An Online Change Point Method For Monitoring Data

In recent years,with the development of society and people's requirement for the quality of products and services is rising,the quality control problem gradually came to the attention of the public.If we can monitor product data,eliminate the unqualified products or stop production when unqualified products producted,than we can greatly reduce production waste,to achieve the purpose of quality control.in the process,we should analysis the product data to test it is in accordance with the law.due to the diversity of product data,different data types need different statistical methods to control,so as to produce different monitor model.This paper mainly studies observed data in accordance with multinomial distribution,the most classical method for the data type is chi-square test,but when the observed data of the possible outcomes are comparable or bigger than the number of subjects,this research does not work well.In the past twenty years,the changing point in terms of theory and application has a very in-depth research and theory results,the change point theory has become one of the center of the statistical inference problem,this paper applied change point model to a number of multinomial type,earlier,Changliang Zou,guang-hui Wang has done some research on the issue,they put forward a suitable statistics and compared with other commonly used statistics,and proved its advantages,but its data used for limited data,so they do the monitor model only can do offline monitoring of historical data.In actual production,the data was produced continuously,people more hope to product at the same time to monitor product data.In this paper,for the problem of on-line monitoring,we improved the test statistics,and the theoretical deduction proves the asymptotic normality of the statistics,and ultimately determine the lines of control chart,make the control process from offline to online,to monitor the new data in the process of production,developed a suitable online change point monitoring model for multinomial data,and the data simulation proved the correctness and effectiveness of the method.This model has a certain reference value for the actual production.