臺灣博碩士論文加值系統

　　管制圖為統計製程管制的重要工具之一，其對於改善品質與生產力非常有效。因此，相當多學者致力於提升管制圖偵測能力的研究。然而傳統的修華特管制圖對於製程均值偏移幅度較小時偵測較不靈敏，無法快速偵測出製程異常。而累積和管制圖和指數加權移動平均管制圖在偵測製程平均數是小幅度偏移上較修華特(Shewhart)管制圖靈敏。
　　本研究以指數加權移動平均管制圖為製程監控工具，應用Duncan(1956)所提出的經濟設計模型為基礎，探討製程失效機制屬韋伯分配之管制圖經濟設計。在本論文中應用田口玄一(Taguchi)博士所提出的二次損失函數(loss function)來衡量社會損失成本，更合乎現今品質之定義。本研究透過最佳化技巧找出EWMA經濟管制圖之最低成本及最佳設計參數組合。同時，再利用敏感度分析，我們可以得知製程參數、成本參數及損失函數的相關參數對指數加權移動平均管圖經濟設計的影響。

　　Control charts are basic and powerful tools in statistical process control and are effective to improve the quality and productivity. Therefore, many researchers have focused on enhancing the capability of various control charts to detect process shifts. Traditional Shewhart control charts are relatively inefficient in detecting small shifts of the process mean. Alternative control charts, such as the CUSUM control and the EWMA control chart, have been developed to compensate for the inefficiency of Shewhart control charts. In this research, we assume that EWMA control chart is used for supervising the process and an economic design based on Duncan’s(1956) cost model for EWMA control charts with a Weibull process failure mechanism has been developed. The Quadratic loss function which was defined by Taguchi was adopted in formulating the cost model. The minimum cost and the optimal design parameters of economical EWMA control charts are determined by using optimal techniques. Our sensitivity analyses also show process parameters which affect the cost significantly.

目 錄
一、緒論 1
1.1 前言 1
1.2 研究動機及目的 2
1.3 研究範圍與限制 4
1.4 研究架構 4
二、相關研究與文獻探討 6
2.1　管制圖之經濟設計 6
2.1.1管制圖經濟設計模式的製程特性 7
2.1.2 管制圖經濟設計模式的成本參數 8
2.1.3 製程週期平均時間 9
2.1.4 成本評估 9
2.2 Duncan管制圖的經濟設模式 10
2.3 指數加權移動平均管制圖 11
2.3.1 指數加權平均管制圖基本原理 12
2.3.2 以EWMA管制圖監控制程平均值 13
2.3.3 EWMA管制圖之設計 14
2.3.4 EWMA管制圖的經濟設計 16
2.4 損失函數 17
2.4.1 傳統品質損失與田口損失的比較 18
2.4.2 EWMA管制圖之經濟性設計-應用損失函數 20
2.5 製程失效機制 21
三、模式之建立 23
3.1 符號定義與模式假設條件 23
3.1.1 符號定義 23
3.1.2 模式之基本假設條件 25
3.2 製程週期平均時間及製程週期總成本 26
3.2.1 製程週期平均時間及製程週期總成本之型式 26
3.2.2 製程週期平均時間與成本因素 30
3.2.3 製程週期平均時間與製程週期總成本 30
3.3 模式的推導 32
四、成本模式之敏感度分析 40
4.1 最佳化求解計算法則 40
4.2 損失函數的效應 43
4.3 韋伯分配參數對成本模式之影響 44
4.4 製程中成本、時間、偏移等參數值對成本模式之影響47
4.5 損失函數參數對成本模式之影響 49
五、結論與建議 57
5.1 結論 57
5.2 可行的後續研究與建議 59
參考文獻 60
表目錄
表4.1 本研究與黃志全(民87)結果之對照表 42
表4.2 v=0.01,k=1 下不同經濟設計模式成本及各決策參數之差異43
表4.3 (a)v=0.002，k變動 之最佳化設計結果 45
表4.3 (b)v=0.01，k變動 之最佳化設計結果 46
表4.3 (c)v=0.02，k變動 之最佳化設計結果 46
表4.3 (d)v=0.05，k變動 之最佳化設計結果 47
表4.4 各參數不同Quntity下之組合的最佳經濟設計解 51
表4.5 不同製程偏移幅度下，最佳經濟設計解 51
表4.6 各參數值遞增時對期望成本與決策參數之影響總表 52
圖目錄
圖2.1 傳統品質損失之觀念 18
圖2.2 田口對稱二次損失函數 19
圖3.1 抽樣方法 27
圖3.2 製程平均週期 28
圖4.1　 程式流程圖 41
圖4.2 期望成本與製程標準差之關係 53
圖4.3　 抽樣間隔與製程標準差之關係 53
圖4.4　 期望成本與產品重製或報廢成本之關係 54
圖4.5　 期望成本與製程平均每小時產量之關係 54
圖4.6　 期望成本與允差之關係 55
圖4.7　 期望成本與製程偏移幅度之關係 55
圖4.8　 抽樣間隔與製程偏移幅度之關係 56
圖4.9　 管制界限與製程偏移幅度之關係 56

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