運用重排資料改善統計製程管制圖

Abstract

我們考慮一個改善SPC的方法，先將每個樣本資料加上間隔差1的數列，作排序後，利用得到的排序數列再指回去原對應的樣本資料，即可得到一組新的數列，此新數列中會發現兩個樣本資料間會產生負相關，將其運用至管制圖上，即可製成非傳統的管制圖。且在跟傳統管制圖有相同型I誤差下，因為負相關使變異數降低，所以型II誤差也會降低，進而提升檢定力，而能在不良品產生前更快偵測出錯誤，以提高企業的競爭力及生產力。

We consider a method that improves the SPC. Firstly, add i to each sample datum at time i the one difference interval sequence. After arranging the sequence in order, we retrieve the arranged sequence to the corresponding original sample data. A new sequence of the data is thus obtained. In the new sequence, we can find the negative correlation between two sample data. We apply the negative correlation to the control chart. Then we can create a non-traditional control chart. Within the similar type I error, the risk of type II will be lowered down because negative correlation reduces the variance. This increases the power and it can detect error very fast before defect is happened. From here, it improves company competitive advantages and increases productivity.