Study On CUSUM Control Chart For Monitoring Multivariate Discrete Data

In recent years,statistical process control(SPC)has been widely concerned,and the traditional SPC theory is mostly used in industrial production quality control.With the rapid development of information technology,the improvement of data storage and computing power,SPC has been more widely used.In these problems,there are a large number of high-dimensional data that are discrete.To describe the distribution of discrete data,we usually use poisson probability model or negative binomial model and similar parametric models.However,in the actual situation,the discrete data is often affected by a variety of unknown factors,usually parametric model can't describe the real distribution of data effectively.In this paper,we study the problem of monitoring discrete data when the parameter distribution is invalid and propose a new nonparametric monitoring graph to monitor counting data.At present,many nonparametric monitoring charts proposed in the literature are mostly used to monitor a univariate data,but there is less research on multivariate discrete data.Zhiqiang Wang(2018)proposed a method to monitor univariate discrete data combined with Pearson-CUSUM control chart,but the article did not mention the monitoring of multivariate discrete data.In recent years,the monitoring of multivariate discrete data has gradually become a popular topic of statistical process monitoring,which also has important research significance for industrial quality monitoring and economic monitoring.On this basis,we will propose a control chart suitable for monitoring multivariate discrete data to monitor process changes.This paper mainly studies and improves the monitoring of CUSUM control chart for multivariate discrete data.Introducing pearson statistics into the design of multivariate CUSUM control chart can effectively improve the monitoring effect of control chart for process shift.Firstly,classify the data with different degrees of dispersion,and then apply the proposed Pearson-CUSUM control chart to monitor the distribution of classified data.This paper compares the effects of different reference_values and the number of categorieson the performance of the monitoring chart.The research shows that the control chart has better performance when_is select[0.01,0.001].For the number of classifications,it is recommended to select between[5,10].This paper considers the detection of the mean shift of the control chart in multiple dimensions and only one dimension.Simulation results show that the proposed control chart has good performance for both multi-dimensional changes and single dimensional.Finally,by comparing the performance of multivariate nonparametric CUSUM control chart based on anti-rank proposed by Qiu Hawkins(2001),the research shows that the proposed method has better performance for monitoring small shift.