Research On Dynamic Nonparametric EWMA Control Chart Based On Wilcoxon Sign Rank

Control chart is an important tool to improve product quality in statistical process control.Traditional control charts usually assume that the process follows known distributions such as normal distribution,binomial distribution,Poisson distribution,and build statistics to monitor the process according to specific distribution forms.Such control charts are also known as parametric control charts.With the development of data acquisition technology and the increasingly complex production process,the quality characteristic values of products in many manufacturing processes such as petroleum,chemical,semiconductor and so on cannot be described by exact specific distribution,and the traditional parametric control chart will no longer be applicable.The nonparametric control chart does not need too many assumptions about the process distribution,and can effectively solve the monitoring problem of unknown process distribution.In addition,some scholars have shown that the monitoring efficiency of control charts can be improved by dynamic design of control charts.Therefore,this paper mainly discusses the dynamic design of nonparametric EWMA control chart(NP-EWMA)based on Wilcoxon sign rank.The main contents are as follows:(1)Nonparametric Wilcoxon signed rank EWMA control chart with variable sampling interval.Firstly,the Wilcoxon signed rank nonparametric EWMA control chart is designed with variable sampling interval,the control limit and warning limit are calculated with dichotomy,and then the average time to signal(ATS)is calculated with Monte Carlo simulation.Secondly,the monitoring effect of VSI-NPEWMA control chart and FSINPEWMA control chart is studied through simulation results and examples under the given five distributions with the average time to signal as the criterion.Finally,in order to verify the universality and robustness of the variable sampling interval nonparametric control chart,VSI-NPEWMA is compared with VSI-NPShewhart and VSI-EWMA under three given distributions.The simulation results show that VSI-NPEWMA has better monitoring effect than the other two control charts.(2)Nonparametric Wilcoxon signed rank EWMA control chart with variable sample size.Firstly,the Wilcoxon signed rank nonparametric EWMA control chart is designed with variable sample size,the control limit and warning limit are calculated by dichotomy,and then the average number of sample observations(ANOS)is calculated by Monte Carlo simulation.Secondly,taking the average time of observations to signal as the criterion,under the given five distributions,the simulation results and examples show that the monitoring effect of VSS-NPEWMA control chart is better than that of FSSNPEWMA control chart.Finally,in order to verify the universality and robustness of the variable sample size nonparametric control chart,VSS-NPEWMA is compared with VSSNPShewhart and VSS-EWMA under three given distributions.The simulation results show that VSS-NPEWMA has better monitoring effect than the other two control charts.(3)Nonparametric Wilcoxon signed rank EWMA control chart with variable sampling interval and sample size.Firstly,the Wilcoxon signed rank nonparametric EWMA control chart is designed with variable sampling interval and sample size.The control limit and warning limit are calculated by dichotomy,and then the average time to signal is calculated by Monte Carlo simulation.Secondly,taking the average time to signal as the criterion,under the given five distributions,the simulation results and examples show that the monitoring effect of VSSI-NPEWMA control chart is better than that of FSSI-NPEWMA control chart.Finally,in order to verify the universality and robustness of the nonparametric control chart with changes in sampling interval and sample size,VSSI-NPEWMA is compared with VSSINPShewhart and VSSI-EWMA under the given three distributions.The simulation results show that VSSI-NPEWMA has better monitoring effect compared with the other two control charts,and also conforms to the characteristics of conventional EWMA control chart,and has better monitoring effect for small deviation.