在工業領域中，針對產品執行品質管控能夠降低成本並提升客戶滿意度，而管制圖作為被廣泛使用的工具之一，可透過持續監控製程，並偵測製程中發生的變異，進而發出警報，以隨時保證產品之品質。除此之外，某些製程有較高機率在初期就發生製程位移，如:製藥業、化工業等，其在製程初期需要混合多項原料，若一出錯將會大幅增加成本；或是參數設定在初期就發生問題，導致後續有一連串的錯誤，便將會造成巨大損失甚至產生危險。為了解決上述問題，本研究將引入快速初始反應機制(fast initial response, FIR)至管制圖當中，並對服從常態分配之製程平均數進行監控。然而，大多數管制圖在使用時須事先設置參數，如: CUSUM管制圖之平均值參數、EWMA管制圖之權重係數等，可能影響使用效率。比起其他管制圖，Kullback-Leibler Information (KLI)管制圖在使用之前不須事先輸入參數，亦對製程之小幅度變異有較高的敏銳度，在偵測與執行績效有較好的表現，因此本研究將使用KLI管制圖。為在管制圖中引入FIR機制，其需在建立管制圖時，於起始統計量中加上一個初始值，該初始值可能為管制界線的一個函數，使製程在發生變異時，管制圖能夠更快偵測到。然而只有在製程初期發生異常時，引入FIR機制才有正面效益；若製程初期並無異常，可能反而會增加監控成本，因此本研究將建立期望成本模型，進而分析導入FIR機制之最佳時機。在實務上，製程位移量可能服從特定機率分配，因此本研究將對製程位移量進行特定機率分配的假設，並推導出可應用於製程後期發生變異情況下之平均連串長度(Average Run Length, ARL)近似式。最後，研究透過計算成本模型找出FIR機制之適用門檻值，當製程初期發生變異之機率超過該門檻值時，則使用FIR機制會最為有效。接著，再針對成本模型之各參數進行敏感度分析，找出影響FIR使用機制之重要變數，以便管理者進行決策。

Implementing statistical quality control via control charts is paramount in industrial manufacturing to minimize scrap and optimize production stability. In specialized sectors like pharmaceutical and chemical refining, severe process shifts are highly prone to occurring during the initial start-up phase, leading to critical economic losses if left undetected. To address this vulnerability, this research integrates the Fast Initial Response (FIR) mechanism into the parameter-free Kullback–Leibler Information (KLI) control chart to monitor process means under a continuous normal distribution. While the FIR KLI chart accelerates the detection of early anomalies, unconditional deployment can backfire—inflating false alarm rates and raising monitoring costs if the start-up period remains completely stable. To solve this trade-off, this study constructs a comprehensive expected economic cost model to systematically analyze the optimal deployment timing for the FIR mechanism. Furthermore, recognizing that real-world shift sizes are non-uniform, this work derives an analytical approximation formula based on a two-parameter Gamma distribution to estimate the Average Run Length (ARL) when shifts manifest later in the timeline. Numerical optimization successfully identifies a quantifiable threshold value u based on early-stage failure probabilities, demonstrating that FIR is most effective when this risk exceeds the threshold. Finally, a single-factor sensitivity analysis identifies critical cost parameters to guide managerial decision-making.

中文文獻:
林煒倫 (2024)，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。[碩士論文] 國立成功大學工業與資訊管理研究所
曾瑋晟 (2025)，導入快速初始反應機制至幾何Kullback-Leibler資訊管制圖及其適用狀況。[碩士論文] 國立成功大學工業與資訊管理研究所
張景富 (2023)，導入快速初始反應機制至Kullback-Leibler資訊管制圖。[碩士論文] 國立成功大學工業與資訊管理研究所
劉乙力 (2025)，應用具有快速初始反應機制之指數Kullback-Leibler資訊管制圖監控分散式阻斷服務攻擊。[碩士論文] 國立成功大學資訊管理研究所
鍾婷珮 (2025)，導入快速初始反應機制至伯努利Kullback-Leibler資訊管制圖及其適用狀況。[碩士論文] 國立成功大學工業與資訊管理研究所
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