Monitoring multivariate Poisson processes: a review and some new results

Evaluation of performance and quality of manufacturing and businessprocesses using statistics is a central issue. Process quality depends on severalcharacteristics that should be assessed using simultaneous multivariatequality control methods. Multivariate variable process control has beenone of the most rapidly developing areas of statistics. The paper is focusedon monitoring quality characteristics of the attribute type and followingnon normal distributions. In particular, the multivariate Poisson processis considered. The main theoretical results on monitoring multivariateattribute processes and the multivariate Poisson process are reviewed anddiscussed. Little work has been carried out on statistical methods to monitormultivariate attribute processes and many problems in developing multiattributemonitoring methods are still open. In the paper, we propose anew index of the overall defectiveness and a two-sided Shewhart-typemultivariate control chart with asymptotic probabilistic limits for monitoringthe defectiveness or demerit degree. The proposed methods provide asolution to the identification problem.