自相关过程的稳健控制新方法  

A New Robust Control Method for Autocorrelation Processes

作　　者：王志坚 罗舒琪 WANG Zhi-jian;LUO Shu-qi(School of Statistic and Methematic,Guangdong University of Finance and Economic,Guangzhou 510320,China)

机构地区：[1]广东财经大学统计与数学学院,广东广州510320

出　　处：《数学的实践与认识》2024年第1期131-139,共9页Mathematics in Practice and Theory

基　　金：广东省普通高校特色创新类项目“复杂大数据的稳健统计过程控制方法研究与应用”(2019KTSCX042)。

摘　　要：常规过程控制图的前提假设条件是过程指标独立同分布.但实际中许多数据表现出异常值与自相关性并存等复杂特点,使常规控制图不能有效发挥作用.如何解决这类问题已成为过程控制研究中的热门课题.鉴于此,研究采用以下技术解决:1)用DAM权函数对自相关过程的异常值进行降权变换,构建一个稳健ARMA模型用以提取自相关性,进而得到无干扰残差;2)用无干扰残差构建残差控制图,并对其控制中心线与上下限进行稳健改进,最终构造稳健残差控制图.模拟实验及实证分析均表明:相比于常规过程控制图与Huber稳健控制图,研究提出的DAM缩尾稳健控制图具有抗干扰性,在对含异常值的自相关过程监控中表现出更优良的异常点识别能力.The premise of conventional process control chart is that process indicators are independent and identically distributed.However,in practice,many data show complex char-acteristics such as the coexistence of abnormal values and autocorrelation,which makes the conventional control chart ineffective.How to solve these problems has become a hot topic in process control research.In view of this,the following technologies are adopted in this study:1)DAM weight function is used to reduce the weight of outliers in the autocorrelation process,and a robust ARMA model is constructed to extract autocorrelation,and then the interference free residual is obtained;2)The residuals control chart is constructed by using the undisturbed residuals,and its control center line and upper and lower limits are improved robustly to finally construct the robust residuals control chart.Both simulation experiments and empirical anal-ysis show that compared with conventional process control charts and huber control charts,the DAM tailed robust control chart proposed in this study are anti-interference and have better ability to identify outliers in the autocorrelation process monitoring with outliers.

关 键 词：过程控制 稳健统计量 DAM权函数 异常值 

分 类 号：O231[理学—运筹学与控制论]