應用移動和管制圖於監控高產出製程之研究

On Using the Moving Sum Control Chart for Monitoring High-Yield Processes

陳榮泰(Jung-Tai Chen)

《品質學報》 22卷6期 (2015/12) Pp. 507-535

https://doi.org/10.6220/joq.2015.22(6).02

摘要

傳統製程不良率 (nonconforming fraction, p) 之管制常以不良率管制圖 (p chart) 或不良數管制圖 (np chart) 為之，然而當現今高產出製程其製程不良率很低的時候，因為此等管制圖所得出之下管制界限為零，形同是一單邊管制圖，雖仍可監測製程良率之惡化，卻無法偵測製程良率之提升，從而其管制效果受到限制；文獻對此提出的解決方法之一：透過管制每檢測出r 個不良品的累積生產件數C_i (cumulative count of conforming)來達成管制製程不良率之目的，此管制圖稱為CCC-r管制圖。在CCC-r管制圖中，直覺地如果所採取的r值越大會有較好的管制效果，然而因為CCC-r管制圖須等到每檢測出r件不良品，才能根據Ci是否在逸出上下管制界限之外，來判定製程失控與否，因而一個較大的r值雖可有較好的管制效果，然而卻也錯失一些判定製程失控與否的時機。有鑑於此，本研究提出一以移動和(moving sum)為判定基礎之管制圖（簡稱MS-CCC-r管制圖），來達成進一步提升管制效果之目的。以r =3為例，點繪在MS-CCC-r管制圖之第1個樣本點為檢測出第1件不良品的累積生產件數，第2個樣本點為檢測出第2件不良品的累積生產件數，第3個樣本點為檢測出第3件不良品的累積生產件數，第4個樣本點為檢測出第1件不良品迄檢測出第4件不良品的累積生產件數，之後依此類推。經與其他管制方法：CCC-r、conditional CCC-1、CCC-1配合k-of-k連串法則等三種管制圖比較之後，結果顯示MS-CCC-r管制圖之管制效果優於其他三種管制圖。本文最後以一組模擬之製程數據來說明MS-CCC-r管制圖之應用。

關鍵字

移動和 ； 負二項分配 ； 平均連串長度(ARL) ； 平均觀測值個數(ANOS) ； 馬可夫鏈

並列摘要

The p chart or np chart has been used to monitor fraction nonconforming (p) in practice. However, as p has become low in contemporary manufacturing, the lower control limits of these charts are zero. This will limit the use of these charts. One of alternative charts to this problem is called the cumulative count of conforming chart (CCC-r chart). In a CCC-r chart, the number of items until the rth nonconforming item is plotted to monitor p. Intuitively, the larger the value of r, the better the performance of the CCC-r chart. Since in a CCC-r chart, the users have to wait for r nonconforming items produced to determine whether the process is in control or not, they miss some opportunities to make decision about the process. Hence, this research will propose a new control chart based on the moving sum, referred to as the MS-CCC-r chart, to further improve the performance of the CCC-r chart. A comparative study on the MS-CCC-r chart with three other charts (CCC-r, conditional CCC-1, CCC-1 with k-of-k runs rule) is performed to reveal the performance of the MS-CCC-r chart. The comparative results show that the MS-CCC-r chart has the better performance than the others.

並列關鍵字

moving sum ； negative binomial distribution ； average run length (ARL) ； average number of observations to signal (ANOS) ； Markov chain

參考文獻

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