系統識別號 | U0002-2208201815180600 |
---|---|
DOI | 10.6846/TKU.2018.00673 |
論文名稱(中文) | 一階自我相關多變量簡單線性輪廓的監控 |
論文名稱(英文) | On the monitoring of first-order autocorrelated multivariate simple linear profiles |
第三語言論文名稱 | |
校院名稱 | 淡江大學 |
系所名稱(中文) | 統計學系應用統計學碩士班 |
系所名稱(英文) | Department of Statistics |
外國學位學校名稱 | |
外國學位學院名稱 | |
外國學位研究所名稱 | |
學年度 | 106 |
學期 | 2 |
出版年 | 107 |
研究生(中文) | 林品瑩 |
研究生(英文) | Ping-Ying Lin |
學號 | 605650232 |
學位類別 | 碩士 |
語言別 | 繁體中文 |
第二語言別 | |
口試日期 | 2018-07-05 |
論文頁數 | 74頁 |
口試委員 |
指導教授
-
王藝華
委員 - 李百靈 委員 - 林建華 |
關鍵字(中) |
多變量簡單線性輪廓 一階自我相關 MEWMA 管制圖 輪廓監控 |
關鍵字(英) |
Multivariate simple linear profiles First order autocorrelation MEWMA control chart Profile monitoring |
第三語言關鍵字 | |
學科別分類 | |
中文摘要 |
近年來,輪廓監控常用來監控產品品質的統計製程管制方法,當一產品的品質好壞可以用解釋變數和反應變數之間的函數關係來描述時,透過監控品質函數關係是否發生改變來判斷產品或製程品質是否穩定,此函數資料即稱為輪廓,而此種監控方法即稱為輪廓監控。在相關的文獻探討過程中,發現多數的文獻中模型都是假設隨機誤差項之間是獨立的,但是在實際的情況下,連續製程會造成輪廓間或輪廓內的相關性,且單變量管制圖常無法滿足現實生活的應用,因此本文針對多變量簡單線性模型且隨機誤差項之間存在一階自我相關性下,提出兩種新管制方法來監控此輪廓資料監控的效率,並與Soleimani 和Noorossana(2014) 所提出的的三種監控方法做比較。從模擬結果可以得知,我們所提出的管制方法監控 效果比舊有的管制方法來的好。 |
英文摘要 |
In recent years, profile monitoring, a method of statistical process control, is often used to monitor the quality of a process or product. When the quality of the product can be described by a functional relationship between explanatory variables and response variables, one can determine whether the quality of a product or process is in-control by monitoring the stability of the functional relationship. The functional data is called a profile, and this kind of monitoring method is called profile monitoring. In the literature, most of the used models are assumed to be independent for the random errors. However, in real applications, the continuous process are often cause between or within correlation, and single variable control charts are often unable to meet the real applications, Therefore, in this article, we propose two control charting schemes to monitoring first-order autocorrelation multivariate simple linear profile data and compare with the schemes proposed by Soleimani and Noorossana(2014). By the simulation results, our proposed schemes have better performance than the existing schemes. |
第三語言摘要 | |
論文目次 |
目錄 第一章緒論...................................... 1 1.1 前言........................................ 1 1.2 文獻回顧..................................... 2 1.3 研究動機與目的................................ 5 第二章現有的輪廓監控方法........................... 6 2.1 T2 管制方法....................................... 8 2.2 MEWMA=c2 管制方法............................... 8 2.3 MEWMA3 管制方法............................... 9 第三章新的輪廓監控方法................................. 11 3.1 V-MEWMA 管制方法......................... 12 3.2 F-MEWMA 管制方法......................... 13 第四章模擬結果與分析.................................... 14 4.1 管制圖的比較準則.............................. 14 4.2 一階自我相關多變量簡單線性模型的模擬設定..............14 4.2.1 單一參數的改變.................................. 15 4.2.2 兩兩參數的改變......................... 18 4.2.3 解釋變數正交化後的模型,兩兩參數的改變............. 23 第五章範例資料....................................... 28 第六章結論與未來研究.................................... 30 附錄.............................................. 31 附錄A.............................................. 31 附錄B................................................ 36 參考文獻................................................ 38 表目錄 表一: 截距參數變動,在不同狀況下,表現較佳的管制圖之整理. . . . . . . . 17 表二: 斜率參數變動,在不同狀況下,表現較佳的管制圖之整理. . . . . . . . 17 表三: 變異數變動,在不同狀況下,表現較佳的管制圖之整理. . . . . . . . . . 18 表四: 截距和斜率同時變動時,在不同狀況下,表現較佳的管制圖之整理. . . 20 表五: 截距和變異數同時變動時,在不同狀況下,表現較佳的管制圖之整理. . 21 表六: 斜率和變異數同時變動時,在不同狀況下,表現較佳的管制圖之整理. . 22 表七: 解釋變數正交化後的模型,截距和斜率同時變動時,在不同狀況下,表 現較佳的管制圖之整理. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 表八: 解釋變數正交化後的模型,截距和變異數同時變動時,在不同狀況下, 表現較佳的管制圖之整理. . . . . . . . . . . . . . . . . . . . . . . . . . . 26 表九: 解釋變數正交化後的模型,斜率和變異數同時變動時,在不同狀況下, 表現較佳的管制圖之整理. . . . . . . . . . . . . . . . . . . . . . . . . . . 27 表1.1 當整體ARL0 200 且w = 0.2 時,Soleimani 和Noorossana(2014) 所使 用的管制界限(其中括號內為標準差) . . . . . . . . . . . . . . . . . . . . . 42 表1.2 當整體ARL0 200 且w = 0.2 時,各管制方法所使用的管制界限. . . 42 表2 : 當b01 !b01+l0s1 時,各管制方法的ARL1 值. . . . . . . . . . . . . . 43 表3 : 當b11 !b11+l1s1 時,各管制方法的ARL1 值. . . . . . . . . . . . . . 44 表4 : 當s1 !gs1 時,各管制方法的ARL1 值. . . . . . . . . . . . . . . . . . 45 表5.1 : 當b01 ! b01 +l0s1 與b11 ! b11 +l1s1 時,MEWMA/c2 與VMEWMA 的ARL1 值比較. . . . . . . . . . . . . . . . . . . . . . . . . . 46 III 表5.2 : 當b01 !b01+l0s1 與s1 !gs1 時,MEWMA/c2 與V-MEWMA 的 ARL1 值比較. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 表5.3: 當b11 !b11+l1s1 與s1 !gs1 時,MEWMA/c2 與V-MEWMA3 的 ARL1 值比較. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52 表6.1 : 解釋變數正交化後的模型,當b01 !b01 +l0s1 與b11 !b11 +l1s1 時,MEWMA/c2 與V-MEWMA 的ARL1 值比較. . . . . . . . . . . . . 55 表6.2 : 解釋變數正交化後的模型, 當b01 !b01 +l0s1 與s1 !gs1 時, MEWMA/c2 與V-MEWMA 的ARL1 值比較. . . . . . . . . . . . . . . 58 表6.3 : 解釋變數正交化後的模型, 當b11 !b11 +l1s1 與s1 !gs1 時, MEWMA/c2 與V-MEWMA 的ARL1 值比較. . . . . . . . . . . . . . . 61 表7 : 實際範例中,V-MEWMA 管制方法監控統計量的值. . . . . . . . . . . . 64 圖目錄 圖1. 當b01 !b01 +l0s1 時,在不同的自我相關係數之下,各管制方法的 ARL1 值. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65 圖2. 當b11 !b11 +l1s1 時,在不同的自我相關係數之下,各管制方法的 ARL1 值. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66 圖3. 當s1 !gs1 時,在不同的自我相關係數之下,各管制方法的ARL1 值. 67 圖4.1 : 當b01 ! b01 +l0s1 與b11 ! b11 +l1s1 時,MEWMA/c2 與VMEWMA 之管制效率的比值. . . . . . . . . . . . . . . . . . . . . . . . . 68 圖4.2 : 當b11 !b11+l1s1 與s1 !gs1 時,MEWMA/c2 與V-MEWMA 之 管制效率的比值. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69 圖4.3 : 當b11 !b11+l1s1 與s1 !gs1 時,MEWMA/c2 與V-MEWMA 之 管制效率的比值. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70 圖5.1 : 解釋變數正交化後的模型,當b01 !b01 +l0s1 與b11 !b11 +l1s1 時,MEWMA/c2 與V-MEWMA 之管制效率的比值. . . . . . . . . . . . 71 圖5.2 : 解釋變數正交化後的模型, 當b11 !b11 +l1s1 與s1 !gs1 時, MEWMA/c2 與V-MEWMA 之管制效率的比值. . . . . . . . . . . . . . 72 圖5.3 : 解釋變數正交化後的模型, 當b11 !b11 +l1s1 與s1 !gs1 時, MEWMA/c2 與V-MEWMA 之管制效率的比值. . . . . . . . . . . . . . 73 圖6 : 監控b 0 、b 1 以及標準差的V-MEWMA 管制方法. . . . . . . . . . . . . 74 |
參考文獻 |
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