A New Scheme for Monitoring Multivariate Process Dispersion

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Construction of control charts for multivariate process dispersion is not as straightforward as for the process mean. Because of the complexity of out of control scenarios, a general method is not available.

In this dissertation, we consider the problem of monitoring multivariate dispersion from two perspectives. First, we derive asymptotic approximations to the power of Nagao's test for the equality of a normal dispersion matrix to a given constant matrix under local and fixed alternatives. Second, we propose various unequally weighted sum of squares estimators for the dispersion matrix, particularly with exponential weights. The new estimators give more weights to more recent observations and are not exactly Wishart distributed. Satterthwaite's method is used to approximate the distribution of the new estimators.

By combining these two techniques based on exponentially weighted sums of squares and Nagao's test, we are able to propose a new control scheme MTNT, which is easy to implement. The control limits are easily calculated since they only depend on the dimension of the process and the desired in control average run length. Our simulations show that compared with schemes based on the likelihood ratio test and the sample generalized variance, MTNT has the shortest out of control average run length for a variety of out of control scenarios, particularly when process variances increase.