CUSUM Control Chart Design For Multivariate Poisson Distribution And Time Series Model

Multiple discrete data are very common in the manufacturing industry.Most control charts are often based on the assumption of the multivariate Poisson model with a single common covariance term,which allows only equal covariance.However,this assumption may not be realistic,for the cases observed in different regions sometimes are not independent with different covariance.Besides,these control charts can only afford monitoring function,but cannot provide fault diagnosis information.This article presents GMP-CUSUM chart based on the multivariate Poisson model with two-way covariance structure.Using Monte Carlo simulation,we compare the average running chain length(ARL)of traditional MP control chart and the new control chart considering various factors.The results show that the latter model is more suitable for modeling multivariate discrete data and the new control chart increases sensitivity to process shifts.When applied to raw data directly,the proposed method is powerful yet simple to use in practice.In addition,statistical process control with autocorrelation properties is also of great significance.The most commonly used control charts for monitoring such data include P-CUSUM and P-EWMA charts.However,the past control charts are based on one-dimensional Poisson integer time series model,ignoring the correlation between multiple dimensions.In this paper,a multivariate control chart is established on the generalized Poissoninteger first-order autoregressive time series model.Monte Carlo simulation was used to compare the average running chain length(ARL)of multivariate control charts with traditional one-dimensional control charts.The new control charts show better performance than the traditional control charts under some parameters.When applied to raw data with multiple autocorrelation,The new control chart in this paper is powerful in the practical production process.