Study Of Autocorrelation Simple Linear Profile Control Chart Method

Statistical process control theory is widely used to monitor various quality problems in production process,and the most important part is the control chart.Traditional control chart theory is based on individual quality characteristics or vectors of quality characteristics,but in recent years,researchers have proposed a simple linear functional relationship to represent some product or process quality,known as a"simple linear profile".The conventional profile control charts assume that the profile observations are independent of each other,but there are sometimes various autocorrelations in the profile data,and this leads to many misclassifications.In order to better monitor the autocorrelated simple linear profile processes,this paper proposes a control chart scheme based on the mean value of profile residuals and second-order origin moments,using a simple linear profile model and a profile model with a general autocorrelation error structure as the objects of research.First,through theoretical proofs and simulation experiments,this paper shows that the performance of the control chart improves significantly with increasing mean and variance of the explanatory variables within the subgroup when the profile slope is shifted individually,and that the increase in variance improves the detection performance of the control chart when the profile intercept and slope are shifted simultaneously and cancelled.The basic theory and properties of the contour residual mean and second-order origin moments are then investigated,and four improved control chart schemes are proposed in combination with the TEWMA and MAXEWMA schemes,and compared with the MAX-EWMA-3-C control chart and TEWMA₃ control chart schemes,and simulation experiments show that the improved control charts are more advantageous in monitoring simple linear profile process parameters.Second,this paper analyzes the profile model with a general autocorrelation error structure and theoretically demonstrates the effect of autocorrelation coefficients on the profile control chart scheme.And then a new transformation model is proposed to overcome the limitation of the original model with fixed explanatory variables,and the improved TEWMA-0)?/W control chart is applied to this model,comparing it with the EWMA-3 control chart,it is shown that the TEWMA-0)?/W control chart is more sensitive in monitoring the autocorrelated profile parameters.Finally,for the simplicity and convenience of the control chart application,as well as further enhancing control chart monitoring performance,a variable sampling interval strategy is added to the MAX-EWMA-W control chart and applied to the new transformation model,followed by a comparison with the FSI-EWMA-3 control chart scheme.The simulation results show that the VSI-MAX-EWMA-W control chart scheme has more advantageous performance.