基于协方差阵收缩估计的MEWMA控制图

MEWMA Control Chart Based on Shrinkage Estimation of Covariance Matrix

多元指数加权移动平均控制图(MEWMA)在实际应用中需要在第一阶段受控状态下的过程参数,目前广泛应用的是对均值向量和协方差阵的经典无偏估计。但是当第一阶段受控过程的样本批次比较少时,MEWMA的受控平均运行长度(ARL)会因为过程参数的估计显著降低。对此,文章给出协方差阵的收缩估计,从而改善了MEWMA控制图的受控表现水平和检测力。与其他协方差阵的估计方法相比,基于收缩估计下的MEWMA控制图的受控ARL受影响较小,且修正控制线后的失控ARL更短,检测力更高。实证分析结果表明,使用收缩估计的MEWMA控制图比其他估计方法提前了5倍采样间隔时间发出失控警报。

In practical applications,the Multivariate Exponential Weighted Moving Average(MEWMA)control chart requires the controlled procedure parameters in Phase I.Currently,the classical unbiased estimation for the mean vector and the covariance matrix is widely used.However,the controlled Average Run Length(ARL)of MEWMA will significantly decrease affected by the estimation of procedure parameters when the number of sample batches in the controlled procedure of Phase I is relatively smaller.In order to solve this problem,the paper proposes the shrinkage estimation of covariance matrix to improve the controlled performance and detection ability of MEWMA control chart.Compared with other estimation methods for covariance matrix,the controlled ARL of the MEWMA control chart based on the shrinkage estimation is less affected,and the uncontrolled ARL is shorter and the detection ability is stronger after control line correction.The empirical analysis results show that the MEWMA control chart using the shrinkage estimation gives an out-of-control alarm five times sampling intervals earlier than other estimation methods.