本研究將快速初始反應(fast initial response, FIR)機制導入至Kullback-Leibler information (KLI)管制圖中，FIR機制是指使用管制圖時，起始點設定為非目標值的特定值，若製程為失控狀態下，此特定值會更快監控出異常，達到初期能夠比標準的管制圖還更快偵測出變異的情形。化工或製藥廠都是需要設定比較複雜參數的製程，比起一般加工廠的製程方面，在設定參數上難度就會更高，設置的參數不符合實際出現偏移情況時，將會影響管制圖的績效表現，若屬於批次生產且批次生產之產品分次產出後，每批生產可能會加入新的原料，而每批生產前需要先進行調整參數，在複雜的製程下初期犯錯的機率將會比一般製程還要高，因此製程初期時偵測出變異的速度就非常重要，也不會比標準管制圖在偵測出異常時，修正製程上的參數浪費更多的時間。累積和管制圖(CUSUM)和指數加權移動平均管制圖(EWMA)都對於較中小的變異發生有較靈敏的偵測能力，針對特別偏移量也需要做最佳化的參數設定。許多學者陸續再研究上導入FIR至CUSUM和EWMA等管制圖來提升績效表現。因此本研究欲藉由Kullback-Leibler資訊理論為基礎，並且不需要設定任何參數下建構KLI管制圖，藉著由後往前檢定法對每一期抽取之觀察值進行檢定，若滿足回溯至第一期的條件下，導入FIR機制於KLI管制圖進行製程監控，將其稱為FIR KLI。本研究將FIR KLI管制圖選擇出適合的初始值，先對不同初始值進行比較後選出比較適合的初始值。再與未導入FIR的KLI、FIR CUSUM和FIR EWMA管制圖進行績效比較。而研究結果得知，變動管制界限的FIR EWMA管制圖在初期平均數發生偏移的情況是有較佳的優勢，而經過一定的穩定樣本之後發生平均數偏移的情況下，FIR KLI管制圖監控小偏移量則是比較有優勢的，而監控中大偏移量則為FIR CUSUM管制圖和FIR EWMA管制圖比較有優勢。

In this study, the fast initial response (FIR) feature is incorporated into the Kullback-Leibler information control chart. The FIR feature is suitable for processes that are prone to errors. The FIR feature refers to setting a specific value as the starting point for the control chart. If the process is out of control, anomalies can be detected more quickly compared to standard control charts, resulting in faster detection during the initial phase. The cumulative sum (CUSUM) control chart and the exponentially weighted moving average (EWMA) control chart exhibit sensitivity in detecting moderate variations. However, for significant shifts, optimal parameter settings are required. Many researchers have introduced the FIR feature into CUSUM and EWMA to enhance their performance. This study also compares the performance of FIR CUSUM and FIR EWMA with the FIR KLI. The performance is evaluated in two scenarios: the initial state and the steady state. The steady state scenario holds higher reference value as it reflects the higher occurrence probability in real-life situations. In the initial state scenario, the FIR EWMA with variable control limits outperforms the FIR KLI. However, in the steady state scenario, the FIR KLI demonstrates excellent performance in monitoring small shift.

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