管制圖在統計品質管制中具有監督和檢驗產品品質是否穩定的能力，品管人員透過管制圖即時的監控品質，並且在發現異常後馬上尋找可能造成品質變異的原因。然而傳統的單變量管制圖只能個別監控單一品質特性，無法同時監控產品品質受到多個相關品質特性影響時之多變量管制問題，於是有學者根據單變量管制圖的概念發展出多變量管制圖。
多變量管制圖主要針對多重品質特性計算出一個綜合性的統計量，並根據此統計量的大小判斷產品品質正常與否。然而多變量管制圖雖然能偵測出品質異常的發生，但是其缺點是無法在得知異常訊號時提供更明確的資訊，以告知品管人員是產品品質中某個或某些品質特性發生異常而造成整體失控訊號的產生。
因此本研究提供多變量管制一個診斷的方法，應用通用迴歸神經網路於多變量管制中平均值偏移之監控，並同時判別出造成多變量管制異常之異常品質特性。在通用迴歸神經網路績效衡量方面，以正確判別出造成異常之品質特性比率來評估網路之偵測效能，最後並比較通用迴歸神經網路與Hotelling’s T2管制法，透過模擬分析的結果驗證通用迴歸神經網路於多變量管制之適用性。

The control charts has the function to supervise and inspect the product quality whether stable or not in statistical quality control. The quality control engineers can supervise the variations through the control charts instant, and find out the reason which may cause the quality variations immediately when finding the abnormality. However, the traditional univariate control chart only can supervise the single quality characteristic separately, but not with the ability to supervise the product quality to be affected by numerous correlated quality characteristics in multivariate control state at the same time. Hence some scholars developed the multivariate control charts based on the univariate control charts concept.
The multivariate control charts mainly aim at calculate a synthetic statistic of the multiple quality characteristic on the product quality, and according to this statistic to judge the product quality whether normal or not. However, the major drawback of multivariate control charts is that could not provide any definite shift-related information to point out the main quality characteristics caused the abnormality when the control chart signals although it can detect the occurrence of the quality variations. If multivariate control charts could extend this function then it will become the real quality supervision tools for user.
This study provides a diagnosis method. Apply the general regression neural network to detect the mean shifts in multivariate control, and discriminate abnormality quality characteristic that cause the multivariate control extraordinary. At the network effects measurement, to evaluate the network performance by using the correct classification percentages of the quality characteristic which cause the abnormality. Finally, compare the general regression neural network and Hotelling’s T2 control method, through simulate and analytical results to test and verify the applicability of the general regression neural network using in multivariate control.

中文摘要i
英文摘要ii
誌謝iii
目錄iv
表目錄vi
圖目錄vii
第一章 緒論1
1.1 研究背景1
1.2 研究動機與目的1
1.3 研究範圍與假設2
1.4 論文架構3
第二章 文獻探討5
2.1 統計製程管制5
2.2 多變量統計製程管制7
2.2.1 Hotelling’s T2管制圖8
2.2.2 MCUSUM與MEWMA管制圖10
2.3 多變量管制之異常判別12
2.3.1 T2分解12
2.3.2 其他方法18
2.4 類神經網路19
2.4.1 基本概念19
2.4.2 倒傳遞網路之應用22
2.4.3 通用迴歸神經網路之應用22
第三章 通用迴歸神經網路24
3.1 GRNN簡介24
3.2 GRNN之理論背景24
3.3 平滑參數之影響27
3.4 GRNN之施行步驟29
3.5 GRNN與其他類神經網路之差異29
第四章 研究方法31
4.1 訓練樣本的產生31
4.2 GRNN多變量管制品質特性判別模式網路架構32
4.2.1 輸入訊號32
4.2.2 輸出訊號32
4.2.3 GRNN之平滑參數33
4.2.4 網路績效指標33
第五章 結果與分析35
5.1 模擬資料35
5.1.1 兩個品質特性35
5.1.2 三個品質特性43
5.2 案例分析47
5.2.1 案例一47
5.2.2 案例二50
第六章 結論與建議53
參考文獻54
附錄一58
附錄二59
附錄三60
附錄四61

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