| Statistical Process Control was initially used in industrial process monitoring and quality improvement.After decades of development,it has been widely used in chemical manufacturing,disease prevention,environmental monitoring and other fields.As one of the important theories in the field of statistical process control,quality control charts use historical data and the latest information to construct upper and lower control limits for monitoring the quality fluctuations,detecting abnormal behaviors beyond the warning lines,and quickly sending out alarm signals.At first,due to the lag of measurement and analysis technology,people only constructed univariate control charts to monitor the valuable feature variables.However,with the development of industry and big data technology,in some complex production processes,high-dimensional data and variable-related data have appeared.Traditional univariate control charts no longer meet the needs of actual production,which has made the study of multivariate control charts gradually become a hot spot in the field of statistical process control.Besides,statistical process control emphasizes the accuracy of data.The quality of measurement data directly affects the subsequent inference and decision-making.Currently,most control chart studies are based on the assumption that measurement data is accurate,however,actual production measurement systems have measurement errors.If there are measurement errors but the monitoring is performed without considering them,the obtained results are often meaningless.The existence of measurement errors may have an adverse effect on the performance of control chart:the true value of the quality characteristics cannot be accurately observed,which leads to a false judgment of the alarm signal and causes unnecessary economic losses.At present,some scholars have analyzed the effect of measurement errors on various univariate control charts.However,there are few related studies on multivariate control charts,and no literature has studied the effect of measurement errors on the multivariate control charts for detecting covariance matrix drift.Therefore,considering the importance and applicability of multivariate control charts,this paper mainly studies the influence of measurement errors on the performance of multivariate quality control charts for detecting out-of-control conditions.We take the KQE control chart for detecting multivariate covariance matrix based on a single observation sample proposed by Zhang(2015)as an example.Combined the commonly used multivariate measurement error model,we construct ME-KQE control chart with measurement error and KME-KQE control chart under multiple measurements.From the perspective of theoretical derivation and Monte Carlo simulation,combining the commonly used ARL index for evaluating the performance of control charts,we investigate the effect of measurement errors on the performance of control charts in detecting out-of-control conditions under different out-of-control conditions and different values of parameters:the initial value?of the correlation coefficient,the different drifts?of the variance of the variable,the valueb in the linear covariance model,the value?_m~2 in the measurement error covariance matrix and the number k of multiple measurements.In addition,we compare the detection capabilities of the ME-KQE control chart and the KME-KQE control chart with the ME-ELR control chart proposed by Amiri(2016).Finally,combining two specific examples,we analyze whether the ME-KQE control chart and the KME-KQE control chart can correctly judge the process status of actual data.The research result indicates that compared to the case without measurement errors,the presence of measurement errors will reduce the ability of the control charts to detect the out-of-control state where the covariance matrix drifts.However,the smaller the value of?_m~2 in the measurement error covariance matrix and the larger the value of b in the linear covariate model,the smaller the adverse effect of the measurement errors.What's more,the improved method of multiple measurements can effectively reduce the impact of measurement errors.The larger the value of k,the smaller the adverse effect.In addition,the ME-KQE control chart and KME-KQE control chart have better ability to detect process covariance matrix shifts than the ME-ELR control chart.Finally,the ME-KQE control chart and KME-KQE control chart can make a correct judgment on the process status in actual production. |
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