An EWMA Control Chart For Zero-inflated Poisson Datas With Time-varing Sample Sizes

In recent years,with the rapid improvement in product quality,products are produced with zero defects and monitoring and control of products has become increasingly difficult.In industrial terminology,this is referred to as a high yield process,while in healthcare it is referred to as a rare health-related event.Also,in industrial quality control the number of rejects per unit of inspection may vary depending on the unit of inspection(batch size)of the sample.In public health surveillance,when monitoring the incidence of certain diseases per unit of population in an area,the number of people at risk often does not remain constant,but changes over time.The above two monitoring problems cannot be solved simultaneously and efficiently by previous solutions.The Poisson distribution has been the most common model for counting relevant data in many previous surveillance processes.However,when there are an unusually large number of zeros in the data,using a Poisson distribution often leads to underestimated means and variances.At the same time,variations in sample size can have an impact on the counting results of events,and the use of fixed sample size schemes when time-varying sample sizes are present can lead to problems such as significantly higher false alarm rates after short runs,and run lengths that do not follow a geometric distribution.However,the monitoring of high yield processes and rare health-related events in the presence of time-varying sample sizes has not yet been investigated.Therefore,when developing control charts for monitoring this type of count data,it is important to take into account the changing sample sizes.In order to improve the efficiency of the counting process,the following work has been done:(1)A zero-inflated Poisson model with time-varying sample sizes is developed using a reparameterised statistical technique that combines incidence,zero-inflated factors and non-constant sample size for the data characteristics.(2)An exponential moving average(EWMA)charting scheme is designed using the developed zero-inflated Poisson model with time-varying sample sizes and a weighted log-likelihood ratio test to monitor and warn of high yield processes and rare medical-related events in real time.(3)A unified and efficient algorithm is designed for solving complex data parameters in a weighted log-likelihood ratio framework.The proposed zero-inflated Poisson EWMA control chart with time-varying sample sizes is compared with two existing control schemes through a simulation study and monitoring of a dataset of adverse events of pharmaceutical products.The proposed control chart is consistently more effective and robust in detecting changes in morbidity and zeroinflation factors simultaneously.