統計製程管制 (Statistical Process Control, SPC) 是監控與改善產品及製程品質的重要方法。現今高科技產業的統計製程管制中，我們常需要針對兩個或多個相關品質特性進行監控；例如半導體製造、印刷電路板及航太工業等許多工業領域之製程，皆屬多變量品質特性之範疇。若這些多變量品質特性以一個或多個解釋變數的函數關係式來表達，則稱之為多變量輪廓資料。由於我們通常無法事先知道其函數關係式，且實際資料往往亦不服從多變量常態分配。故本研究擬透過無母數迴歸模型描述輪廓資料的函數關係，並提出多變量非線性輪廓資料的監控方法。
我們首先藉由支持向量迴歸 (Support Vector Regression, SVR) 模型對輪廓資料進行模型配適，取得參考剖面 (Reference Profile)後，再計算觀測值與參考剖面間的平均絕對偏差作為其測度 (Metric)，並結合測度與SREWMA (Spatial Rank Exponential Weighted Moving Average) 提出RSREWMA (Revised Spatial Rank Exponential Weighted Moving Average) 管制圖作為第二階段不滿足共同固定設計 (Common Fixed Design, CFD) 的條件下多變量非線性輪廓資料監控的依據。接著針對製程產生偏移的各種狀況進行統計模擬，並以平均連串長度 (Average Run Length, ARL) 作為管制圖偵測能力的評估標準。最後，我們透過一組多變量非線性輪廓資料做數值實例的驗證與說明。

The SPC control charts play an important role in monitoring and improving the product and process quality. Two or more correlated quality characteristics are often required for monitoring the product and process quality in today’s high-technology industries, such as semiconductor manufacturing, printed circuit board and aerospace, etc. If the multivariate quality characteristics are assumed to be represented by functions of one or more explanatory variables, they are usually referred to as a multivariate profile data. Generally speaking, the functional relationships of the multivariate nonlinear profile data can’t be known in advance and the real data usually don’t follow a multivariate normal distribution. Thus, in this research, the functional relationships of multivariate nonlinear profile data is described via a non-parametric regression model. We first fit the multivariate nonlinear profile data and obtain the reference profiles through support vector regression (SVR) model. The differences between the observed multivariate nonlinear profiles and the reference profiles are used to calculate the vector of metrics. Then, a non-parametric revised spatial rank exponential weighted moving average (RSREWMA) control chart is proposed in the Phase II monitoring.
Moreover, a simulation study is conducted to evaluate the detecting performance of our proposed non-parametric RSREWMA control chart under various process shifts using out-of-control average run length (ARL_1). The simulation results indicate that the SREWMA control chart coupled with the metric of mean absolute deviation (MAD) can be used to monitor the multivariate nonlinear profile data when a common fixed design (CFD) is not applicable in Phase II study. Finally, a realistic multivariate nonlinear profile example is used to demonstrate the usefulness of our proposed RSREWMA control chart and its monitoring schemes.

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