現今製造業的產品或製程的品質特性大多可用一個反應變數對多個解釋變數的函數關係式來表達，這種函數關係式所產生的資料類型稱為輪廓資料 (profile data)。而輪廓資料的函數關係式大致上可分為線性與非線性關係。但我們通常無法輕易地表達其關係式，且實際資料亦往往不服從常態分配。針對此一情況，在沒有任何分配的假設下，本研究利用無母數迴歸模型表達輪廓資料的函數關係，並發展出無母數的輪廓監控方法。
我們首先藉由支援向量迴歸 (support vector regression, SVR) 對輪廓資料進行模型配適並透過 SVR 模型得到配適值，再求算其測度 (metrics)。以期結合測度與本研究所提出的無母數 EWMA 管制圖作為監控第 II 階段輪廓資料的依據。接著我們利用統計模擬的方式，針對製程產生偏移的各種狀況以平均連串長度 (average run length, ARL) 作為無母數 EWMA 管制圖偵測能力的評估標準。最後，透過一組非線性輪廓資料進行數值實例的驗證與說明。

In today’s manufacturing industries, if the quality characteristic of a product or a process is assumed to be represented by a functional relationship between the response variable and one or more explanatory variables, then the data generated from such a relationship is called profile data. Generally speaking, the functional relationship of the profile data can’t be known in advance and the real data usually are not follow normal distribution. Thus, the functional relationship of profile data is described via a non-parametric regression model, and a revised non-parametric EWMA control chart is proposed in the Phase II monitoring.
In this research, we first fit the profile data through a support vector regression (SVR) model, then the fitted values are used to calculate the metrics. It is expected that the revised non-parametric EWMA control chart coupled with the metrics can be used for monitoring the profile data in the phase II study. Moreover, a simulations study is conducted to evaluate the detecting performance of the new control chart under various process shifts using average run length (ARL). Finally, a realistic nonlinear profile example is used to demonstrate the usefulness of our proposed non-parametric EWMA control chart and its monitoring schemes.

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