應用計數值管制圖於高產出製程之研究

The development of attributes control chart for high-yield process

陳佩雯(Pei-Wen Chen)

指導教授 ： 鄭春生

元智大學/工程學院/工業工程與管理學系/碩士(2004年)

摘要

由於p管制圖是假設二項分配滿足逼近常態分配之前提下所建立，當製程不合格率p0很低時，會因二項分配無法滿足常態性假設之條件，而造成p管制圖錯誤警告增加。且因不合格率小，管制圖上易出現許多為零的點，而管制下限亦容易產生等於零之情形，無法作為判斷製程是否有顯著改善之依據。因此，p管制圖並不適合用來監控低不合格率製程，後續才發展出CCC管制圖用來取代p管制圖監控高產出製程。為了進一步地提升CCC管制圖偵測製程不合格率偏移之效率，比CCC管制圖多考慮r組樣本統計量之CCC-r管制圖因而產生。
然而CCC-r管制圖，當製程不合格率開始偏離目標值p0之初，其平均連串長度呈現遞增現象，亦即無法快速地發出警訊。故本研究之最大貢獻在於推導出CCC-r管制圖之管制界限調整係數通式kr，並證明經由調整係數kr修正後之CCC-rmodified管制圖，確實能夠改進CCC-r管制圖無法即時偵測製程偏移之能力，有效地提升CCC-r管制圖偵測製程偏移之靈敏度，提供一個更有效率的管制方法來監控低不合格率之高產出製程。

關鍵字

p管制圖 ； 高產出 ； CCC管制圖 ； 平均連串長度

並列摘要

The p chart approximated by normal distribution is widely used to monitor the fraction nonconforming. However, the low process fraction nonconforming due to process improvement and small sample size usually make the assumptions invalid and generate too many false alarms. Since the fraction nonconforming is low, the lower control limit of a p chart is usually negative and no process improvement can be detected. For above mentioned reasons, the p chart is inadequate for monitoring and control of product attributes in the processes of very high yields.
The cumulative count control (CCC) chart based on cumulative count of items produced until r nonconforming items are detected has been proposed for the processes with low fraction nonconforming. In this research, an adjustment coefficient kr was developed to avoid the undesireable feature that the out-of-control ARL will increase as process deteriorates. With the adjusted control limits, we can assure that the in-control ARL is maximized.

並列關鍵字

p chart ； high yield ； CCC chart ； ARL

參考文獻

1. Bourke, P. D. ,“Detecting a shift in fraction

nonconforming using run-length control charts with 100%

(1991)

2. Calvin, T. W. ,“Quality control techniques for“Zero

And Manufacturing Technology, CHMT-6, 323-328 (1983)