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。