稳健MEWMA控制图的构建与应用

Construction and Application of Robust MEWMA Control Chart

针对传统MEWMA控制图对离群值比较敏感,导致监控效果与实际情况不符这一现象,文章引入稳健统计的思想,将稳健MM估计与传统MEWMA控制图相结合,构造出稳健MEWMA控制图以达到抵御离群值影响的目的,同时进行了模拟和实证分析。模拟和实证分析的结果均表明:当数据中不存在离群值时,传统MEWMA控制图方法与稳健MEWMA控制图方法得到的结果基本保持一致;当数据中存在离群值时,传统MEWMA控制图不能很好地监测出过程的不受控状态,容易发生漏报的现象,而稳健MEWMA控制图可以很好地监测出过程的不受控状态,并发出出界报警信号。相对于传统MEWMA控制图,稳健MEWMA控制图能更有效地抵抗离群值的影响,具有良好的抗干扰性和抗差性,同时能够更好地监测到过程的失控状态。

In view of the phenomenon that the traditional MEWMA control chart is sensitive to outliers,which leads to the inconsistency between the monitoring effect and the actual situation,this paper brings in the thought of robust statistics and combines the robust MM estimation with traditional MEWMA control chart to construct robust MEWMA control chart to resist the effect of outliers,with simulation and empirical analysis carried out at the same time.The results of simulation and empirical analysis show that when there is no outlier in the data,the results obtained by the traditional MEWMA control chart and the robust MEWMA control chart are basically consistent,that when there exist outliers in the data,the traditional MEWMA control chart cannot well detect the uncontrolled state of the process,andmissing alarm is easy to occur,while the robust MEWMA control chart can well detect the uncontrolled state of the process and send out the boundary alarm signal.Compared with the traditional MEWMA control chart,the robust MEWMA control chart can resist the influence of outliers more effectively,with good anti-interference and anti-difference performance,and also can better detect the uncontrolled state of the process.