管制圖是統計品質管制中重要的工具，一般狀況管制圖通常是在常態假設下利用管制圖進行監控，若直接以管制圖監控非常態製程，將會造成製程監控與製程能力指標判斷的錯誤。
本研究探討多變量管制圖監控二維變量非常態製程之績效，首先模擬出二維非常態製程資料，再應用多變量常態性轉換法，將多變量非常態製程轉換至常態，並以P-P圖與卡方機率圖作常態性分析與檢定，再以Hotelling’s 管制圖進行監控，分析製程之平均連串長度ARL0。另外也探討當二維非常態分配製程產生偏移時，製程同時產生偏移與一個維度製程的偏移情況，分析平均連串長度ARL1在此兩種偏移情形之差異。
研究中針對不同的樣本數、相關係數進行模擬。結果顯示樣本數越大， 管制圖製程監控績效較佳；相關係數越高影響製程績效較大，當製程產生偏移時，相關係數對於製程一個維度偏移的影響較大。由模擬結果中顯示，以Hotelling’s 管制圖監控經多變量常態性轉換後的非常態分配製程績效，其製程的誤警率會因而降低。

Monitoring process by using control chart is one of the primary techniques in statistical process control (SPC). Basically, most of control charts function well when the underlying distribution of inspected characteristics follows normal. If the underlying distribution deviates from normal, it may cause a serious mistake of judgment in monitoring the capability of manufacturing.
In this research, we discuss the performance of a multivariate control chart when the inspected 2 correlated variables is non-normal distributed. Firstly, we simulate a set of non-normal two-dimension manufacturing data, then, the simulated data is transformed to normal data by the Multivariate transformation method. We assure the distribution of the transformed data by these data under which the P-P plot and chi-square probability plot. The average of run length (ARL) of the Hotelling’s T 2 control chart is treated as our performance index in this study. We also discuss various conditions with the shift of process mean which in one or two dimensions. The ARLs under those conditions are calculated and compared.
In our experiments, we compare the vary of ARL under different combination of sample sizes and correlation. The results show that the performance of T 2 control chart gets better with the increasing of sample sizes, regardless of the correlation and shape parameter of Gamma distribution. The manufacturing effects increase with the increasing of correlation. The affection of performance is higher with a larger correlation. When the process is out of control, the study shows that effect of correlation to the process is relatively higher when the shift of only in single-mean occurs dimension. Also, the simulation study reveals that false alarm rate of manufacturing effects of Hotelling’s control chart is decreased after a multivariate normal transformation is applied to the process.

摘 要.....................................................i
英文摘要..................................................ii
圖目錄...................................................vii
表目錄.....................................................x
第一章 緒 論.............................................1
1.1 研究背景與動機........................................1
1.2 研究目的..............................................2
1.3 研究範圍與假設........................................3
1.4 研究架構與流程........................................3
第二章 文獻回顧與探討.....................................6
2.1 單變量管制圖..........................................6
2.1.1 單變量管制圖之介紹..................................6
2.1.2 EWMA管制圖之相關研究 ...............................8
2.2 多變量管制圖..........................................8
2.2.1 Hotelling’s T 2管制圖.............................10
2.2.2 Hotelling’s T 2管制圖之相關研究...................13
2.2.3 MEWMA管制圖 .......................................15
2.2.4 MEWMA管制圖之相關研究..............................16
2.3 非常態資料之轉換法...................................17
2.3.1 Box-Cox轉換法之介紹................................17
2.3.2 Johnson轉換法......................................19
2.3.3 Box-Cox轉換法之介紹之相關研究......................20
2.4 資料模擬.............................................20
第三章 研究方法..........................................24
3.1 資料模擬與參數設定...................................25
3.1.1 資料模擬...........................................25
3.1.2 Gamma分配..........................................25
3.2 多變量常態轉換法之應用...............................27
3.3 常態性檢定...........................................29
3.3.1 單變量常態性檢定...................................29
3.3.2 多變量常態性檢定...................................30
3.4 Hotelling’s T2管制圖之監控績效 .....................33
3.5 電腦之模式驗證.......................................33
3.5.1 假設...............................................33
3.5.2 參數設定...........................................33
3.5.3 常態轉換法.........................................34
3.5.4 計算ARL............................................34
第四章 多變量非常態製程監控之模式驗證....................35
4.1 多變量常態分配之驗證.................................35
4.2 Hotelling’s T2管制圖監控績效........................38
第五章 結論與未來研究方向................................62
5.1 結論 ................................................62
5.2 建議與未來研究方向...................................63
參考文獻..................................................64
附錄A.....................................................66
附錄B.....................................................78
B.1 資料模擬之驗證 .......................................78
B.2 T2統計量之驗證........................................79
B.3 T2管制圖之驗證 .......................................79
B.4 單一shewhart管制圖....................................84

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