自我相關性製程管制圖之研究:以C化工廠製程為例

A Study of Auto-correlated Process Control Chart From the C Chemical Factory

郭哲彰(Che-Chang Kuo)

指導教授 ： 陳雲岫

元智大學/工程學院/工業工程與管理學系/碩士(2011年)

摘要

傳統之統計製程管制通常是建構在製程觀測值為互相獨立、且符合常態分配的假設條件下。然而實務上有許多製程並不符合獨立性假設而是具有自我相關結構，例如化學產業，或是密集的自動化檢測程序等。自我相關性製程若以傳統管制圖作監控，最典型的影響就是平均連串長度(ARL)的縮短，導致過多的假警訊(false alarm)。本研究主要以C化工廠所施行的個別值管制圖為例，針對AR（1）模型，找出實務上可導入實施的自我相關性管制圖作法，以改善其使用傳統管制圖過高的false alarm rate。研究發現使用監控殘差的自我相關性管制圖，當製程出現連續性異常時易出現誤判情況；Montgomery與Mastrangelo提出的 EWMA 移動中心線管制圖透過選擇適當的λ值可解決複雜ARIMA 模型配適上的困難性，但其管制界線隨著時間變動，實務上較難實施；Wheeler 與 Gilbert 調整管制界線管制圖則可直接使用於傳統管制圖的架構上，僅需考慮自我相關結構重新估計標準差並對管制界線作調整，實施較容易，經以蒙地卡羅模擬計算兩者的ARL值，結果指出在低度到中度自我相關時Gilbert 調整管制界線管制圖與獨立製程所使用的傳統管制圖表現相近，但當製程為高度自我相關時則檢定力過低，並不適用；Wheeler調整管制界線對於ARL值過短的情況則改善有限，整體表現皆不如Gilbert。C化工廠製程為中度自我相關，品質特性對平均值小量偏移不感興趣，因此建議使用Gilbert 調整管制界線取代原本使用的Shewhart個別值管制圖，可以有效減少假警訊並正確偵測到可歸屬原因。

關鍵字

管制圖 ； 自我相關 ； 平均連串長度 ； ARIMA ； 蒙地卡羅模擬

並列摘要

The statistical process control was usually based on the assumptions of normality and independence. However, the observations from the process are often against such assumptions and show auto-correlation in many situations, such as continuous process of chemical industry and auto-inspection process with shorter sampling intervals. The typical effect of auto-correlated process using traditional control chart was the decrease of average run length, which results in higher false alarm rates. This study aimed to investigate methodologies for improving the performance of the individual control chart from the C factory, which observations were fitting AR (1) model. We found that the residue based control charts have higher type Ⅱ error when the abnormal behavior is successive. Montgomery and Mastrangelos’ MCEWMA chart can solve the problems of fitting complicated ARIMA model through choosing appropriate λ , but it is hard to practice in reality since the control limit is variable. Wheeler and Gilbert adjusted control limits are easier to use, they can be used in existing frame. The simulation result shows that performance of Gilbert’s control chart is better than Wheelers’, but they are not suit for high level auto-correlated process. The C factory process is moderately auto-correlated, therefore, we suggest using Gilbert’s control chart instead of Shewhart individual control chart to decrease false alarm rates and detect assignable causes appropriately.

並列關鍵字

Monte Carlo Simulation ； Control Chart ； Auto-correlated ； Average Run Length ； ARIMA

參考文獻

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