計數值c管制圖是以卜瓦松分配逼近常態收斂的基礎下所構建而成，隨著高品質製程的出現，製程缺點數大幅降低，c管制圖已經無法滿足中央極限定理之常態分配的假設條件，造成錯誤警報次數增加，且管制圖中產生大量的零計數值，也使得管制界線發生等於或小於零之狀況，在此狀況下管制圖之監控能力已等同失效，因此如何改善高品質製程管制圖之機率分配適用性便成為重要課題。由於目前實務界與學術界對此文獻之著墨甚少，本研究為了改善其機率分配適用性，提出零值膨脹卜瓦松模型(Zero-inflated Poisson Model, ZIP)作為改善方法，並以某高品質製程公司個案為例，進行實證研究。
本研究提出了一項分析步驟，以TFT-LCD(Thin film transistor liquid crystal display, TFT-LCD)玻璃基板端面加工缺點數資料為研究對象，使用Vuong test進行模型適合度檢定以及應用最大概似估計法(Maximum likelihood estimation method, MLE method)推估模型參數，最後藉由管制圖的平均連串長度(Average run length, ARL)值來進行ZIP與卜瓦松分配之效能比較，透過此一分析步驟，證實ZIP模型具有顯著的效果，可以作為實務應用上的一項參考。

Attribute c control chart is a Poisson distribution based on the central limit theorem (CLT). With the emergence of high-quality process, the number of defects was substantially reduced. However, the reduction in defects created an excessive amount of zero counts on the c chart. Additionally, it caused the control limit to approach zero or negative. The c control chart was led to invalid CLT assumptions and generated many false alarms. Therefore, the c chart was inadequate. Due to very few numbers of defects on process, the zero count was inadequate in monitoring and controlling attribute data in this high-quality process. Hence, searching for a more appropriate probability distribution is important. Due to the reasons mentioned above, the use of zero-inflated Poisson (ZIP) distribution will be more appropriate than Poisson distribution.
In this research, a positive approach was proposed to prove the feasibility assessment of ZIP with a case study. In this paper, the Vuong test and maximum likelihood estimation method (MLE) was presented to estimate parameters, and then the average run length (ARL) applied for performance evaluation. This approach was ensured that ZIP model was a significant improvement and could be a useful reference for high-quality process.

中文部分
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