The Statistical And Economic Performance Of PEWMA Control Chart

Multivariate quality control charts are of great significance on the improvement of product quality and product competitiveness,which are widely used in enterprise production practice.Therefore,the design of multivariate control charts and the optimization of the control chart parameters for designing high-quality,low-cost products,become the focus of attention in the statistical quality control field.Besides,with the different economic models,there are uncertainties in the control chart cost parameters,which will make the economic and statistical optimization of the control chart face a greater challenge.The topic of this thesis comes from the National Natural Science Foundation of China(71271078).Aiming at the multivariate exponentially weighted moving average(MEWMA)control chart cannot applied to the relevance problem of quality characteristics,this paper presents a modified PEWMA control chart,in which the smoothing coefficient matrix is extended to a full-rank matrix and the correlation of multivariate quality characteristics has been considered.Based on the proposed PEWMA control chart,the interval model with unique characteristics and the ellipsoid convex model with related characteristics to measure the uncertainty of cost parameters are proposed when uncertainty exists,and then the optimization analysis and research of uncertainty of statistical and economic performance of PEWME control chart are carried out.The main contents of this thesis are as follows:(1)Aiming at the relevance problem of quality characteristics,by improving the smoothing coefficient matrix of MEWMA control chart,that is,in the matrix of non-diagonal elements on the introduction of offset weighted average,a modified PEWMA control chart is proposed.The average run length(ARL)of the in-control state and out-of-control state of the PEWMA control chart and MEWMA control chart are calculated,so as to analyze the in-control and out-of-control statistical performance.Based on the Lorenzen-Vance economic model,the economic performance of the PEWMA control chart is studied,and compare to the MEWMA control chart,the result shows that the modified PEWMA control chart is better.(2)Aiming at the cost parameters uncertainty of PEWMA control chart,an uncertainty analysis method based on interval model is proposed and applied to the analysis of economic and economic-statistical of the PEWMA control chart.First,when cost parameters are independent,the interval uncertainty model is proposed to measure the uncertainty of the cost parameters.Second,in order to improve the efficiency of economic total cost optimization analysis,the midpoint of the interval parameter is approximated by the first-order Taylor expansion,so the uncertainty optimization of the total cost is degenerated into the deterministic optimization of the interval midpoint and interval radius.Considering that the above conversion is based on small uncertainty,when facing the large uncertainty,the interval is separated into multiple subinterval model to optimize each subinterval model,in order to search the optimal cost and the corresponding parameters in all subinterval models.Finally,the sensitivity analysis of the cost parameters interval change is made to find the most obvious parameters combination that makes the control chart performance better.(3)Aiming at the uncertainty cost parameters are relevant of PEWMA control chart,an uncertainty analysis method based on ellipsoidal convex model is proposed and applied to the analysis of economic and economic-statistical of the PEWMA control chart.Firstly,considering the uncertain economic cost parameters with correlation,the ellipsoidal convex model is introduced to measure the cost parameters uncertainty.Then,the economic total cost is approximated by the first-order Taylor expansion at the ellipsoid midpoint of the uncertainty parameters,so the total cost uncertainty of economic optimization is transformed into the deterministic optimization of the cost mean and the volatility difference.In order to ensure the accuracy of optimization,the ellipsoid radius is discredited into multiple sub-ellipsoid models with concentricity.Each sub-ellipsoid model is solved by the above-mentioned optimization method to obtain the most excellent cost and corresponding parameters.Finally,the sensitivity analysis of the cost parameters uncertainty and the correlation of the uncertainty parameter is proposed,to elucidate the influence of the correlation between the uncertainty parameter and uncertainty level of the uncertainty parameters on the total cost and the control chart parameters of the control chart.