利用OAAT方法監控第一階段非線性剖面資料之研究

Abstract

Shiau 和 Sun (2006) 針對第一階段製程監控提出OAAT法，即研究一次只剔除一個最極端的管制外樣本點的作法。模擬研究顯示，「OAAT」法可大幅降低假警報之發生，因此，我們將此方法推廣到剖面資料的監控。本文使用一個建構於加權最小橢球體積(Reweighted Minimum Volume Ellipsoid)估計量之 T2 控制圖來監控剖面資料。我們比較OAAT法和傳統的方法(每次管制界限外的樣本點全部刪除)的假警報率(製程在穩定狀態，但監控統計量落在管制界限建以外的比例)和偵測力(製程發生改變，而監控統計量落在管制界限以外）。我們證明OAAT法可以降低製程監控的假警報，而且研究結果也發現當製程偏移的夠大和管制界限是單邊的時候，這兩個方法的假警報是非常接近的。因為傳統的方法在計算上是較經濟的，所以我們提出一個統計量當準則去決定何時使用哪個方法，可使製程監控更精確更有效率。最後，我們利用兩個真實資料去證明我們所提出的理論方法。

Shiau and Sun (2006) proposed an one-at-a-time (OAAT) scheme for Phase I process monitoring that only discards the most extreme out-of-control sample at a time. Using Shewhart chart as an example, they demonstrated that the OAAT scheme reduces dramatically the occurrences of false alarms. In this paper, we extend this scheme to nonlinear profile monitoring. We consider a T2 chart constructed based on the reweighted minimum volume ellipsoid (RMVE) for profile monitoring. We compare the false-alarm rate (the possibility that an in-control sample is claimed as out of control) and detecting power (an out-of-control sample is detected) of the OAAT scheme with that of the traditional delete-all scheme and confirm that the OAAT scheme reduces the false-alarm rates while attaining the detecting power in profile monitoring. It is also found that when the process shift is large enough, the false-alarm rates of the two schemes are very close for one-sided control charts. Since the Delete-All scheme is more economic in computation, we provide a statistic as a guide on when to use it for achieving the efficiency. Finally, we demonstrate the methodologies described in the thesis with two real-life examples.