基于Copula模型的多维数据空间扫描监测方法  

Spatial Scanning Monitoring Method for Multidimensional Data Based on Copula Model

作　　者：郝澜宇 李艳婷[1] 潘尔顺[1] Hao Lanyu;Li Yanting;Pan Ershun(School of Mechanical Engineering,Shanghai Jiao Tong University,Shanghai 200240,China)

机构地区：[1]上海交通大学机械与动力工程学院,上海200240

出　　处：《统计与决策》2022年第14期5-9,共5页Statistics & Decision

基　　金：国家自然科学基金面上项目(71672109,72072114)。

摘　　要：多维数据的监控问题已成为现代质量监控中的重点和难点。传统的多元统计过程控制方法往往假设数据符合特定分布,直接影响后续分析结果的准确性。在实际应用中,大多数多变量监测过程并不独立,不同维度数据之间存在一定的相关性,这也是容易被忽略的关键点。文章通过引入Copula模型,充分利用变量之间的相关性,给出合理的联合分布模型,然后建立了一种基于Copula模型的新的空间扫描统计量监测方法。与目前较流行的MEWMA控制图监测方法相比,所提出的方法能灵活有效地监测失控数据。算例表明,所提出的方法能够尽早发现数据的上升趋势,为防治系统提供预警。The monitoring of multidimensional data has become the focus and difficulty in modern quality control.Traditional multivariate statistical process control methods often assume that data conform to a specific distribution,which directly affects the accuracy of subsequent analysis results.In practice,most multivariate monitoring processes are not independent,and there is a certain correlation between data of different dimensions,which is also a key point easily ignored.This paper introduces Copula model,makes full use of the correlation between variables,gives a reasonable joint distribution model,and constructs a new spatial scanning statistics monitoring method based on Copula model.Compared with the current popular MEWMA control chart monitor-ing method,the proposed method can monitor uncontrolled data flexibly and effectively.The numerical example shows that the proposed method can detect the rising trend of data and provide early warning for the prevention and control system.

关 键 词：多维数据 COPULA模型 空间扫描统计量监测 MEWMA控制图监测 

分 类 号：TP277[自动化与计算机技术—检测技术与自动化装置]