An Improved Study Of Mixed Residual Control Charts Based On First-order Autocorrelation

With the rapid development of modern society and economy,how to improve product quality and reduce unnecessary economic losses while controlling production costs has become an increasingly important focus.In statistical process control,control chart is the most commonly used method.When an error occurs,the control chart can effectively monitor the process and issue an alarm in order to correct the process and reduce losses.When the process observations are independent,we can use conventional control charts.However,autocorrelation is commonly existed among the real production activities.To solve this problem,the residual sequence of observations can be used to eliminate the autocorrelation in process and establish residual control charts to optimize the monitoring effect and improve the monitoring efficiency.This paper first introduces the most representative AR(1)model in time series,and deduces residual sequence of the model.According to the definition of the average run length,the expression of the residual control charts’ ARL is obtained,and the stochastic simulation method is summarized.Five kinds of residual control charts’ ARL under different drifts were numerically simulated and the design process of residual control charts was summarized.Secondly,based on the statistics of EWMA control chart and CUSUM control chart,two improved first order MEC and MCE mixed residual control chart are proposed.Through the method of random simulation,average run length(ARL),extra quadratic loss(EQL)and relative average run length(RARL)are used as the main indicators for evaluating the effect of the control chart,from which we can reach a conclusion that the improved mixed residual control chart for the process has better detection for the mean drift.Finally,a set of data values of peroxides in vegetable oils was used to analyze and verify the autocorrelation process.Matlab was used to test and fit the autocorrelation of the experimental data,and to obtain the residual sequence.Through the comparison of the different control charts and the improved mixed residual control charts,it can be concluded that the CUSUM and MCE control charts have the best control effect,and other control charts are beyond the control line in a stable and controlled state,the effects are not so good.In the out of state,the MCE control chart can send out an alarm earlier than the CUSUM control chart,so the effect of the MCE control chart is better.