以類神經網路為基礎監控事件時間間隔數據之管制程序

A Neural Network-based Process Control Procedure for TBE Data

湯淑惠(Shu-Huei Tang)

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(2009年)

摘要

在統計管制製程中，通常利用傳統 c 管制圖來監控製程缺點率之變化。然而，在缺點率很低的高產出製程中，c 管制圖並無法滿足使用者所要求之統計特性。事件時間間隔管制圖 (time-between-events charts，簡稱 TBE 管制圖) 被認為是用來監控高產出製程的較佳方法。當製程的缺點率很低的情況下，TBE 管制圖比傳統計數值管制圖擁有較佳偵測製程異常之能力，並且更適合應用於線上即時監控系統。目前用來監控事件時間間隔數據之統計方法為：累積計量管制圖 (cumulative quantity control chart，簡稱 CQC 管制圖)、Exponential CUSUM 與 Exponential EWMA 管制圖。
本研究之主要目的為建構類神經網路之監控系統，以探討事件時間間隔數據之管制程序，並且利用平均連串長度作為衡量績效之評估指標。利用類神經網路監控服從指數分配之 TBE 數據，比較類神經網路與其他 TBE 管制圖之偵測績效。由於 TBE 數據為偏歪型的指數分配，除了使用 TBE 管制圖外，另一個監控 TBE 數據的方法即為數據轉換，以改善此種不對稱的資料型態。本研究加入數據轉換之前處理過程，使指數分配之數據能近似常態分配，期望能提升類神經網路監控 TBE 數據之績效。為了研究類神經網路之穩健性，將服從指數分配之 TBE 數據延伸至韋伯分配，期望類神經網路之偵測績效具有穩健性。研究顯示，類神經網路在偵測 TBE 數據擁有不錯之績效，並且在偵測服從韋伯分配之 TBE 數據具有穩健性。

關鍵字

事件時間間隔 ； 類神經網路 ； CQC 管制圖 ； CUSUM 管制圖 ； EWMA 管制圖

並列摘要

In statistical process control, we usually use Shewhart c chart to monitor the defect rate. However, Shewhart c chart was shown to be inadequate to monitor the processes when the defect rate is extremely low. In order to provide a proper control scheme, the procedure of monitoring the time-between-events (TBE) data is suggested to be as an alternative to the traditional control charts. Instead of monitoring the number or the proportion of events occurring in a sampling interval, TBE charts focus on the time between the occurrences of events. There are several different ways in monitoring the TBE data, such as the Cumulative Quantity Control (CQC) chart, the exponential CUSUM, and the exponential EWMA control charts.
In this paper, we proposed a control technique based on the Artificial Neural Networks (ANN) for monitoring the TBE data. The TBE data is usually considered to follow an exponential distribution which is quite highly skewed. Three data transformation methods are also introduced in this research to make the statistics become more symmetric. Some performance comparisons between the ANN and the statistical control schemes are evaluated by the average run length (ARL) and the robustness of the ANN control procedure is also discussed. The results show the ANN monitoring system proposed in this research has superior performance than the statistical control charting techniques. And the robustness of the ANN is also established.

並列關鍵字

time-between-event ； ANN ； CQC chart ； CUSUM chart ； EWMA chart

參考文獻

1. Abbasi, B., and Akhavan Niaki, S. T., “Monitoring high-yields processes with defects count in nonconforming items by artifician neural network,” Applied Mathematics and Computation, 188, 1, 262-270, 2007.

2. Borror, C. M., Montgomery, D. C., and Runger. G. C., “Robustness of the EWMA control chart to non-normality,” Journal of Quality Technology, 31, 3, 309-316, 1999.

5. Cheng, C. S., and Tzeng, C. A., “A neural network approach for detecting shifts in the process mean and variability,” Journal of the Chinese Institute of Industrial Engineers, 11, 67-75, 1994.

6. Cheng, C. S., “A neural network approach for the analysis of control chart pattern,” International Journal of Production Research, 35, 667-697, 1997.

7. Chan, L. Y., Xie, M., and Goh, T. N., “Cumulative quantity control charts for monitoring processes,” International Journal of Production Research, 38, 2, 397-408, 2000.