利用連串法則提升累積計量管制圖偵測高產出製程異常之靈敏度

Increasing the Sensitivity of Cumulative Quantity Control Charts for Monitoring High-Yield Processes with Runs Rules

10.6220/joq.2012.19(5).01

陳佩雯(Pei-Wen Chen)；鄭春生(Chuen-Sheng Cheng)；陳思蓉(Ssu-Jung Cheng)

累積計量管制圖 ； 高產出製程 ； 連串法則 ； 馬可夫鏈 ； CQC (cumulative quantity control) chart ； high-yield process ； runs rules ； Markov chain

品質學報

19卷5期（2012 / 10 / 01）

405 - 422

繁體中文

在統計製程管制中，我們通常使用計數值c管制圖來監控製程缺點率的變化。然而，當製程缺點率很低時，若繼續使用計數值c管制圖進行製程監控，由於此時常態分配之逼近效果不佳，因此容易導致錯誤警告增加，且管制下限也容易出現為零之情形，無法有效偵測製程改善。學者建議使用累積計量管制圖（cumulative quantity control chart, CQC管制圖）進行高產出製程之監控，作為c管制圖之替代方法。CQC管制圖對於高產出製程之監控績效雖然優於傳統計數值管制圖，但由於其判斷製程異常方式與傳統計數值管制圖相同，皆採用最近一組樣本統計量是否落在管制界限外作為其判斷依據，此種判定方式雖可快速地偵測出製程參數大量偏移之情形，但對於偵測製程參數之微量偏移能力較差。過去許多文獻建議採用連串法則來改善蕭華特管制圖之靈敏度，然而傳統的連串法則大多為適用於對稱型常態分配之情形，而且使用法則也會導致管制圖之型I誤差增加，使得錯誤警告次數增加。本研究之主要目的為利用連串法則來提升CQC管制圖偵測製程參數微量偏移之靈敏度。本研究提出六種連串法則，並說明如何利用馬可夫鏈模型來求解平均連串長度，作為績效評估之依據。研究結果顯示，本研究所建立之連串法則不僅能夠有效地提升CQC管制圖偵測製程缺點率增加的能力，同時也能維持預設之型I誤差，避免傳統連串法則之缺點。

The cumulative quantity control (CQC) chart has shown to have better performance than the traditional c chart in monitoring a high-yield process. In this research, we consider incorporating the runs rules into the CQC chart for enhancing the detection of small process changes. A Markov chain approach is used to evaluate the ARL (average run length) performance of various control schemes studied in this research. The results show that the proposed design approach can result in a significant reduction in ARL for detecting increases in the process parameters in comparison with the basic CQC chart and possess the desired type I error.

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