An Accurate Design Of S~2 Control Chart Based On Conditional Perspective

With the continuous improvement of product quality requirements in contemporary society,the traditional counting control chart is difficult to detect the defective rate in the production process.Therefore,this the adopts the monitoring of the sample variance(S2)in the production process to realize effective monitoring in the production process.At present,most of the control chart research is carried out under the assumption that the parameters are known.However,in real life,due to the unknowability of the parameters,the parameters often need to be estimated from the in-control sample data in the Phase I,but different in-control samples will produce different control limits,resulting in different control chart performance.And in real life,people often only get a set of sample data.Therefore,this thesis starts from the conditional perspective of a sample data set in the Phase I,selects control charts with different sub-charts for comparison,and comapre each other.The performance of in-control and out-of-control conditions under the equal-tailed design and ARL-unbiased design are more in line with realistic requirements.And use accurate correction methods to correct the control chart,which effectively improves the monitoring efficiency of the control chart.The specific content arrangement is as follows:(1)With the parameters known,the control limit coefficient of the SyntheticS2 control chart,the Side-Sensitive Synthetic-S2 control chart and the Side-Sensitive Group Run-S2 are given.And the control limit coefficients of the control chart are under equal-tailed design and ARL-unbiased design,thus the thesis gives the out-of-control performance.And this thesis compare the Synthetic-S2 control chart and the Side-Sensitive Synthetic-S2 control chart to study the influence of the Side-Sensitive design on the control chart.What's more,thisthesis compare the Side-Sensitive Synthetic-S2 control chart and the Side-Sensitive Group Run-S2 control chart to study the influence of different sub-chart designs on the control chart.(2)With the parameter unknown,this thesis derives the the precise distribution of the Synthetic-S2 control chart,Side-Sensitive Synthetic-S2 control chart and Side-Sensitive Group Run-S2 control chart.With the precise distribution of the conditional average run length in the control chart,this thesis depicts the distribution function image.The precise distribution is used to solve the performance of out-of-control and in-control conditions of the above three control charts,and a variety of indicators are used to evaluate the influence of parameter estimation on the performance of the control chart.The study found that in order to ignore the impact of parameter estimation,a sufficiently large number of samples in the Phase I is required.Therefore,this thesis gives the minimum number of samples that meets the in-control conditions.(3)Based on the fact that the number of samples required for the control chart in the Phase I cannot be met in real life,this thesis uses precise methods to modify the above three control charts to make the in-control performance of the control chart under the equal-tailed design and ARL-unbiased design more ideal.