Estimating the change point of the parameter vector of multivariate Poisson processes monitored by a multi-attribute T~2 control chart

摘要

When a control chart signals an out-of-control condition, knowing when the process has really changed (the change point) accelerates the identification of the source of special causes and makes the corrective measures to be taken sooner. In this paper, a new multi-attribute T~2 control chart based on two transformation methods is initially proposed to monitor the parameter vector of multi-attribute Poisson processes. Then, the maximum likelihood estimators (MLE) of the process change point designed for both linear trend and step change disturbances are derived. Next, using Monte Carlo simulation, we show the performances of the proposed estimators are satisfactory. Finally, through performance comparisons, we conclude the MLE of the change point designed for linear trends outperforms the MLE designed for step changes when a linear trend disturbance is present and conversely, the MLE of the change point designed for step changes outperforms the MLE designed for linear trend disturbances when the real change type is step change.