Detecting and estimating the time of a step-change in multivariate Poisson processes

In multi-attribute process monitoring, when a control chart signals an out-of-control condition indicating the existence of a special cause, knowing when the process has really changed (the change point) accelerates the identification of the source of the special cause and makes the corrective measures to be employed sooner. This, of course, results in a considerable amount of savings in time and money. Since many real world multi-attribute processes are Poisson and most process changes are step-change, a new method is proposed, in this paper, to derive the maximum likelihood estimator of the time of a step-change in the mean vector of multivariate Poisson processes. In this method, two transformations are first employed to almost remove the inherent skewness involved in multi-attribute processes and make them almost multivariate normal, and also to almost diminish correlations between the attributes. Then, a T2T2 control chart is employed for out-of-control detection and a maximum likelihood estimator is used to estimate the change point. The performance of the proposed methodology is illustrated using some simulation experiments in which we show that the proposed procedure is relatively accurate and reliable in detecting and estimating the change point.