ARMA控制图的稳健构建方法及其比较

Construction of Robust ARMA Control Chart and Its Comparison

针对传统ARMA控制图对离群值较为敏感从而导致其监控效果不佳这一现象,文章引入稳健统计的思想,并将它与传统ARMA控制图相结合,构建了稳健ARMA控制图算法,新算法对离群值有较强的监测能力。模拟和实证研究的结果均表明:当样本中不存在离群值时,传统ARMA控制图和稳健ARMA控制图得到的结果基本保持一致;当样本中含有离群值时,传统ARMA控制图易受离群值的影响,控制限被拉高,容易导致漏发报警的现象,但稳健ARMA控制图对离群值的抗干扰性较好,控制限不容易受到离群值的影响,可以很好地监测到离群值的位置,并发出警报。

Aiming at the phenomenon that traditional ARMA control chart is sensitive to outliers,which leads to poor monitoring effect,this paper introduces the idea of robust statistics and combines it with the traditional ARMA control chart to construct robust ARMA control chart algorithm,which has a strong ability to monitor outliers.The results of both simulation and empirical studies show that when there are no outliers in the samples,the results of the traditional ARMA control chart and the robust ARMA control chart are basically consistent,and that when there are outliers in the sample,the traditional ARMA control diagram is susceptible to outliers,with the control limit raised,easy to cause the phenomenon of missing alarm,while robust ARMA control chart has good anti-interference performance to outliers,with the control limit not easily affected by outliers,so the position of outliers can be well monitored and an alarm issued.