臺灣博碩士論文加值系統

傳統管制圖經常假設樣本之量測值為常態分配，可是許多實務上的案例卻非如此。在這些實例中常常由於樣本組內之量測值較少，無法應用中央極限定理，使得常態分配的假設並不恰當。
由於較少文獻探討具警告界限之平均數管制圖經濟─統計性設計，因此本研究主要是探討在非常態性資料對於具警告界限之平均數管制圖經濟─統計性設計的影響。選擇經濟─統計性設計模式除了可以保有管制圖預期應有的偵測能力外，同時也能在經濟因素考量下，降低所需付出之成本。本研究在經濟性設計的部份是以Gordon 和Weindling（1975）成本模式，並以生產每件良品之平均成本為績效衡量指標；而統計性設計的部份則是採「平均連串長度」作為統計限制條件。本研究應用基因演算法進行求解，也就是要以基因演算法在滿足所設定的統計限制條件下搜尋管制圖最適參數組合：樣本大小（n）、抽樣間隔（s）、連串長度（r）、警告界限係數（w）與管制界限係數（k），使得生產每件良品的平均成本最小化。
研究結果顯示，固定抽樣成本（CF）與調查並消除可歸屬原因的成本（CA2）變動時，對於單位平均成本並無明顯的影響；而變動抽樣成本（CV）、不良品所花費的成本（CD）、調查錯誤警告的成本（CA1）與製程發生隨機偏移的頻率增加時，單位平均成本明顯遞增。另外，製程發生偏移程度與誤差容許率增加時，單位平均成本則明顯遞減。

Traditionally, when the issue of designing control chart is discussed, one usually assumes the observations in each sampled subgroup are normally distributed; therefore, the sample mean is also normally distributed. Even if the size of subgroup is large enough, the observations will be distributed normally according to the central limit theorem. However, the assumption may not be acceptable in practice.

In this research, an economic-statistical design of X-bar chart with warning limit under Non-normal distributions will be developed using the Burr distribution. In the part of economic design, Gordon and Weindling (1975) cost model is used to minimize average cost per part produced. In the part of statistical design, average run length (ARL) is used as the statistical limiting conditions. The genetic algorithm (GA) is adopted to search for the optimal parameters, i.e. the sampling size (n), the sampling interval (s), the run length (r), the warning limit coefficients (w) and the control limit coefficients (k).

By sensitive analysis we can get fixed sampling cost (CF) and cost correcting the assignable cause (CA2) don’t affect average cost per part produced. An increase in variation sampling cost (CV), cost of defective product (CD), cost of searching for assignable cause (CA1) and mean number of shift (θ) leads to increase average cost per part produced. In addition, An increase in shift coefficient (δ) and allowable semi-tolerance leads to increase average cost per part produced.

目錄

中文摘要 -------------------------------------------------------------------------- i
英文摘要 -------------------------------------------------------------------------- ii
誌謝 -------------------------------------------------------------------------- iii
目錄 -------------------------------------------------------------------------- iv
表目錄 -------------------------------------------------------------------------- vi
圖目錄 -------------------------------------------------------------------------- vii
符號說明 -------------------------------------------------------------------------- viii
第一章 緒論-------------------------------------------------------------------- 1
1.1 研究背景-------------------------------------------------------------- 1
1.2 研究動機與目的----------------------------------------------------- 2
1.3 研究範圍與假設----------------------------------------------------- 3
1.4 研究架構-------------------------------------------------------------- 4
第二章 文獻探討-------------------------------------------------------------- 7
2.1 管制圖經濟性設計-----------------------------------------------
7
2.2 管制圖經濟─統計性設計--------------------------------------
8
2.3 具警告界限之管制圖----------------------------------------------- 10
2.4 非常態性資料之探討----------------------------------------------- 11
2.5 基因演算法應用在管制圖相關研究----------------------------- 12
2.6 田口實驗設計應用在管制圖相關研究-------------------------- 13
第三章 研究方法-------------------------------------------------------------- 15
3.1 Burr分配-------------------------------------------------------------- 15
3.1.1 Burr分配之簡介----------------------------------------------------- 15
3.1.2 應用Burr分配之轉換方式---------------------------------------- 16
3.2 基因演算法----------------------------------------------------------- 19
3.2.1 編碼-------------------------------------------------------------------- 19
3.2.2 初始族群-------------------------------------------------------------- 21
3.2.3 定義適應函數-------------------------------------------------------- 21
3.2.4 基因運算子----------------------------------------------------------- 21
3.2.5 停止條件-------------------------------------------------------------- 26

第四章 模式的建立----------------------------------------------------------- 27
4.1 模型的假設----------------------------------------------------------- 27
4.2 成本模式之介紹----------------------------------------------------- 27
4.3 模型中機率的推導-------------------------------------------------- 30
4.4 統計性設計之說明-------------------------------------------------- 36
第五章 模式的求解----------------------------------------------------------- 37
5.1 求解程序-------------------------------------------------------------- 37
5.2 範例說明-------------------------------------------------------------- 38
5.3 基因演算法之參數設定-------------------------------------------- 46
5.3.1 田口實驗設計-------------------------------------------------------- 46
5.3.2 基因實驗參數設定-------------------------------------------------- 46
5.3.3 實驗分析-------------------------------------------------------------- 48
第六章 模式的分析----------------------------------------------------------- 50
6.1 經濟性與經濟─統計性設計之比較------------------------------ 50
6.2 敏感度分析----------------------------------------------------------- 53
第七章 結論與建議----------------------------------------------------------- 59
7.1 結論-------------------------------------------------------------------- 59
7.2 建議-------------------------------------------------------------------- 61
參考文獻 -------------------------------------------------------------------------- 62

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