本文主要探討的議題是圓柱體製程輪廓模型的管制圖監控。首先我們會說明如何以線性輪廓來描繪圓柱體製程的資料。在現有的輪廓監控方法當中，大多數都對模型誤差項假設為常態分配，而我們所利用的無母數監控管制圖搭配無母數的線性輪廓參數估計方法，能使得當圓柱體線性輪廓模型的誤差項非常態分佈時，管制圖依然能夠擁有良好的監控效率。此外，我們也在管制圖發生失控警訊後提出後續的改變點估計與參數診斷方法，以便找出輪廓發生偏移的時間點與發生偏移的參數。在本文中，我們會先介紹圓柱體的線性輪廓模型以及所使用的無母數監控方法。接著我們會以統計模擬的方式來評估這個無母數輪廓監控管制圖的監控效率，並和現有的輪廓監控有母數管制圖進行比較。我們也會用統計模擬來評估無母數管制圖發生失控警訊後，改變點估計和參數診斷方法的準確度。最後，我們會使用一組引擎汽缸的圓柱體資料來說明本文所利用的無母數管制圖在實務上的使用效果。

The main topic discussed in this article is to use control charts to monitor cylinder profiles. First, we explain how to describe data of cylinders using linear profiles. In the existing profile monitoring methods, error term in models is usually assumed to be normally distributed. However, in certain applications including cylinder linear profiles, the error term may not be normal. Therefore, we use a robust estimation method to estimate the parameters in the profiles and a nonparametric control chart to monitor cylinder linear profiles. The proposed control chart is show to have a great monitoring efficiency when the error term is not normal. In addition, we also propose a change point estimation method and parameters diagnosis method after the out-of-control signal occurs. The rest of the paper is organized as follows. We first introduce the linear profile models for cylinders and the nonparametric monitoring method that will be used. Then, we use statistical simulation to evaluate the monitoring efficiency of the proposed control chart and compare with an existing parametric control chart. We also present the accuracy of the change point estimation and parameters diagnosis method after the out-of-control signal occurs. Finally, we apply our method to engine cylinder data as a practical example.

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