Monitoring Process Variability with Individual Measurements Following Elliptically Contoured Distributions

An exponentially weighted moving average (EWMA) control chart of squared distance is developed by means of a double EWMA approach to monitor process dispersion with individual measurements distributed within the class of elliptically symmetric distributions. Several examples highlighting possible extensions of the control chart to multivariate processes are provided. In particular, for multivariate normal processes, an investigation on the detection power of the chart is carried out through Monte Carlo studies. The results show that the proposed control chart performs well, especially when a process has a small or moderate shift.     

Adaptive Kalman Filtering with Multivariate Generalized Laplace System Noise

An adaptive Kalman filter is proposed to estimate the states of a system where the system noise is assumed to be a multivariate generalized Laplace random vector. In the presence of outliers in the system noise, it is shown that improved state estimates can be obtained by using an adaptive factor to estimate the dispersion matrix of the system noise term. For the implementation of the filter, an algorithm which includes both single and multiple adaptive factors is proposed. A Monte-Carlo investigation is also carried out to access the performance of the proposed filters in comparison with other robust filters. The results show that, in the sense of minimum mean squared state error, the proposed filter is superior to other filters when the magnitude of a system change is moderate or large.