应用于IID变量的ARMA控制图性能分析  

Performance analysis of ARMA control chart for IID variables

作　　者：崔敬巍[1] 谢里阳[1] 刘晓霞[1] 

机构地区：[1]东北大学机械工程与自动化学院,沈阳110004

出　　处：《仪器仪表学报》2007年第10期1891-1896,共6页Chinese Journal of Scientific Instrument

基　　金：高等学校博士学科点专项科研基金(20050145027)资助项目

摘　　要：首先从历史数据加权角度对应用于ⅡD(independent identical distribution)变量的ARMA控制图统计量进行了分析,结果表明,ARMA统计量对历史数据处理的灵活性优于文中提到的一元控制图,尤其是对当前数据的处理更能适应不同情况的需要,可以选择不同的控制图参数来提高控制图检测异常原因的能力。而且从统计量的变化形式来看,文中提到的一元控制图均可视为ARMA控制图的特殊情况;其次,提出了具有某ARL要求的,正态分布观测值ARMA控制图的设计方案,并应用蒙特卡罗模拟方法,总结出检测均值一次永久偏移的最优参数取值范围;最后,介绍应用信噪比方法,可对ARMA控制图的参数进行粗略的选择,同时也验证了最优参数取值范围选择的正确性。Firstly, the statistic of ARMA control chart for IID （Independent Identical Distribution） variable is investigated from the weighting aspect of historical data, the result shows that ARMA statistic is more flexible than other simple control charts discussed in the paper in processing history data. Especially in processing current data, it can meet different needs and can select different parameters to improve the sensitivity of special cause. In addition, from the pattern of statistic, simple control chart can be seen as a special case of ARMA control chart. Secondly, when ARL has a special need, a design scheme for ARMA control chart with normal distribution observation data is pro- posed. Using Monte Carlo simulation, the optimal parameter range for detecting the mean one-step permanent deviation is summarized. Lastly, a new signal/noise ratio method is introduced. Using this method, the parameters of ARMA control chart can be selected roughly ; at the same time, the correctness of the optimal parameter range is verified.

关 键 词：数据加权 平均链长 最优参数 信噪比 ⅡD ARMA 控制图 

分 类 号：TB114.2[理学—运筹学与控制论] O213.1[理学—概率论与数理统计]