Selection Of Autoregressive Model In Quality Control Of Residual Control Chart And Analysis Of Enterprise Application

With the continuous development of society,people have more restricted requirements for product quality.Statistical Process Control(SPC)technology plays an important role in ensuring a high-quality production process.As one of the important tools of SPC,the control chart has been widely utilized in the quality control of various product production processes.With the contribution of the control chart,we can find the process deviation in time and take effective measures to ensure that the production process is always under statistical control.With the rapid development of automation and sensor technology,high-speed automatic data acquisition has become available.However,since the high frequency and short time interval of data acquisition,data is likely to produce autocorrelation itself.The autocorrelation process violates the basic condition that the observation values required by the traditional control chart are independent of each other.Therefore,the autocorrelation process cannot be directly monitored by using the traditional way.The residual control chart based on the autoregressive model is a reliable method to solve the autocorrelation process monitoring.The monitoring statistics of the residual control chart is the residual of the predicted value and the actual value of the control chart monitoring autoregressive model,in which the establishment of the autoregressive model is essential.Most of the existing studies assume that the data are the first-order autocorrelation,but few of them are considered the multi-order autocorrelation data,which does exist in reality.For multi-level autocorrelation data,building an appropriate autoregressive model needs rich practical experience,especially in the judgment of autoregressive order.It is not clear how the different order autoregressive models affect the performance of the residual control chart.Accordingly,aiming at the p-order autocorrelation data,this paper mainly studies the influence of the first-order and p-order Autoregression Models on the monitoring performance of the residual control chart.Monte Carlo simulation is the main tool of experiment and enterprise application analysis.For the p-order autocorrelation data,the first-order and p-order autoregressive models,namely AR(1)and AR(P)were constructed,respectively.Two kinds of residuals were obtained along with two kinds of residual control charts,respectively.Taking the average running chain length and its standard deviation as the index to evaluate the performance of control charts,the performance of residual X-bar control chart with individual observation and residual CUSUM control charts with different autocorrelation coefficients and different offsets were compared.The results showed that for the residual X-bar control chart with individual observation,when the offset is relatively small,the AR(1)model performed better,and the autocorrelation degree was weakened;when the offset is relatively large,the AR(1)model was equivalent to the AR(p)model.For the residual CUSUM control chart,when the offset is relatively small,the AR(1)model had a better performance with a strong autocorrelation;when the offset is relatively large,the AR(1)model had the same effect as that of the AR(p)model.In general,the overall performance of the residual control chart based on AR(1)model is better than that based on AR(p)model.Therefore,AR(1)model was used directly for p-order autocorrelation data,which not only saved the modeling cost but also meet the actual requirements of the residual control chart.Finally,as an example,the humidity data of an internal electrode of a fuel battery was selected to validate the simulation model.The suggestion of using a residual control chart is given based on the results.A number of samples are needed in order to determine the parameters in the control chart before using it.