以歷史數據為基礎提升管制圖偵測平均值變化能力之研究

A Study of Charting Procedure Based on Historical Data for Improvement the Detection Ability of

鄭盛樹(Cheng Sheng Su)

指導教授 ： 鄭春生

元智大學/工程學院/工業工程與管理學系/博士(2002年)

摘要

在生產過程中生產環境或原物料的改變均可能導致製程狀態偏離目標值，這些使產品品質產生變異的原因包含了製程平均值與變異數的改變，因此為了能即時監控製程狀態，在本研究中將分別探討管制圖的偵測能力並提出改善方法，以期進一步提升管制圖的整體偵測成效。
在計量值管制圖方面，當母體分配為常態時我們將提出多重累積和管制法及合併多重累積和管制法與輔助法則，這兩種方法以改善累積和管制法之偵測效益，並探討輔助法則的建立與相關管制法的參數設定。當製程之母體分配為指數分配時，我們將以類神經網路管制法與合併類神經網路-累積和管制法。來改善累積和管制法之偵測能力，並探討合併類神經網路與累積和管制法的管制效益。
在計數值管制圖方面，本文將探討不合格點數管制圖，在不合格點數產生群聚現象時 管制圖的應用與缺點，並提出以尼曼分配為不合格點之機率模型時，累積和管制法之改善效益。再者，當產品品級為多項等級分類時，本研究亦將提出以多項分類為基礎的累積和管制法。以及使用機率密度函數估計方法來建立逐次機率比檢定管制法以監視製程平均值的改變。
這些改善方案的共同特徵為，同時使用歷史數據為依據，並藉由異常數據之出現順序，以獲得更多製程資訊及增進管制方法之偵測能力。整個研究的重點為使用類神經網路及統計方法為工具，並以實例說明這些改善方案的整體偵測成效。在這些改善方案的研究結果中，吾人發現多重累積和管制法之偵測成效將優於單一累積和管制法。而類神經網路管制法的偵測成效則稍優於指數累積和管制法，但與指數累積和管制法合併後將可更進一步提升偵測能力。在計數值管制圖改善方法中，本研究也發現，當不合格點產生群聚現象時，可經由適當的參數設定來使用累積和管制法以改善製程。另外在一些以類別資料為基礎的管制法中，本文則發現，經由適當的機率密度函數估計再套用逐次機率比管制法將可大幅提升偵測製程微量變動的能力。

關鍵字

統計製程管制 ； 類神經網路 ； 平均連串長度 ； 累積和管制法 ； 計量值管制圖 ； 計數值管制圖

並列摘要

Control charts are widely used for both manufacturing and service industries. Cumulative sum (CUSUM) charts are known to be very sensitive in detecting small shifts in the process mean. In this research, first, we proposed a multiple CUSUM which used several simultaneous conventional CUSUM statistics with different resetting boundaries. Secondary, we proposed a neural network as an alternative approach to CUSUM charts when monitoring exponential mean. Finally, we also explore the attribute control charts for a clustering phenomenon of defective items and multiple classifications for quality level described by linguistic variables.
The performance of these procedures was evaluated by estimating the average run lengths (ARL’s) using theoretical computing or simulation. The results obtained with simulated and real-world data suggest that both multiple CUSUM and neural network are significantly more sensitive to process shifts than CUSUM charts. As for attribute control charts, the presented formula of reference value can form a CUSUM control chart for monitoring the clustering phenomenon of defective items. The results suggest that proposed method are sensitive than exists control chart, especially in small mean shifts. By way of estimated probability density function of based variable of categorical data, the charting procedure based on sequential probability ratio testing also work better than fuzzy control charts under multiple classification.

並列關鍵字

SPC ； neural network ； average run length ； CUSUM charts ； variable control charts ； attribute control charts

參考文獻

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