A multivariate control chart for monitoring trivariate Poisson processes with spatial correlation

Abstract

The multivariate and discrete data are commonly used to monitor product defects and epidemic diseases. It is difficult to model their complex structure and design a suitable control chart to monitor them in the area of statistical process control. To monitor the tri-variate Poisson process, this paper establishes a one-parameter copula function to describe the spatial correlation and designs a control chart based on the log-likelihood ratio test. The Markov chain is employed to approximate the average run length and to measure the performance of the control chart. Simulation results show that the proposed chart is efficient for detecting upward shifts and can achieve better monitoring performances when the target mean shift in control chart design is equal to a true mean shift. Compared with D chart, the proposed chart achieves a better performance when the correlation level is high.

Keywords

• multivariate and control chart
• poisson process
• copula function
• markov chain
• average run length