Study On Statistical Process Control Chart Of Multivariate Count Data

In recent years,the process monitoring of count data,which is widely used in finance,biomedicine,psychology,actuarial insurance,road safety,manufacturing and many other fields of life,has become a research hotspot.For multivariate count data follows multivariate Poisson distribution,especially when the process mean is less than 5,the validity of the normal approximation hypothesis of the Poisson distribution is very uncertain,and the normal distribution model commonly used becomes less reliable.In order to solve this problem,this paper introduces the heterocovariance multivariate Poisson model proposed by Johnson et al into the construction of MEWMA control chart,and establishes the Y-MEWMA control chart.In addition,in our previous work,we designed a new MEWMA control chart based on a multivariate Poisson model derived by He Daojiang.In this paper,we call it H-MEWMA control chart and extend it to discuss the case where a single process observation is a quintuple variable.In this paper,we focus on phase II online process monitoring of multivariate count data,assuming that poisson parameters are known and process observations are generated by random simulation of the involved multivariate Poisson model.Through a lot of numerical simulation experiments,the control limits of different smooth parameters are determined.Various process shifts are simulated by adding one or more Poisson parameters by one or two units,and the resulting out-of-control average run lengths are given in several tables.Numerical simulation results show that the proposed control charts perform well under the conditions of consideration and can provide satisfactory monitoring effects.