Research Of On-line Monitoring Linear Profiles With A Control Chart Based On Quantile Regression

Most statistical quality control researches assume that some properties of a product can be characterized by profiles at present.In the article,we discuss the general linear profile model with independent identically random errors.Firstly,we review the multivariate exponentially weighted moving average(MEWMA)control chart proposed by Zou et al based on the least squares estimators for on-line monitoring intercept,slope and standard deviation of the model.Then we monitor the quantile of intercept and slope online based on quantile regression.Discussing the methods of calculating quantile regression,such as simplex algorithm,interior point algorithm and smoothing algorithm.We propose a new control chart for on-line monitoring profiles combined with MEWMA control chart.By means of a simulation study we know in-control average run length(ARL)of proposed control chart,comparing the out-of-control ARL of standard normal distribution with t distribution and gamma distribution for MEWMA control chart,the monitoring performance of the control chart of standard normal distribution and t distribution is same basically.And the monitoring performance of the control chart of standard normal distribution and gamma distribution is different obviously;however,their monitoring performance is same basically when we select the appropriate sample size and quantile.We illustrate efficiency of the control chart for detecting shifts in the model coefficient,and the control chart can detect the moderate and small shifts.