An adaptive variable-parameters scheme for the simultaneous monitoring of the mean and variability of an autocorrelated multivariate normal process

Due to advances in technology, sampling procedures and short lag times between successive sampling, autocorrelation among the measured data has become common in most applications. Neglecting autocorrelation leads to a poor false alarm performance. In the current paper, the effect of the autocorrelation on the performance of a variable-parameters multivariate single control chart is investigated in the case of the simultaneous monitoring of the mean and variability. At first, formulas for the sample mean and variability of a multivariate autoregressive-moving average process are derived. Then, a variable-parameters single control chart is developed for the simultaneous monitoring of the mean vector and the covariance matrix of an autocorrelated multivariate normal process. Next, the performance of the proposed control chart is evaluated by using eight performance measures based on a dedicated Markov chain model. Finally, by presenting an illustrative example, the application of the proposed scheme is demonstrated in practice.