A Support Vector Regression Based Control Procedure for Detecting a Range of Unknown Mean Shifts

應用支援向量回歸於製程平均數變化之監控

陳佩雯(Pei-Wen Chen) ； 黃國格(Kuo-Ko Huang) ； 李彥儒(Yen-Lu Lee) ； 鄭春生(Chuen-Sheng Cheng)

《品質學報》 22卷5期 (2015/10) Pp. 427-440

https://doi.org/10.6220/joq.2015.22(5).04

摘要

累積和管制圖（CUSUM）之績效，主要是由管制圖所要偵測的偏移量大小和預設之參數來決定。由於製程之偏移量通常無法事先得知，因此，我們需要一個有效的管制方法，能夠偵測一個範圍內之平均數偏移。在過去，使用多個累積和管制圖（CUSUM multi-chart）可以達到此種製程目的。本研究以支援向量回歸（support vector regression, SVR）為基礎，建立一個製程平均數之監控方法。此SVR可以監控製程平均數之變化，其輸入向量包含CUSUM管制圖之管制統計量及一些相關的特徵。本研究使用平均連串長度（average run length, ARL）做為績效指標。模擬結果顯示，本研究所提出之 SVR 可以比多個累積和管制圖更快的偵測到一個範圍內之平均數偏移。

關鍵字

累積和管制圖 ； 平均數偏移 ； 支援向量回歸 ； 平均連串長度

並列摘要

Cumulative sum (CUSUM) control scheme is an effective alternative to the Shewhart control chart to detect small process shifts. It is well known that the performance of CUSUM charts mainly depends on the pre-specified size of the shifts in the monitored quality characteristics. Since the shift size is usually unknown in advance, a control method capable of detecting a range of shifts is therefore required. The combination of several CUSUM charts (called CUSUM multi-chart) has been proposed to deal with this problem. This paper presents a support vector regression (SVR) based method to monitor the stability of process mean. The input vector of SVR comprises a mixture of charting statistics and statistical features that allow for the quick detection of a range of mean shifts. The performance of the proposed SVR was evaluated in terms of average run length (ARL). An extensive simulation study shows that the proposed method is better than the CUSUM multi-chart in detecting a range of mean shifts, especially for moderate to large shifts.

並列關鍵字

CUSUM multi-chart ； mean shifts ； support vector regression ； ARL

參考文獻

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