用無母數迴歸方法監控曲線型品質特性之製程

Abstract

此篇論文的重點在，對品質特性為一個函數或一條曲線的製程，我們提出一些新的控制圖來做監控；除了平滑的假設外，在此不限定曲線的形式。 我們提出了三個新的監控方法：(1)用無母數迴歸方法“B-spline”對曲線做配適，再利用T2控制圖對製程做監控；(2)用典型的控制圖EWMA、EWMSD或R控制圖對樣本曲線和參考曲線間的殘差做監控；(3)用事先制定的測度(metrics)及其臨界值對品質特性曲線做監控。 經過多次的模擬，利用平均連串長度(ARL)來比較所有方法，結果顯示在曲線型品質特性為指數函數時，我們所提出的新方法都表現得相當良好。最後在面對製程的各種偏移情形，該使用何種控制圖做監控，我們也提出了一些建議。

In this paper, we propose and study some control chart methods for monitoring processes for which the quality is characterized by a profile or a function. No assumptions are made on the form of the function except that it represents a smooth curve. Three approaches of monitoring schemes are proposed: (1) Use the “B-spline” smoothing method to fit the profiles of processes and design a T2 chart to monitor the deviations of the sample profiles from the in-control reference profile. (2) Use typical control charts – the EWMA, or EWMSD, or R chart to monitor the residuals between the sample profiles and the in-control reference profile. (3) Use some metrics defined to measure the deviations of the sample profiles from the in-control reference profile to monitor the sample profiles. We construct a simulation study using an exponential profile as an example to investigate the effectiveness of the proposed schemes. The performances of these schemes are evaluated and compared in terms of the average run length. The results of the simulation study show that all approaches appear to perform well for exponential profiles. It is found that some control schemes are preferable to others for particular types of process changes.