據文獻中，心率資料具有自我相關的性質(self-similarity)，其程度可由自我相關係數(Hurst參數)量化表示；另一方面，I(d)過程中的d值可以量度長相關的程度，在殘差值符合常態分佈的假設之下，其與自我相觀係數的關係式為H=0.5+d，本文第一部分，我們嘗試用EBP(Embedded Branching Process)方法來估計H值，進而求得I(d)過程的d值。而蒐集到的心率資料中，d值大約介於0.6~1之間，為了使資料平穩，我們將每筆資料差分0.5次之後，再觀察其基本統計量並對資料配適GARCH模型，因每分鐘心跳紀錄值為整數值，所以高度差分(0.8~0.9)次後的資料接近整數值，容易拒絕常態分佈的假設；因此在第二部分，我們以physionet上提供的RR區間資料，作0.5皆差分後重新估算d值，再利用王琪玲(2001)提出的I(d)過程EWMA及EWRMS管制圖來監測RR區間資料，其中I(d)過程的EWMA在常態假設之下超出管制線比例在可接受的範圍內；而I(d)過程的EWRMS管制圖的超出管制線比例則明顯與偏態及峰態係數有關。在常態分配的假設之下，兩類管制圖能有效的反應病人的平均心率變化及變異。

An recent finding shows that heart rate data possess self-similar property, which is characterized by a parameter H, as well as a long range dependent parameter d. We estimate H by the EBP(Embedded Branching Process) method to derive the fractional parameter d in the first part. The heart rate and R-R interval data are found to have high differencing parameter(d=0.8 ~0.9) and against the
normality assumption. Thus the heart rate and R-R interval data are first fractionally differenced of order 0.5 to achieve stationarity. In the second part, we analyze the
RR-interval data on the physionet and obtain the long range
parameters. After fractionally differencing 0.5 order, the EBP method is adapted to estimate the long range parameter d.

The EWMA and EWRMS control charts of the I(d) processes are constructed to monitor the heart rate mean level and variability, respectively for the 18 RR-interval data sets from the physionet. For the EWMA control chart the out of control percentages are chosen to the nominal probability. However, the out of control percentages are affected by the skewness and kurtosis of the process distribution for the EWRMS control carts. Generally speaking, the I(d)-EWMA and I(d)-EWRMS control charts provide a proper monitor system for heart rate mean level and variability.

1.緒論....................................................1
2.ARFIMA模型介紹與自我相似過程............................5
3.I(d)過程的EWMA管制圖與EWRMS管制圖......................13
4.實證結果...............................................19
5.結論...................................................22
參考文獻.................................................23
圖表.....................................................25

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