研究提出針對可能性分佈情形配式之函數於模糊管制圖建立模式,係根據模糊分配情形選用可能性分佈函數針對其特徵值訂定管制界限,避免不論任何分配皆使用常態分配近似所產生之誤差,以及有別於先前模糊管制圖所使用線性隸屬函數,本研究提出非線性之二次曲線隸屬函數用於純模糊評定等級情況使用。

    The statistical process control (SPC), an internationally recognized technique for improving products quality, has been widely applied throughout various industries including construction engineering. The SPC relies on the use of control charts to monitor the manufacturing or construction process for identifying special causes in the process variation and indicating the necessity of effective corrective actions for the process to ensure quality stability. The widely used traditional control chart techniques are X ̅–R, X ̅–S and P , which consist of Center Line, Upper Control Limit and Lower Control Limit. These limits are represented by the numerical values on the basis of the sample average and variance. The process is either “in-control” or “out-of-control” depending on numerical observations. However, for many problems, control limits could not be so precise due to linguistic assessments, vague data or uncertainty deriving from the measurement system including operators, gauges and environmental conditions. Numeric control limits can be transformed to fuzzy control limits by using membership functions. So as to provide a more reasonable and flexible evaluation. In this research, we will propose new fuzzy X ̅–R, X ̅–S and P control charts, whose fuzzy control limits are constructed by using fuzzy set theory. Finally, a case study including some practical construction process will be employed to interpret its results, illustrate the performance of the proposed techniques, and to show the potential application in monitoring its average and variability while its fuzzy sample data are taken into consideration.

    摘要 I Extended Abstract II 誌謝 V 表目錄 VIII 圖目錄 IX 第一章 緒論 1 1.1. 研究背景與動機 1 1.2. 研究目的 4 1.3. 研究範圍與限制 5 1.4. 研究流程 6 1.5. 研究架構 7 第二章 文獻回顧 8 2.1. 傳統管制圖 8 2.2. 模糊管制圖 9 2.3. 模糊管制圖之判讀 17 2.4 小結 18 第三章 研究方法回顧 19 3.1管制圖 19 3.1.1. 計量值管制圖 20 3.1.2. 全距管制圖 21 3.1.3. 計數值管制圖 21 3.1.4缺點數管制圖(C管制圖) 22 3.1.5管制圖之判讀 22 3.2. 模糊理論 24 3.2.1模糊集合(Zimmermann, 2001) 26 3.2.2凸性模糊集合(Zimmermann, 2001) 26 3.2.3正規模糊集合(Zimmermann, 2001) 26 3.2.4模糊數(Zimmermann, 2001) 26 3.2.5 α 截集 (α- cut) 28 3.3. 建立模糊管制圖之方法 29 3.3.1以α截集合建立模糊管制圖 31 3.4. 模糊管制圖判讀 38 第四章 模式建立 41 4.1.可能性分配函數之類型 41 4.1.1 近似常態分配之可能性分配函數 42 4.1.2 近似韋伯分配之可能性分佈函數 43 4.1.3 近似卜瓦松分配之可能性分佈函數 47 4.2. 二次曲線型式之隸屬函數 49 4.3. 二階段權重管制圖之建立 50 4.3.1 模糊平均數管制圖 52 4.3.2模糊不合格率管制圖 52 4.3.3模糊不合格數管制圖 53 4.3.4模糊全距管制圖 54 4.4.可能性分佈函數之選用 55 4.4.1 模糊直方圖 55 4.4.2 可能性分佈函數 56 4.5.管制左右界限倍距之決定 57 4.5.2韋伯分配之可能性分配函數之特徵值計算量 59 4.4.2 卜瓦松分配之可能性分配函數之特徵值計算 61 4.4.4 二次分配型式之隸屬函數之特徵值計算 63 4.5.模糊管制圖之判讀 65 4.5.1 對稱函數型式之模糊管制圖的判讀準則 65 4.5.2 使用非對稱隸屬函數的模糊管制圖判讀準則 67 4.5.3 各可能性函數可能性判斷數據 67 第五章 案例分析與探討 73 5.1.案例一分析 73 5.2. 案例二之分析 79 5.3 案例三之分析 92 第六章 結論與建議 98 6.1. 結論 98 6.2. 研究貢獻 99 6.3. 未來研究建議 100 參考文獻 101 附錄 105

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