Research And Application Of Two Kinds Of Non-parametric EWMA Control Charts

Statistical Process Control is a quality management technique which uses statistical information to evaluate and monitor each stage of a process.SPC technology can be used to establish and maintain processes at an acceptable and stable level to ensure that products and services meet defined requirements.Control chart is a common real-time monitoring tool of SPC technology,while non-parameter control chart is a tool applicable when the underlying distribution of monitoring objects or corresponding parameters are unknown.We know that the problem of statistical monitoring in non-parametric environment is closely related to the non-parametric hypothesis testing in the background of statistical inference.Although there have been many literatures on non-parametric testing,there are very few cases in which these tests can be applied to the online monitoring of processes.Therefore,this paper has done the following two aspects of the non-parametric likelihood ratio test and empirical likelihood ratio test.First,non-parametric control charts are very useful in the absence of relevant information about the basic distribution or parameters of the sample.Most existing non-parametric control charts are used to monitor location parameters,and they may not perform well when scale parameters vary arbitrarily over time.In this paper,we proposes a new nonparametric control chart based on powerful likelihood ratio test and exponential weighted moving average control chart.The non-parametric estimation is realized by the exponential series density estimation.Furthermore,the proposed control chart does not require historical reference samples and can be controlled by fixed control limits.Monte Carlo simulation results show that the proposed control chart performs well in monitoring mean and variance shifts,especially when monitoring variance or large mean shifts.Finally,the proposed method is applied to the process monitoring of the baking process in the semiconductor manufacturing industry.Secondly,with the gradual improvement of sensor technology and data acquisition system,a large number of complex and high-dimensional data can be collected.Monitoring multivariable and high-dimensional data streams is often a basic requirement of modern manufacturing industry and quality management departments.However,in the field of high dimensional data monitoring,most traditional multivariate control charts are no longer applicable because of the “curse of dimension” and the distribution of variables is usually complex and unknown.To solve this problem,an EWMA type non-parametric monitoring scheme based on high dimensional empirical likelihood ratio test is proposed in this paper,which is used to monitor the mean vector of multiple and high dimensional processes.The proposed control chart is not only easy to implement and interpret,but also the Monte Carlo numerical simulation results show that the proposed scheme has obvious advantages in detecting small shift.Finally,the proposed control chart is applied to the semiconductor manufacturing process,and the results show that our method has a good monitoring effect on the semiconductor that has not passed the test.