可变抽样区间ARMA控制图经济设计  

Economic Design of VSI ARMA Charts

作　　者：张黎[1] 董晓阳[1] Zhang Li, Dong Xiaoyang(Zhengzhou Institute of Aeronautics, Zhengzhou 450046, China)

机构地区：[1]郑州航空工业管理学院,河南郑州450046

出　　处：《系统仿真学报》2018年第10期3869-3874,共6页Journal of System Simulation

基　　金：国家自然科学基金(U1404702);河南省高等学校重点科研项目(17A630069);河南省科技攻关项目(172102210078);郑州航空工业管理学院研究生创新基金(2016CX014)

摘　　要：为提高统计过程监控灵敏度并减少监控费用,研究了可变抽样区间自回归移动平均(VSI ARMA)控制图的经济设计问题。构建了VSI和FSI (Fixed Sampling Interval)ARMA控制图的经济设计模型,通过构建三维向量利用马尔科夫链的方法计算该控制图的平均运行时间(ATS)。针对具体算例模型,利用遗传算法对该模型进行求解,并通过仿真分析比较了FSI ARMA控制图与VSI ARMA控制图的经济性能,结果表明,在模型设计参数相同的情况下VSI控制图比FSI控制图的费用低。证明VSI ARMA控制图比FSI ARMA控制图更能低成本的监控自相关过程。To improve the sensitivity of statistical process control reducing costs for process monitoring at the same time, the economic design of autoregressive moving average control chart with variable sampling interval （VSI ARMA） was discussed. The economic model of autoregressive moving average control chart with variable sampling interval （VSI ARMA） was established based on Lorenzen and Vance＇s model in which Markov chain was used to calculate the average time to signal （ATS） through constructing a three dimensional random vector. Using genetic algorithm to search for the optimal combination of seven parameters of VSI ARMA model made the cost of economic model at unit time to be minimum at the same time. Meanwhile, FSI ARMA control chart was used to monitor the same process, and the economic design ofFSI ARMA control chart is also carried out. The results of the two models are compared, which indicates that the loss cost ofVSI ARMA control charts is consistently lower than that of the FSI scheme when the design parameter is identical.

关 键 词：ARMA控制图 马尔科夫链 可变抽样区间 经济设计 

分 类 号：O213.1[理学—概率论与数理统计]