Long range dependent processes occur in many fields, it is important to monitor these processes to early detect their shifts. This paper considers the problem of detecting changes in an I(d) process or an ARFIMA(p,d,q) process by statistical control charts. The control limits of EWMA and EWRMS control charts of I(d) processes are established and analytic forms are derived. The average run lengths of these control charts are estimated by Monte Carlo simulations. In addition, we illustrate the performance of the control charts by empirical examples of I(d) processes and ARFIMA(1,d,1) processes.

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.