臺灣博碩士論文加值系統

　　當Shewhart博士在1924年提出管制圖後，各種管制圖技術便不斷地被發展出來，並且成為工業製程管制之主要工具。在管制圖的應用中，最常見的就是平均數管制圖（ 管制圖）。當 管制圖被應用在監控製程之品質特性時，必須先決定三個參數，這三個管制圖參數分別為樣本數（n）、抽樣間隔時間（h）與管制界限（k）。在1956年，Duncan發表 管制圖之經濟性設計，以決定 管制圖的三個參數，其目標函數為使抽樣與檢驗之相關成本極小化。
　　傳統上，當我們使用管制圖於統計製程管制時，一般均假設觀測值呈常態分配而且彼此獨立。然而，在實務上卻有許多的案例顯示樣本間不一定服從常態而且存在著相關性。如果量測值不呈常態分配，傳統的管制圖設計方法可能會降低管制圖偵測非機遇原因的能力。如果忽略樣本間之相關性時，製程犯型一誤差的機率也明顯地大於傳統管制圖。
　　本研究之主要目的為非常態性與相關性資料下對 管制圖之經濟性設計的影響。此份研究總共可分為三個主題，第一、在非常態性的資料下，分別引用Duncan與Alexander的成本函數於平均數管制圖的經濟統計性設計；第二、假設品質特性具備常態性與相關性，並結合Duncan的成本模式，探討平均數管制圖的經濟性設計；第三、探討非常態性與相關性的資料下，引用Duncan與Alexander的成本模式，進行平均數管制圖的經濟性設計。
　　結果顯示，在相關性資料下，使用Duncan提出的成本模式，抽樣個數隨著相關係數遞增而成遞減之狀態；抽樣間隔時間隨著相關係數遞增而遞減之趨勢；管制界限因相關係數由負轉正而變寬。在相關資料下，使用Alexander提出的成本模式，當相關係數逐漸遞增時，抽樣個數卻是呈遞減狀態；抽樣間隔時間則是隨著相關係數遞減而遞增；管制界限會隨相關係數由負轉正而變寬。如果只考慮在非常態的資料下，使用何種成本模式，抽樣個數沒有任何的變化；抽樣間隔時間卻隨著偏態、峰態的增加而有遞增之趨勢；管制界限則對偏態、峰態具有較高之穩健性。如果同時考量非常態與相關性資料時，抽樣間隔時間與管制界限會產生些微地變化。

Since 1924 when Dr. Shewhart presented the first control chart, statistical methods provide a useful application in industrial process control. Duncan (1956) proposed the first model for determining the sample size (n), the interval between successive samples (h), and the control limits of an control chart which minimizes the average cost when a single out-of-control state (assignable cause) exists.
Traditionally, when conducting the design of control charts, one usually assumes the measurements in the sample are normally distributed and independent. However, this assumption may not be tenable. If the measurements are asymmetrically distributed and correlated, the statistic will be approximately normally distributed only when the sample size n is sufficiently large and may reduce the ability that a control chart detects the assignable causes.
In this paper, the economic design of chart under non-normality and correlated samples will be developed using the Burr distribution. There are three sections in this research which including, the economic statistical design of the chart using Duncan’s and Alexander’s cost model for non-normality data; the economic design of the chart using Duncan’s cost model under normality and correlated data; the economic design of the chart using Duncan’s and Alexander’s cost model for non-normality and correlated data.
The results of comparison show that an increase in correlation coefficient leads to increases on both the sample size and the sampling interval, and a wider control limit under Duncan’s cost model with correlated data. An increase in correlation coefficient leads to decreases in the sample size, the sampling interval and a wider control limit under Alexander’s cost model with correlated data. The sample size is not significantly affected by non-normality under both Duncan’s and Alexander’s cost models. Increasing in skewness and kurtosis coefficient results in an increase in sampling interval; control limits are robust both on skewness and kurtosis coefficient under non-normality data. A slight effect may be observed under the consideration of non-normally correlated data.

目錄
頁次
中文摘要 i
英文摘要 ii
目錄 iii
表目錄 v
符號說明 vii
一、緒論 1
1.1　研究背景 1
1.2　研究目的 2
1.3　研究範圍與架構 2
1.4　研究方法與步驟 2
二、文獻回顧與探討 5
2.1　Duncan平均數管制圖之經濟性設計 5
2.2　田口損失函數 6
2.3　相關性樣本 7
2.4　Burr分配 8
三、模式建立 10
3.1　成本模式 10
3.1.1　Duncan成本模式 10
3.1.2　Alexander成本模式 11
3.2　 誤差機率 12
3.2.1　非常態下Duncan成本模式之誤差機率 12
3.2.2　非常態下Alexander成本模式之誤差機率 13
3.2.3　常態與相關性樣本下平均數管制圖之誤差機率 15
3.2.4　非常態與相關性樣本下平均數管制圖之誤差機率 16
四、模式求解與分析 18
4.1　Duncan成本模式 18
4.1.1　非常態資料下平均數管制圖之敏感度分析 19
4.1.2　常態與相關性資料下平均數管制圖之敏感度分析23
4.1.3　非常態與相關性資料下平均數管制圖之敏感度分析26
4.1.4　非常態與相關性資料下三個管制參數之敏感度分析31
4.2　 Alexander成本模式 34
4.2.1　非常態資料下平均數管制圖之敏感度分析 34
4.2.2　非常態與相關性資料下平均數管制圖之敏感度分析39
4.2.3　非常態與相關性資料下三個管制參數之敏感度分析45
五、結論 49
參考文獻 51

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