Phase? Control Chart Study Of Linear Profile Monitoring Using Quantile Regression

For the monitoring problem of phase?linear profile data,it is assumed that the whole data changes at some unknown moment,that is the intercept,slope or other parameters have changed.Generally,for the changepoint identification problem,the least square method can be used to estimate the intercept and slope in each sample and then the monitoring problem of linear profile data can be transformed into the monitoring parameter of the linear model.However,the least square method is very strict in the distribution of random error terms in the practical problems study.When the distribution of random error terms is asymmetric,peaked and heavy tail,the least square estimation is no longer unbiased and effective.Compared with the least square method,quantile regression has less requirements for the distribution of random errors,especially when the distribution is asymmetric,peaked and heavy tail.Therefore,quantile regression has a unique advantage in application.Firstly,this paper introduces the development of quantile regression and changepoint problem,and process of relevant calculation process,which provides theoretical basis for quantile regression in practical application.Secondly,the application of quantile regression combined the changepoint method in industry is given by using quantile regression theory and statistical process control theory.Finally,numerical simulation analysis is carried out to monitor the shift of regression coefficient and estimate the position of changepoint.For the first step of linear profile data monitoring,this paper assumes that the binary profile data collected with fixed samples over time is subject to the standard normal distribution,the t distribution with degree of freedom of 10,and the exponential distribution.And proposes the changepoint method combined quantile regression to give the likelihood ratio test statistics to monitor the shift of regression coefficients and estimate the location of the changepoint.In this paper,the robustness of quantile method is studied from different binary profile data.The simulation results show that the control chart given in this paper can effectively monitor the model change and estimate the position of the changepoint when the system shift occur.