VSI EWMA控制图的性能分析与优化  

Performance Analysis and Optimization of Vsi Ewma Control Chart

作　　者：马树华 张伟[2] 郑辉 MA Shu-hua;ZHANG Wei;ZHENG Hui(Hebei Normal University for Nationalities institute e of Mathematics and Computer Science,Chengde 067000,China;China Aerospace Academy of Systems Science and Engineering,Beijing 100048,China;Tianjin university of science and technology institute of mechanical engineering,Tianjin 300222,China)

机构地区：[1]河北民族师范学院数学与计算机科学学院,河北承德067000 [2]中国航天系统科学与工程研究院,北京100048 [3]天津科技大学机械工程学院工业工程系,天津300222

出　　处：《数学的实践与认识》2018年第19期132-143,共12页Mathematics in Practice and Theory

基　　金：教育部哲学社会科学研究重大课题攻关项目(16JZD014);天津市哲学社会科学规划项目(TJGLWT15-006);天津科技大学青年教师创新基金(2014CXLG17);天津市轻工与食品工程机械装备集成设计与在线监控重点实验室资助项目

摘　　要：ATS（平均报警时间）对VSI（可变抽样区间）EWMA控制图性能分析与优化有着十分重要的作用．应用马尔科夫链建立了VSIEWMA控制图的ATS计算模型，并就该模型的收敛特点进行了分析，分析发现，ATS的马尔科夫模型的收敛速度与设计参数取值有关；并且不同的设计参数对其性能影响程度不同，控制限系数和抽样区间对其影响程度相对较大；分析还发现，ATS的OC曲线存在交点δ＊，当过程偏移δ处于[0，δ＊]与（δ＊，＋∞）两个区间时，平滑系数具有不同的取值策略，给出δ＊的求解程序并绘制出了δ＊与控制限系数的函数曲线，发现交点δ＊随控制限系数增加而减小．ATS （the average time to signal） plays an important role to the performance analysis and optimization of the VSI（variable sampling interval） EWMA control chart. In this paper, markov chain approach is used to establish an ATS computation model of the VSI EWMA control chart, and the convergence characteristics of the model are analyzed, the analysis results show that the convergence speed of the output is influenced by the design parameters; and the performance of the control chart differs to the design parameters, the effect of the sampling interval and control limit coefficient is relatively larger than other parameters; the analysis results also show that there exists a point of intersection δ＊ in the ATS OC curve, when the process mean is in the different interval of [0, δ＊] and [δ＊,＋∞], the choosing strategy of the smoothing parameter is different; a program for δ＊ is given in this paper, and the function curve of δ＊ and control limit coefficient is drawn and show that the point of intersection δ＊ is reduced with the increase of the control limit coefficient.

关 键 词：VSI EWMA控制图 平均报警时间 马尔科夫链 参数优化 

分 类 号：O213.1[理学—概率论与数理统计]