The Monitoring And Application Of A Class Of Mixed Pth-Order Integer-Valued Autoregressive Models

Count data with autocorrelation are common in the life.Integer valued time series,which has received widespread attention from scholars recently,could well fit such data.Monitoring these data is crucial in epidemiological prevention,social security maintenance,and product quality monitoring.Control charts are one of the important tools for process control.Many previous studies have assumed that the monitored model is integer valued time series with Poisson marginal distributions.However,the characteristic of Poisson distribution with equal mean and variance is difficult to satisfy in actual.It is found that a class of p-order mixed integer valued time series models have good performance in the process of studying actual data,such as the number of patients infected with meningococcus,the number of victims of hate crimes,and the number of product quality complaints,etc.As far as we know,there is little research on monitoring the effect of control charts for this model in the literature.Therefore,two control chart methods are used to monitor the increase in the process mean of this class of p-order mixed integer valued time series models.The two charts are the rounding exponential weighted average control chart(abbreviated as the rounding EWMA control chart)and the cumulative sum control chart(abbreviated as the CUSUM control chart).This paper will analyze the efficiency of the two control charts through a large number of numerical simulation results.Meanwhile,three sets of empirical analyses are presented to demonstrate the application methods in detail.These methods include establishing a p mixed integer time series model for actual data,designing a control chart,and then monitoring the data.