VSI多变量自相关过程VAR控制图经济设计  

Economic Design of Vector Auto-regression Control Chart for Monitoring Multivariate Autocorrelation Process with Variable Sampling Intervals

作　　者：薛丽 李聪凯 贾元忠 曹逗逗 XUE Li;LI Cong-kai;JIA Yuan-zhong;CAO Dou-dou(School of Management Engineering,Zhengzhou University of Aeronautics,Zhengzhou 450046,China;College of Management and Economics,Tianjin University,Tianjin 300072,China)

机构地区：[1]郑州航空工业管理学院管理工程学院,河南郑州450046 [2]天津大学管理与经济学部,天津300072

出　　处：《数理统计与管理》2023年第4期626-636,共11页Journal of Applied Statistics and Management

基　　金：国家自然科学基金项目(71701188,71871204,72261147706,72231005);教育部人文社科项目(21YJC630151);中国博士后科学基金(2016M601266);河南省自然科学基金(232300420125);郑州航空工业管理学院科研团队支持计划专项(23ZHTD01008)。

摘　　要：当多变量自相关过程中存在较小波动时,向量自回归(VAR)控制图的监控效果优于残差T²控制图。为了降低控制图监控过程运行成本以及提高过程监控效率,本文研究可变抽样区间(VSI)多变量自相关过程VAR控制图的经济设计。首先,介绍VSI多变量自相关过程VAR控制图;其次,构造VSI多变量自相关过程VAR控制图的经济模型,利用蒙特卡洛模拟方法,计算控制图的平均报警时间以及平均抽样个数;然后,结合提出的经济模型,给出具体的算例,并利用遗传算法对其进行求解;接下来,对所建立的经济模型进行灵敏度分析,通过正交试验以及方差分析,得到控制图设计参数和经济模型参数之间的影响关系;最后通过最优性分析,验证在同样的模型参数水平下,所提出的经济模型具有更低的成本。When there is small fluctuation in the process of multivariable autocorrelation,the monitoring effect of vector autoregressive model(VAR)control chart is better than that of residual T?control chart.In order to reduce the operation cost of monitoring process and improve process monitoring eficiency,this paper studies the economic design of VAR control chart with variable sampling interval.Firstly,the economic model of VAR control chart of variable sampling interval is established.Secondly,the economic model of VSI VAR control chart for multivariable autocorrelation process is constructed,and the average alarm time and the average sampling number of the control chart are calculated by Monte Carlo simulation method.Thirdly,combining with the proposed economic model,a specific example is given and solved by genetic algorithm;Fourthly,the sensitivity analysis of the established economic model is carried out,and the influence relationship between the design parameters of the control chart and the parameters of the economic model is obtained through the orthogonal test and variance analysis.Finally,through the optimization analysis,it is verified that the proposed economic model has lower costs under the same level of model parameters.

关 键 词：多变量自相关过程 VAR控制图 经济设计 灵敏度分析 

分 类 号：O212[理学—概率论与数理统计] O213.1[理学—数学]