The Design Of The Variance Control Charts Based On Conditional Performance

Process variance has a large impact on product quality stability,and process variance stability plays a crucial role in the performance of the mean control chart However,the range control chart and the standard deviation control chart based on the traditional 3? principle have the disadvantage that the lower control limit is zero.Using them,the process variance cannot be found to be small.Therefore,from the two perspectives of equal-tailed and ARL-unbiased,the Shewhart-S2 control chart is designed to monitor the variance change of the normal population.Because the Shewhart-S2 control chart is not sensitive enough when the process variance changes slightly.In this paper,the EWMA-S2 control chart and the CUSUM-S2 control chart are used to monitor the variance of the normal population by using the integral equation method from the two perspectives of equal-tailed and ARL-unbiasedSince the process parameters are often unknown in the actual production process,the Phase I data set is required to estimate the process parameters.Different Phase I data sets will result in different parameter estimates and different estimation control limits,ultimately resulting in different control chart performance.The most common situation in actual production is that the operator only has a set of Phase I data sets.Therefore,it is more practical to study the performance of the control chart based on the given set of Phase I data sets,which is the conditional performance of the control chart.Based on the exact distribution of the conditional ARL,especially the standard deviation of the conditional ARL,this paper uses the precise method to study the influence of the parameter estimation of the control chart.The results show that the parameter estimation has a serious impact on the Shewhart-S2 control chart,EWMA-S2 control chart and CUSUM-S2 control chart performance,resulting in excessive false alarms and unnecessary interference to the process.However,the sample size required to achieve the ideal condition is too large.Based on the available sample size of the Phase I,this paper designs the modified control chart in an accurate way,so that the conditional ARL value is higher than the ideal value with a high probabilityThe main conclusions are as follows:For the Shewhart-S2 control chart,the EWMA-S2 control chart and the CUSUM-S2 control chart,whether the parameters are known or the parameters are unknown,the larger sample size will have better control chart performance;compared to the equal-tailed control chart,the ARL-unbiased control chart performs better.Since the conditional out-of-control ARL of the Shewhart-S2 chart is too large when the process variance is downward,it is recommended to use EWMA-S2 and CUSUM-S2 control chart when the parameters are unknown.When the process variance is greatly drifted,it is recommended to select the Shewhart-S2 control chart.When the process variance has a small change,it is recommended to select the EWMA-S2 control chart with a small smoothing constant or the CUSUM-S2 control chart with a small deviation from the steady-state variance.A relatively stable modified EWMA-S2 control chart is more recommended when applying the modified control chart.