本論文針對反應變數與輔助變數可能不服從常態分配假設的問題，希望考慮參數管制圖容易操作的優點與輸入變量的抽樣分配提供彈性選擇，對運用單一輔助變數資訊的產品品質特徵均值的監控，設計出一套具體可行的管制圖方法。我們使用線性方程式將反應變數與輔助變數之間的關係模型化，並利用最小極值分配來取代常態分配，放寬常態分配假設的限制，建議使用多變量符號指數加權移動平均 (MSEWMA) 管制圖針對多變量參數估計量對製程進行監控，以解決反應變數與輔助變數的分配可能不為常態分配的難題。模擬結果發現MSEWMA管制圖有不錯的監控製程偏移績效，也評估MEWMA管制圖與Hotelling T^2管制圖的監控績效。最後，我們使用一組汽車煞車系統的模擬資料示範MSEWMA管制圖的操作。

In statistical process control applications, the distributions of the response and auxiliary variables could not be normal. Assume that the relationship between the response and auxiliary variables is linear, a new process monitoring method is proposed to monitor the conditional mean response when the value of auxiliary variable is given. We assume that the response and auxiliary variables follow smallest extreme value distributions and use the estimates of model parameters as input variables. Then the multivariate sign exponential weighted moving average control chart is recommended to monitor the process. Simulation results show that the proposed monitoring method works better with less false alarms than the Hotelling T^2 and multivariate exponential weighted moving average control charts to release the multivariate normal distribution assumption for the input vectors of the estimates of model parameters. Finally, the operation of the proposed monitoring method is demonstrated through using an example of car brake system.

目錄

論文提要	                        I
目錄	                        IV
圖目錄		                V
表目錄		                VII
第一章 緒論	                1
1.1 研究主題概述與文獻回顧	1
1.2 研究動機與論文架構           	7
第二章 使用輔助變數之MSEWMA管制圖	10
2.1 統計模型	                10
2.2 MSEWMA管制圖          	14
第三章 模擬研究	                18
第四章 案例研討              	32
第五章 結論	                39
參考文獻	                        42

圖目錄

圖3.1：在ARL_0=200，m=800，1000，1200，1500之下，MSEWMA、MEWMA與Hotelling T^2管制圖的ARL值	                          22
圖3.2：在ARL_0=370，m=800，1000，1200，1500之下，MSEWMA、MEWMA與Hotelling T^2管制圖的ARL值	                          22
圖3.3：在ARL_0=500，m=800，1000，1200，1500之下，MSEWMA、MEWMA與Hotelling T^2管制圖的ARL值	                          23
圖4.1：45個殘差值之直方圖	                                  34
圖4.2：45個殘差值之機率圖	                                  34
圖4.3：在λ=0.2，ARL_0=370之下，前250筆模擬資料建構的MSEWMA管制圖                                                        36
圖4.4：在λ=0.2，ARL_0=370之下，後75筆模擬資料建構的MSEWMA管制圖	                                                  36
圖4.5：在λ=0.2，ARL_0=370之下，前250筆模擬資料建構的MEWMA管制圖	                                                  37
圖4.6：在λ=0.2，ARL_0=370之下，後75筆模擬資料建構的MEWMA管制圖	                                                  37
圖4.7：在ARL_0=370之下，前250筆模擬資料建構的Hotelling T^2
管制圖	                                                  38
圖4.8：在ARL_0=370之下，後75筆模擬資料建構的Hotelling T^2
管制圖	                                                  38


表目錄

表3.1： 最大概似估計量與最小平方－最大概似估計量的模擬比較	  19
表3.2： Phase I MSEWMA管制圖在 m=300，500，800，1000，   1200，1500與λ=0.2之下的ARL值	                          20
表3.3：管制狀態下MEWMA管制圖與Hotelling T^2管制圖           在 m=800，1000，1200，1500與λ=0.2之下的ARL值	          21
表3.4：位置參數μ_W失控狀態8種組合下MSEWMA管制圖在 m=1000與 λ=0.1之下的ARL_1值	                                  24
表3.5：位置參數μ_W失控狀態8種組合下MSEWMA管制圖在 m=1000與 λ=0.2之下的ARL_1值	                                  25
表3.6：迴歸係數b_0失控狀態8種組合下MSEWMA管制圖在 m=1000與 λ=0.1之下的ARL_1值	                                  27
表3.7：迴歸係數b_0失控狀態8種組合下MSEWMA管制圖在 m=1000與 λ=0.2之下的ARL_1值	                                  27
表3.8：迴歸係數b_1失控狀態8種組合下MSEWMA管制圖在 m=1000與 λ=0.1之下的ARL_1值	                                  27
表3.9：迴歸係數b_1失控狀態8種組合下MSEWMA管制圖在 m=1000與 λ=0.2之下的ARL_1值	                                  28
表3.10：尺度參數σ_W失控狀態8種組合下MSEWMA管制圖在 m=1000與 λ=0.1之下的ARL_1值	                                  30
表3.11：尺度參數σ_W失控狀態8種組合下MSEWMA管制圖     
在 m=1000與 λ=0.2之下的ARL_1值	                          30
表3.12：尺度參數σ_ϵ失控狀態8種組合下MSEWMA管制圖
在 m=1000與 λ=0.1之下的ARL_1值	                          30
表3.13：尺度參數σ_ϵ失控狀態8種組合下MSEWMA管制圖
在 m=1000與 λ=0.2之下的ARL_1值	                          31
表4.1 ： Constable et al. (1988) 提供的70筆數據    	  32
表4.2 ：經轉換的前45筆數據	                          33

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