Multivariate Exponentially Weighted Moving-Average Chart for Monitoring Poisson Observations

In many practical situations, multiple variables often need to be monitored simultaneously to ensure the process is in control. In this article, we develop a feasible multivariate monitoring procedure based on the general multivariate exponentially weighted moving average (MEWMA) to monitor the multivariate count data. The multivariate count data is modeled using Poisson log-normal distribution to characterize their interrelations. We systematically investigate the effects of different charting parameters and propose an optimization procedure to identify the optimal charting parameters. In particular, we provide a design table to the quality engineers as a simple tool to design the optimal MEWMA chart. To further improve the efficiency, we integrate the variable sampling intervals (VSI) in the monitoring scheme. We use simulation studies and an example to elicit the application of the proposed scheme. The results are encouraging and demonstrate effectiveness of the proposed methods well.