管制圖依照監控之品質特徵分為計數型及計量型，監控之品質特徵為連續型數據其管制圖為計量型管制圖，針對離散行數據進行監控之管制圖為計數型管制圖。實務上計數型管制圖的應用非常廣泛，例如：監控製程中的不良品數、監控地震發生的次數、急診室到達的病患數。在過去的文獻中常見的管制圖例如：Shewhart管制圖、指數加權移動平均管制圖(EWMA)、累積和管制圖(CUSUM)，皆有建構計數型之管制圖。其中若是監控之離散型數據的品質特徵為針對固定單位的到達率，過去的文獻常假設其服從Poisson過程。Shewhart管制圖、EWMA及CUSUM在實務上都存在各自的優缺點，例如：不同偏移程度的績效表現、需要事先進行參數設定。因此本研究透過Kullback-Leibler information (KLI)之概念建構不須事先進行參數設定之計數型管制圖，監控在phase II情況下品質特徵為服從Poisson過程樣本之到達率，並利用由後往前逐期回溯計算樣本到達率。本研究以平均連串長度(ARL)作為管制圖績效指標，再以蒙地卡羅模擬法估計管制圖績效並與累積和管制圖(CUSUM)、指數移動平均管制圖(EWMA)進行比較。研究結果顯示本研究建構之管制圖在監控上升偏移、下降偏移及同時監控上升下降偏移，在某些偏移區段會輸給其他管制圖，但整體績效表現都顯著優於累積和管制圖(CUSUM)及指數移動平均管制圖(EWMA)，且不須事先進行參數設定。最後以美國2020年心血管疾病每週死亡人數做為實例利用本研究建構之管制圖進行監控。

It is more convenient to use counts in a unit to indicate if a process is in control in some monitoring processes. These kinds of counting data are often well fitted by the Poisson distribution. Various cumulative sum (CUSUM), exponentially weighted moving average (EWMA) and Shewhart-type control charts have been recommended. CUSUM and EWMA control charts are more effective in detecting small shifts than the Shewhart c chart. However, both CUSUM and EWMA control charts need to set up control chart parameter(s) for monitoring processes. A parameter-free Poisson Kullback-Leibler information control chart for the arrival rate monitoring is introduced. The backward empirical sequential test method for arrival rate estimating is applied to this study, and its average run length is compared to other charts for Poisson data. By contrast, the Poisson Kullback-Leibler information control chart outperforms the overall performance of CUSUM and EWMA control charts. The use of the Poisson Kullback-Leibler information control chart is illustrated with an example.

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