监控多变量自相关过程的可变抽样区间残差T^(2)控制图  

Residual Based T^(2) Control Chart for Monitoring Multivariate Autocorrelation Process with Variable Sampling Intervals

作　　者：薛丽 XUE Li(School of Management Engineering,Zhengzhou University of Aeronautics,Zhengzhou 450000,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450000 [2]天津大学管理与经济学部,天津300072

出　　处：《数理统计与管理》2021年第2期257-265,共9页Journal of Applied Statistics and Management

基　　金：国家自然科学基金项目(71701188,U1204702,71661147003,71871204);航空科学基金项目(2016ZG55021);中国博士后科学基金(2016M601266);河南省高等学校青年骨干教师资助计划项目(2016GGJS-112);河南省高校科技创新人才支持计划(19HASTIT032);河南省科技攻关计划(202102310638,172102210517).

摘　　要：残差T^(2)控制图消除统计量的自相关性,满足统计过程控制理论关于统计量彼此独立的基本假设,可以用于监控多变量自相关过程.为了提高多变量自相关过程监控效率,研究可变抽样区间的残差T^(2)控制图.首先,对多变量自相关过程的残差T^(2)控制图进行可变抽样区间(VSI)设计;然后,用蒙特卡洛模拟方法计算其平均报警时间;最后,以平均报警时间为评价准则,对所设计的VSI残差T^(2)控制图与固定抽样区间(FSI)的残差T^(2)图的监控性能进行对比分析,发现过程失控时,VSI残差T^(2)控制图的平均报警时间较小,能更快地检测出异常波动.Residual based T^(2) control chart eliminates the autocorrelation of statistics and satisfies the basic hypothesis of statistical process control theory that statistics are independent of each other,so it can be used to monitor multivariate autocorrelation process.To improve the monitoring efficiency for multivariate autocorrelation process,residual based T^(2) control chart with variable sampling intervals(VSI)is studied.Firstly,residual based T^(2) control chart with variable sampling intervals for monitoring multivariate autocorrelation process is designed;Secondly,the average time to signal of this control chart is calculated using Monte Carlo simulation method;Finally,taking the average time to signal as the evaluation criterion,residual based T^(2) control chart with variable sampling intervals and fixed sampling intervals are compared.The computing results show that the VSI residual based T^(2)control chart is the more efficient in detecting shifts than the fixed sampling interval(FSI)residual based T^(2)control chart when the process is out of control.

关 键 词：可变抽样区间 多变量自相关过程 残差T2控制图 平均报警时间 

分 类 号：O212[理学—概率论与数理统计] O213.1[理学—数学]