Monitoring multivariate Poisson processes: a review and some new results

Evaluation of performance and quality of manufacturing and business processes using statistics is a central issue. Process quality depends on several characteristics that should be assessed using simultaneous multivariate quality control methods. Multivariate variable process control has been one of the most rapidly developing areas of statistics. The paper is focused on monitoring quality characteristics of the attribute type and following non normal distributions. In particular, the multivariate Poisson process is considered. The main theoretical results on monitoring multivariate attribute processes and the multivariate Poisson process are reviewed and discussed. Little work has been carried out on statistical methods to monitor multivariate attribute processes and many problems in developing multiattribute monitoring methods are still open. In the paper, we propose a new index of the overall defectiveness and a two-sided Shewhart-type multivariate control chart with asymptotic probabilistic limits for monitoring the defectiveness or demerit degree. The proposed methods provide a solution to the identification problem.