在許多醫學研究中，心率變異（HRV）的頻譜分析已經被廣泛的用來探討自主神經的調節作用情況，
由過去的研究中發現心率變異的高低頻譜功率比值（LF/HF
Ratio）是交感神經與副交感神經交互作用的有效測量值且
偏低的心率變異值（Low
HRV）是心臟血管疾病病人重要的生理狀態指標。在本文中我們應用管制圖來監測
心率變異值與高低頻譜功率比值，希望能夠幫助醫生及早發現病人緊急狀況進而加以控制病人病情。
本論文主要分為兩個部分：第一部份是建立監測心率與心率變異的管制圖，我們利用數值的
方法去計算精確的指數加權均方根（EWRMS）與指數加權移動變異（EWMV）的管制界限。傳統醫學上使用的
高低頻譜功率比值的分佈不易推導，故無法有效偵測心率變異參數的顯著變動。於是在第二部份我們提出一
個新的高低頻譜功率比值統計量（RG）且有可推導之分佈，我們利用統計量的分佈計算其機率管制界限。
在最後的實例應用，本文針對由高雄榮民總醫院心臟外科加護病房所蒐集之每分鐘平均心率資料進行
統計分析。我們建立心率變異的高低頻譜功率比值統計量的~Shewhart~管制圖與~EWRMS~、
~EWMV~管制圖，利用上述建立的管制圖來監測心臟血管加護病房（VICU）中病人的危險因子並合併考慮
心率變異與高低頻譜兩個變量定義出一個危險指數。結果發現
手術後恢復狀況為死亡或病危之病人其危險指數顯著比長／短期鬱血性心
臟衰竭（CHF）及順利復原（Normal）病人偏高。

Spectral analysis of heart rate variability (HRV) has been applied
in many medical research to study autonomic nervous system
activity. In these studies, the researchers found that (i) ratio
of low frequency (LF) to high frequency (HF) spectrum power is a
useful measure of sympathetic/parasympathetic balance, and (ii)
low heart rate variability is an important risk factors for
patients. Therefore, continuous monitoring of the ratio and heart
rate variability have the potential to early detect physiological
deterioration of patients. This thesis consists of the following
two parts. In the first part, we establish control charts
monitoring heart rates and low HRV. Numerical method is applied
to compute exact control limits of the EWRMS and EWMV charts. The
distribution of the conventional LF/HF ratio statistic is
difficult to derive, significant of alterations in HRV parameters
can not be assessed efficiently. We resolve this problem in the
second part, a new equivalently useful ratio statistic is proposed
whose distribution can be derived more easily. Based on the
derived distribution, the probability control limits of the
proposed statistic are calculated. In application, we construct
Shewhart charts of the newly proposed ratio statistic and EWRMS,
EWMV charts of the heart rate variability to monitor the risk
factors of patients in vascular intensive care unit. Furthermore,
we define a risk score which combining the two risk factors
together, heart rate variability and LF/HF spectrum power ratio.
The results show that the higher risk scores corresponding to
patients after operation in severer condition.

1 緒論 1
1.1 背景介紹....................................1
1.2 資料收集與分類..............................3
2 心率變異之監測 5
2.1 研究動機....................................5
2.2 EWMA管制圖..................................6
2.3 EWRMS及EWMV管制圖...........................9
3 高低頻譜功率比值之監測 13
3.1 自主神經調節與高低頻譜功率的關係............13
3.2 頻譜分析....................................17
3.3 高低頻譜功率比值............................20
4 實證分析 27
4.1 偏低心率變異值與病人恢復狀況的關係..........27
4.2 高低頻譜功率比值與病人恢復狀況的關係........28
4.3 危險因子合併與病人恢復狀況的關係............29
A 附圖 35
B 附表 50

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