基于数据深度的EWMA控制图方法研究

Research on EWMA Control Chart Method Based on Data Depth

数据深度是一种不依赖于概率分布类型,且能有效处理多元数据问题的理论方法,EWMA(指数加权移动平均)控制图可以有效地解决检测过程中的小偏移问题。为了提高在数据分布未知或非正态分布情况下控制图的性能,本文提出基于数据深度理论的EWMA控制图,选取数据深度函数中常见的马氏深度和单纯型深度,建立了MD-CUSUM控制图和SD-CUSUM控制图。运用Matlab仿真模拟二元正态分布,以平均链长(ARL)作为仿真结果,并与Messaoud提出的基于数据深度的rMEWMA控制图进行对比。仿真结果表明:当偏移量小于等于0.8时,本文提出的控制图效果比Messaoud的控制图好;当偏移量大于0.8时,Messaoud的控制图略好一些。

Data depth is a theory to analysis multivariate data,which has no connection with the distribution of the data.EWMA(Exponentially Weighted Moving Average) control chart has the access to detect small mean shifts.To improve the preference of control chart under the situation of non-normal or unknown data distribution,this paper proposes to establish control charts of MD-CUSUM and SD-CUSUM selecting Mahalanobis depth(MhD) and simplicial depth(SD) based on the EWMA control chart with deep theory.The results of Matlab simulation are compared with the charts that was proposed by Messaoud,denoted by rMEWMA.The simulation results of average rusn length(ARL) show that in bivariate normal distribution,the proposed charts are better when shift is not more than 0.8,and the Messaoud's charts are just a little better when shift is more than 0.8.