单边指数加权移动平均t控制图设计  

Design of One-sided Exponentially Weighted Moving Average t Control Chart

作　　者：胡雪龙 仲建兰[2] 吴姝[3] 屈明剑[4] HU Xue-long;ZHONG Jian-lan;WU Shu;QU Min-jian(School of Management,Nanjing University of Posts and Telecommunications,Nanjing 210003,China;School of Management,Fujian Agriculture and Forestry University,Fuzhou 350002,China;School of Logistics,Wuhan University of Technology,Wuhan 430063,China;National Center for Science and Technology Evaluation,Beijing 100081,China)

机构地区：[1]南京邮电大学管理学院,江苏南京210003 [2]福建农林大学,管理学院,福建福州350002 [3]武汉理工大学物流工程学院,湖北武汉430063 [4]科技部科技评估中心,北京100081

出　　处：《数理统计与管理》2020年第3期478-486,共9页Journal of Applied Statistics and Management

基　　金：国家自然科学基金资助项目(71802110,71801049,11701437);江苏省自然科学基金资助项目(BK20170894);教育部人文社会科学青年基金项目(17YJC630043,17YJC630231);南京邮电大学资助项目(NYY217007,NY218041);江苏高校哲学社会科学重点研究基地——信息产业融合创新与应急管理研究中心。

摘　　要：针对过程总体方差未知的情形,构造t统计量代替传统X统计量对过程进行监控,通常可以获得更好的效果。实际中,往往可以获得过程总体均值偏移的方向信息,根据该方向信息,提出采用单边指数加权移动平均(Exponentially Weighted Moving Average,EWMA) t控制图来监控过程总体均值的偏移。通过马尔科夫链构建单边EWMA t控制图的状态转移矩阵,进一步推导出其平均运行链长(Average Run Length,ARL)指标。在保证单边EWMA t控制图受控状态的统计性能基础上,使得其失控状态的ARL最小,从而获得控制图的最优决策变量和最优性能指标。仿真结果表明,当过程均值偏移方向已知时,单边EWMA t控制图的性能优于传统双边EWMA t控制图。Under the case of unknown process variance,statistic t shows a better performance than the traditional statistic X for process monitoring.In practice,directions of mean shift can usually be obtained.According to this,a one-sided exponentially weighted moving average(EWMA) t chart is proposed to monitor the process mean shift,according to the information of the shift direction.The Markov chain method is used to construct the transition matrix of the one-sided EWMA t chart,and the average run length(ARL) can be further obtained using this method.The optimal parameters and properties of the one-sided EWMA t chart can be obtained by minimizing the out-of-control ARL,with the constraints on the in-control ARL.The simulation results show that,when the process shift direction is known in advance,the one-sided EWMA t chart performs better than the traditional two-sided EWMA t chart.

关 键 词：EWMA t控制图 单边EWMA t控制图 平均运行链长 

分 类 号：F273[经济管理—企业管理] O212[经济管理—国民经济]