隨著科技的進步與品質管理觀念的發展，統計製程管制的概念逐漸受到企業重視，成為現代品質管理的重要工具，管制圖是其中一種常用的手法，用於監控製程是否發生變異並及時發出警訊，確保產品品質的穩定性。伯努利過程是由一系列完全相同的獨立試驗所組成，每次試驗僅有成功或失敗兩種可能，適合監測大量二元事件的比例變動，伯努利過程的應用範圍廣泛，適用於許多品質監控的實務場景，包括工廠中的合格品與不合格品、醫學治療的成功與否、顧客對產品的滿意與否，因此本研究選擇使用伯努利過程建構管制圖。常見的管制圖包括傳統的修華特管制圖、累積和管制圖（CUSUM）及指數加權移動平均管制圖（EWMA），但這些管制圖均需事先設定參數，而參數設定若與實際製程情況不符，可能影響監控效果。為了解決參數設定的問題，一般化概似比管制圖（GLR）被提出，然而在以伯努利GLR 管制圖監控不合格率時，仍需設立參數上限，以避免連續出現不合格品時計算統計量無定義的情況，這表明部分 GLR 管制圖仍存在參數設定的限制。為了進一步解決此問題，本研究使用Kullback-Leibler information建構伯努利管制圖，該管制圖無需設立參數，且能分別監測不合格率的上升、下降，以及同時監控上升與下降情況。快速初始反應機制（Fast Initial Response, FIR）是一種管制圖提升製程初期監控績效的機制，目的是為了提高對製程初期發生異常的偵測速度，該機制的優點為即時識別製程初期的變化或異常，從而快速做出干預和調整策略，適用於製程初期不穩定的狀況，但若製程初期已處於穩定狀態，使用FIR機制反而可能產生更多的負面影響，導致製程的生產成本增加，因此本研究將FIR導入至伯努利Kullback-Leibler資訊管制圖，並建構期望成本模型，透過期望成本之比較，幫助使用者分析和判斷導入此機制的適用狀況，以提高管制圖偵測績效。

This study investigates the applicable situations for implementing Fast Initial Response (FIR) scheme in Bernoulli KLI control charts from a cost perspective. A simulationbased cost model incorporating linear and quadratic delay components is developed to evaluate expected monitoring costs under various FIR settings. Monte Carlo simulations estimate the Average Number of Observations to Signal (ANOS) across different ratios and out-of-control probabilities. FIR is designed to enhance the performance of control charts in the early stages of process monitoring. Its primary objective is to improve the detection speed of abnormalities occurring at the beginning of a process. However, if the process is already in a stable state at the beginning, applying FIR may increasing production costs. Therefore, this study constructs an expected cost model. By comparing the expected costs, this research aims to assist users in analyzing and determining the appropriate situations for implementing FIR, enhancing the detection performance of control charts.

王尊輿(民110)。用於監控不良率之幾何Kullback-Leibler資訊管制圖。國立成功大學工業與資訊管理研究所碩士論文。
李哲維(民110)。伯努利Kullback-Leibler資訊管制圖用於監控不合格率。國立成功大學工業與資訊管理研究所碩士論文。
呂倢瑩(民111)。用於監控批次生產之不合格率Kullback-Leibler資訊管制圖。國立成功大學工業與資訊管理研究所碩士論文。
房宣名(民113)。建構多項分配Kullback-Leibler資訊管制圖。國立成功大學工業與資訊管理研究所碩士論文。
林煒倫(民113)。導入快速初始反應機制於Kullback-Leibler資訊管制圖監控製程平均數以及變異數並分析其使用時機。國立成功大學工業與資訊管理研究所碩士論文。
張景富(民112)。導入快速初始反應機制至Kullback-Leibler資訊管制圖。國立成功大學工業與資訊管理研究所碩士論文。
趙昱琳(民111)。用於監控不良率之負二項Kullback-Leibler資訊管制圖。國立成功大學工業與資訊管理研究所碩士論文。
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