Research On Construction And Evaluation Of Non-parametric Control Chart Based On Maximum Entropy Distribution

With the further research of Statistical Process Control(SPC),the control chart has been continuously developed.In order to control the process better and improve the monitoring ability of the control chart,some scholars construct a non-parametric control chart based on the principle of maximum entropy,which lays a good theoretical foundation for this thesis.However,how to improve the reliability of the maximum entropy estimation of the quality characteristic parameters,how to construct the non-parametric control chart according to different maximum entropy distribution functions,and how to evaluate the performance of the non-parametric control chart are all lack of targeted research,which also provides an opportunity for the study of this thesis.Hense,this thesis has carried out research on the construction and evaluation of non-parametric control charts based on the above problems.On the one hand,this thesis studies the construction of the Shewhart control chart and the CUSUM control chart based on maximum entropy.Aiming at the estimation of the distribution of quality characteristic parameters,the maximum entropy distribution of quality characteristic parameters are constructed.Through comparison analysis,a more accurate optimization algorithm for determining the unknown parameters of maximum entropy function is studied,and the reliability of estimation is improved.Aiming at the shortcoming of the normal distritution of the traditional control chart,an improved method of Shewhart control chart and CUSUM control chart is proposed.The non-parametric Shewhart control chart and CUSUM control chart are constructed.For the Shewhart control chart,we propose the economic principle based on the statistical principle of the control chart and construct the economic control chart,which improves the Shewhart control chart.For the CUSUM control chart,we propose the calculation method of control limit under the general distribution and construct the maximum entropy CUSUM control chart,which avoids the assumption of normal distribution and improves the accuracy of monitoring.On the other hand,our thesis studies the evaluation of the Shewhart control chart and the CUSUM control chart based on maximum entropy.The ARL(average run length)is used as the performance evaluation index of the control chart,and the performance of the control chart is evaluated by the simulation method.Three representative distributions,namely heavy tail distributions,non-heavy tail distributions and symmetric distributions are selected.The method of generating random numbers is used to evaluate the constructed control charts.The results show that the ARL required to detect out-of-control in the economic control chart and the maximum entropy CUSUM control chart is less than that the pre-improvement control chart.So the monitoring effect is better.Also,the ARL of the maximum entropy CUSUM control chart is closer to the true value,which means the degree of fit is better.By analyzing the simulation results of the three distributions,it is known that the improved control charts have the best monitoring ability under the heavy-tailed distributions,while the non-heavy tail distributions is second and the symmetric distributions is the last.Thus,the selection principle of the control chart in the case of heavy tail distributions,non-heavy tail distributions and symmetric distributions is given.