A CONTROL CHART BASED ON MOVING AVERAGE AND MOVING RATIO FOR MONITORING WEIBULL DATA

應用移動平均與移動比值監控韋伯資料之研究

10.6220/joq.201808_25(4).0001

陳榮泰(Jung-Tai Chen)

Weibull distribution ； moving average ； moving ratio ； shape parameter ； scale parameter ； 韋伯分配 ； 移動平均 ； 移動比值 ； 型態參數 ； 尺度參數

品質學報

25卷4期（2018 / 08 / 30）

211 - 240

英文

This study focuses on monitoring the joint shifts of the shape parameter c and the scale parameter θ for Weibull data. Previous work on this issue demonstrated an undesired phenomenon, the so-called average run length-biasedness (ARL-biasedness). To eliminate this phenomenon, this study proposes a novel control scheme, the MA-MRa chart: a moving average (MA) chart combined with a moving ratio (MRa) chart. An analytical approach is developed to compute the performance of the proposed chart. A simulation study shows that the analytical approach is reasonably accurate in estimating the performance of the proposed chart. In addition, a comparative study is conducted to show that the proposed chart outperforms the other charts. Finally, an example demonstrates how to apply proposed chart.

本研究旨在探討同時偵測韋伯資料其型態參數c與尺度參數θ之偏移，文獻有關此議題的研究呈現出所謂的平均連串長度偏誤(average run length-biasedness, biasedness)的情形，此一情形將對管制圖的管制效果產生不利的影響。為了解決此問題，本研究提出以一新的移動平均管制圖，搭配移動比值管制圖，來同時管制韋伯資料其型態參數與尺度參數；並提出一解析方法以計算此管制圖之管制績效，模擬結果顯示此解析方法有非常合理的準確性，之後應用此解析方法並配合窮舉搜尋求出此管制圖的管制界限，以供實務界參採。研究結果顯示，在與文獻所提的方法相較之下，本研究有較好的管制效果。最後以一例子，示範如何使用本研究所提出的管制圖。

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