在工業產品製程中，管制圖為監控產品品質重要的工具。大多數的產品資料屬於多維度且不一定服從常態分配，因此無分配假設的多維度管制圖之研究更是相當重要。本文提出結合資料深度 (data depth) 與符號管制圖 (sign chart) 。建立一個新的指數加權移動平均 (EWMA) 的追蹤統計量來監控產品製程平均數向量是否有失控，並利用平均連串長度 (ARL) 來衡量所提出的新管制圖的表現。此外，我們加入變動抽樣區間時間 (VSI) 的監控技巧與考慮變動維度 (VD)的想法以降低偵測製程失控所需的時間及成本。我們利用管制圖偵測出異常訊息所需的平均時間 (ATS) 來衡量所提出之VSI管制圖。接下來與文獻上存在的管制圖做偵測力表現比較。經由許多不同平均數偏移情況的數值比較分析後，本文所提出的管制圖在製程平均數偏移幅度中等及大時，比其他管制圖有更好的偵測效果。因此，建議可以使用本文提出的新管制圖追蹤製程平均數向量。最後以礫石資料及半導體製程資料來示範本文所提出的管制圖之應用。

In industrial product process, control chart is an important tool for monitoring the process quality. Since many data are multivariate and do not follow normal distribution, this makes traditional Shewhart control charts cannot be applied. So the study of non-normal multivariate control chart is very important.
This paper combines the methods of data depth and constructing sign chart to design a new exponentially weighted moving average (EWMA) chart for monitoring the multivariate process location. Performance measurement of the proposed control chart is the average run length (ARL). In addition, techniques for variable sampling interval (VSI) and variable dimension (VD) are added to reduce the detection time of an out-of-control process and sampling cost of detecting the out-of-control process. Performance measurement of the proposed VSI control chart is using the average time to signal (ATS) under an out-of-control process.
We would compare the detection performance of the proposed control charts with existing control charts exist in the literatures. The proposed charts show superior detection performance compared the existing control charts when the mean shifts is medium and large under the out-of-control process. Therefore, it is recommended that the proposed control charts in this paper might be applied to detect the shifts in process location. Finally, we would demonstrate the proposed control charts via using gravel data and semiconductor process data.

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