Study Of Control Chart For Zero Inflated Poisson Process

Statistical process control (SPC) is a very effective method for enterprise toimplement the process monitoring and improve the product quality. In the traditionalstatistical process control, we often assume that the number of nonconformingproducts follows Poisson distribution or negative binomial distribution, and thenmonitor the process. However, with the improvement of technology and productionlevels, the proportion of substandard products share is getting smaller and smaller andthe proportion of qualified products occupy more and more, and the early assumptionthat the number of non-conforming product complies with the Poisson distribution isnot a good description of the existing production process now.A situation which is becoming more and more common is that a large number ofzeros are presented in the data, and then the Poisson distribution does not fit countingdata well and tends to result in higher false alarm rates than we expected in manycases. In order to solve this problem, this paper first describes the characteristics ofthe ZIP process, and then propose a CRL-CUSUM control charts and ZTP-CUSUMcontrol chart to monitor the parameters of ZIP individually, and use CRL-ZTPCUSUM to indicate their combination to monitor the ZIP process. This paper useMarkov chain method to get the ANOS values of CRL-CUSUM control charts andZTP-CUSUM control charts, which can make gets the the control chart ANOS valuesfaster than simulation. In order to obtain the ANOS value of CRL-ZTP CUSUM chart,this paper use the combination of Markov model and simulation method. And then,introduce the basic setup and application of the the CRL-ZTP CUSUM control charts,also introduce the evaluation of control charts----ANOS, and then compare theperformance of various control charts based on the ZIP process. Finally, an exampleof the application of our proposed methods is illustrated.