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.

This dissertation investigates the effects of autocorrelation on the performances of various sampling plans for control charts in detecting special causes that may produce sustained or transient shifts in the process mean and/or variance. Observations from the process are modeled as a first-order autoregressive process plus a random error. Combinations of two Shewhart control charts and combinations of two exponentially weighted moving average (EWMA) control charts based on both the original observations and on the process residuals are considered. Three types of sampling plans are investigated: samples of n = 1, samples of n > 1 observations taken together at one sampling point, or samples of n > 1 observations taken at different times. In comparing these sampling plans it is assumed that the sampling rate in terms of the number of observations per unit time is fixed, so taking samples of n = 1 allows more frequent plotting. The best overall performance of sampling plans for control charts in detecting both sustained and transient shifts in the process is obtained by taking samples of n = 1 and using an EWMA chart combination with a observations chart for mean and a residuals chart for variance. The Shewhart chart combination with the best overall performance, though inferior to the EWMA chart combination, is based on samples of n > 1 taken at different times and with a observations chart for mean and a residuals chart for variance. / Ph. D.

<p>The multivariate cumulative sum (MCUSUM) and the multivariate exponentially weighted moving average (MEWMA) control charts are the two leading methods to monitor a multivariate process. This thesis focuses on the MEWMA control chart. Specifically, using the Markov chain method, we study in detail several aspects of the run length distribution both for the on- and off- target cases. Regarding the on-target run length analysis, we express the probability mass function of the run length distribution, the average run length (ARL), the variance of run length (V RL) and higher moments of the run length distribution in mathematically closed forms. In previous studies, with respect to the off-target performance for the MEWMA control chart, the process mean shift was usually assumed to take place at the beginning of the process. We extend the classical off-target case and introduce a generalization of the probability mass function of the run length distribution, the ARL and the V RL. What Prabhu and Runger (1996) proposed can be derived from our new model. By evaluating the off-target ARL values for the MEWMA control chart, we determine the optimal smoothing parameters by using the partition method that provides an easy algorithm to find the optimal smoothing parameters and study how they respond as the process mean shift time changes. We compare the ARL performance of the MEWMA control chart with that of the multivariate Shewhart control chart to see whether the MEWMA chart is still effective in detecting a small mean shift as the process mean shift time changes. In order to apply the model to semiconductor manufacturing processes, we use a bivariate normal distribution to generate sample data and compare the MEWMA control chart with the multivariate Shewhart control chart to evaluate how the MEWMA control chart behaves when a delayed mean shift happens. We also apply the variation transmission model introduced by Lawless et al. (1999) to the semiconductor manufacturing process and show an extension of the model to make our application to semiconductor manufacturing processes more realistic. All the programming and calculations were done in R</p> / Master of Science (MS)